Contract Options for Buyers and Sellers of Talent in Professional Sports [1st ed.] 9783030495121, 9783030495138

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PALGRAVE PIVOTS IN SPORTS ECONOMICS

Contract Options for Buyers y and Sellers of Talent in Professional Sports Duane W Rockerbie Stephen T. Easton

Palgrave Pivots in Sports Economics

Series Editors Wladimir Andreff Emeritus Professor University Paris 1 Panthéon-Sorbonne Paris, France Andrew Zimbalist Department of Economics Smith College Northampton, MA, USA

This mid-length monograph series invites contributions between 25,000– 50,000 words in length, and considers the economic analysis of sports from all aspects, including but not limited to: the demand for sports, broadcasting and media, sport and health, mega-events, sports accounting, finance, betting and gambling, sponsorship, regional development, governance, competitive balance, revenue sharing, player unions, pricing and ticketing, regulation and anti-trust, and, globalization. Sports Economics is a rapidly growing field and this series provides an exciting new publication outlet enabling authors to generate reach and impact.

More information about this series at http://www.palgrave.com/gp/series/15189

Duane W Rockerbie · Stephen T. Easton

Contract Options for Buyers and Sellers of Talent in Professional Sports

Duane W Rockerbie Department of Economics University of Lethbridge Lethbridge, AB, Canada

Stephen T. Easton Department of Economics Simon Fraser University Burnaby, BC, Canada

ISSN 2662-6438 ISSN 2662-6446 (electronic) Palgrave Pivots in Sports Economics ISBN 978-3-030-49512-1 ISBN 978-3-030-49513-8 (eBook) https://doi.org/10.1007/978-3-030-49513-8 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Palgrave Macmillan imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

Sports economics is a relatively new field of research that is gaining popularity and momentum. The authors of this book have produced research and publications in the field for the last two decades, focusing mainly on sports labor market issues and issues relating to sports league policies, such as revenue sharing, parity, and changes in rules of the game. It has always been our purpose (and pleasure) to introduce models and methods borrowed from other economic research fields, such as auction models, models of multiple equilibria, consideration of talent conjectures, exchange rate risk exposure, time series methods, and other innovations. We do this to expand the sports economics literature and bring it to a level of analysis consistent with other fields. This is an ambitious, and sometimes challenging, endeavor but we strive to produce new research that breaks new ground in sports economics that does not merely add to the list of previously published results that are well-known and accepted. Our purpose in this short book is to import another established method from a field of economics outside of sports economics to attempt to answer a problem. Professional athletes are paid large sums relative to other professions, to play a game accessible to most children at a much higher level that fans will pay to watch. Many publications exist in sports economics that address the question of what financial compensation a professional athlete should receive using profit-maximizing principles. However very few consider the issue of how players and team owners actually bargain for salaries using the incentives and leverages available v

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PREFACE

to them. Instead, sports economists vaguely refer to “bargaining power” when a player or a team owner gets the upper hand over salary negotiations. Our motivation is provided by a relatively standard estimation of marginal revenue product for baseball players that is well-known in the sports economics literature. We find that certain groups of players exhibit a consistent ability to exploit team owners, while other groups have no ability to do so. Our “import” in this book is options theory as a logical explanation for why some players are able to extract vast amounts of money from owners, while others appear to be exploited. When one thinks of the argument we make, it is clearly logical, however formalizing the argument into an economic model of a profit-maximizing team owner is not so easy. The payoff is that we are able to provide insights into the salary negotiation process that would not otherwise be possible by developing a formal model. It is our hope that our contribution to this literature is well-received and offers up an incentive for future research in the field, perhaps in other professional sports than baseball. We would like to thank Anthony Krautmann for specific comments and encouragement, as well as the attendees of our NAASE session at the 94th annual conference of the Western Economics Association in San Francisco, June 2019. Lethbridge, Canada Burnaby, Canada May 2020

Duane W Rockerbie Stephen T. Easton

Contents

1

2

On the Rise: Player Compensation and Multi-year Contracts 1.1 Introduction 1.2 A Brief History of Multi-year Contracts: Early Years (1876–1975) 1.3 Early Years of Free Agency 1.4 Free Agency Since 2000 1.5 Multi-year Contracts in Basketball, Football, and Hockey 1.6 Player Salaries and Marginal Revenue Products: the Scully Method 1.7 Real Options References The 2.1 2.2 2.3

Puzzle of Overpaid and Underpaid Players Introduction A Revenue Model Estimates of the Revenue and Winning Percentage Functions 2.4 Calculating a Player’s Net MRP 2.5 A Linear Probability Model 2.6 Summary References

1 1 5 11 12 13 16 19 20 23 23 27 32 36 47 49 51 vii

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CONTENTS

3

Contract Options for Buyers and Sellers of Talent 3.1 Introduction 3.2 Employment Contracts that Include Real Options 3.3 Setup of the Real Options Model 3.4 The Player’s European Put Option 3.5 The Owner’s European Put Option References

53 53 54 57 60 64 66

4

Extensions to the Put Option Model 4.1 The Player’s Option Value in a Three-Year Contract 4.2 The Owner’s Option Value in a Three-Year Contract 4.3 Option Values with Different Career Profiles 4.4 Contract Values with Player and Owner Put Options 4.5 Multi-year Contracts with Option Years 4.6 No-Trade Clauses in Multi-year Contracts References

69 70 74 75 78 81 82 83

5

Concluding Remarks 5.1 An Empirical Test 5.2 Extensions to the Real Options Model References

85 86 89 91

Index

93

List of Figures

Fig. 1.1

Fig. 1.2 Fig. 3.1 Fig. 3.2 Fig. 4.1 Fig. 4.2 Fig. 4.3 Fig. 5.1

MLB average team payroll, average team revenue and payroll share of revenue, 1980–2018 (Source https://sites. google.com/site/rodswebpages/codes taken on December 20, 2019. These figures are taken from Financial World and Forbes magazine) Monopsony model of talent acquisition (Source Author’s creation) Possible states during the two-year player contract (Source Author’s creation) Options available to the player after one season (Source Author’s creation) Possible states during the three-year player contract (Source Author’s creation) Possible paths for the player after two seasons (Source Author’s creation) Player paths that give positive put option value for the owner (Source Author’s creation) Scatter plot of surplus to team owner versus number of years of player contract (Source Author’s creation)

2 17 58 62 70 72 75 87

ix

List of Tables

Table 2.1 Table 2.2 Table 2.3 Table 2.4 Table 2.5 Table 2.6 Table 2.7 Table 2.8 Table 2.9 Table 2.10 Table 2.11 Table 5.1

Free-agent fielding players by playing position, 2000–2012 Estimates of the (natural logarithm of the) revenue function Estimates of the (natural logarithm of the) revenue function (2.1) Estimates of the logistic winning percentage function in (2.2) Estimated surpluses for MLB free agents, 2006–2012, (η S = 2) Estimated surpluses for MLB free agents, 2000–2006, (η S = 2) Exploitation rates for MLB free agents versus salary, 2000–2012, (η S = 2) Exploitation rates for MLB free agents versus salary, 2000–2012, (η S = ∞) Exploitation rates of free-agent players by contract length, 2000–2012, (η S = 2) Exploitation rates for MLB free agents versus salary using linear probability model, 2000–2012, (η S = 2) Exploitation rates of free-agent players by contract length, 2000–2012, (η S = 2) Weighted least squares estimate of surplus model

26 29 34 36 41 42 43 46 47 49 50 88

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CHAPTER 1

On the Rise: Player Compensation and Multi-year Contracts

Abstract A salary anomaly has been identified in the sports economics literature suggesting that some athletes are overpaid relative to their marginal revenue product, while others are underpaid. The use of real options theory answers this anomaly by tying the under or overpayment of salaries to contract lengths. We begin this chapter with a brief history of multi-year contracts in Major League Baseball and find that multi-year contracts are much more prevalent after the repeal of the reserve clause in 1976. The so-called Scully method to estimate a player’s marginal revenue product is standard in the sports economics literature and we review it here. We close the chapter by intuitively explaining how real options theory explains the salary anomaly to motivate the rest of the book. Keywords Real options · Marginal product · Contract lengths · Baseball

1.1

Introduction

Since the beginning of the 1990 season, the date at which systematic financial data for Major League Baseball teams became available, it has been a boom time for the professional sport. Attendance at games has increased from an average of 26,000 per game to over 28,000 and overall © The Author(s) 2020 D. W. Rockerbie and S. T. Easton, Contract Options for Buyers and Sellers of Talent in Professional Sports, Palgrave Pivots in Sports Economics, https://doi.org/10.1007/978-3-030-49513-8_1

1

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D. W. ROCKERBIE AND S. T. EASTON

350

0.8

300

0.7 0.6

$ millions

250

0.5

200

0.4 150

0.3

100

0.2

50

0.1

0

0 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 Revenue

Payroll

Payroll/Revenue

Fig. 1.1 MLB average team payroll, average team revenue and payroll share of revenue, 1980–2018 (Source https://sites.google.com/site/rodswebpages/ codes taken on December 20, 2019. These figures are taken from Financial World and Forbes magazine)

league attendance has grown from 54.8 million to 68.5 million in 2019.1 Between 1990 and 2016 average revenue for clubs increased more than sixfold, and even adjusting for inflation rose 550%. At the same time payroll for the average major league club expanded even faster. From 1990 to 2016 the average payroll paid to players’ salaries rose by 800% in real (inflation adjusted) terms. Major League Baseball (MLB) finance has undergone considerable change since the 1980s, most notably the rapid increase in salaries has coincided with the even greater increase in revenues. Figure 1.1 plots the average team payroll from 1980 to 2018, the average team revenue from 1990 to 2018, and the payroll share of team revenue.2 The average annual rate of increase of average team payroll is 28.4%. The average team

1 https://www.baseball-reference.com/leagues/MLB/misc.shtml 2020.

taken

March

27,

2 Source: https://sites.google.com/site/rodswebpages/codes taken on December 20, 2019. These figures are taken from Financial World and Forbes magazine.

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ON THE RISE: PLAYER COMPENSATION AND MULTI-YEAR CONTRACTS

3

payroll increased from $17.3 million in 1990 (39% of total expenses) to $154.7 million in 2019 (53.3% of total expenses).3 Average team revenue increased from $51.5 million in 1990 to $329.8 million in 2018. The payroll share of team revenue increased from 27.6% in 1990 to 32.6% in 2018, however this is still well below the 50% payroll share of revenue in the salary cap systems used in the National Football League (NFL), National Basketball Association (NBA), and National Hockey League (NHL).4 Gate revenue’s share of total revenue has decreased from an average of 33.3% in 1990 to 28.7% in 2019. The salary shares presented in Fig. 1.1 are underestimates of the true figures as a number of excluded payroll categories are difficult to measure (Zimbalist 2011). Some of these include deferred salary payments, signing bonuses, non-roster players, player benefits, minor league payrolls, and whether the payroll is measured at the start of the season, mid-season, or end of the season. It is also not clear what revenues should be included in reported revenues and to what extent these are related to baseball operations. For instance, lands adjacent to ballparks that are owned by the team owner that generate annual revenue, and would not otherwise generate revenue if not for the operation of the team in the adjoining stadium, are not included in baseball-related income (BRI). We rely on Forbes estimates throughout this book, but we acknowledge the possible errors in their calculations. Team values have increased from a median value of $102.5 million in 1990 to $1.58 billion in 2019, yielding an average annual growth rate of 48.0% (without compounding). New expansion clubs have appeared in Miami, Tampa Bay, Denver, Phoenix, and one club relocated from Montreal to Washington, DC. A new, more extensive revenue sharing system was adopted in 2002 that is even more extensive today, and in the late 1990s a competitive balance tax on payrolls above a given threshold level was phased in. Increased attendance resulted in the construction of 21 new ballparks at a total estimated cost to clubs and taxpayers of $7.8 billion.5 Even after general inflation (the all items Consumer Price

3 Source: https://sites.google.com/site/rodswebpages/codestaken on December 20, 2019. These figures are taken from Financial World and Forbes magazine. 4 1994 is an exception as the baseball lockout shortened season inflated the share going to players. 5 Source: http://www.ballparks.com/ taken on February 8, 2017.

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Index increased by 85.6% between 1990 and 2016), MLB operates on a much larger dollar scale that it did in the 1980s.6 The impressive growth in player salaries in MLB begs the question of whether players are being paid what they are worth. Economics suggests that player salaries are proportional to the revenue a player generates for the team owner, more specifically, the player’s marginal revenue product (MRP). Players do not generate revenue directly for their owners, rather their talent contributes to a team production function that generates winning results. These wins then translate into a greater demand for the team’s product (tickets, television and media subscriptions, etc.) that result in greater revenue for the owner. The owner pays the player for his skills on the field and keeps a share of the revenue generated by these skills: what we term the surplus from talent. Owners and players determine the relative shares when negotiating salary contracts in MLB. Player salaries in the National Football League (NFL), National Basketball Association (NBA), and National Hockey League (NHL) have definite ceilings due to salary caps agreed to in their collective bargaining agreements (CBAs), however MLB has no salary caps, so players are better able to capture the full value of their MRPs. Our task in this monograph is to suggest an answer to the apparent anomaly in MLB that many players are paid well above the MRPs. This evidence is supported by a number of studies that we discuss later. An early study by Scully (1974) found convincing evidence that players were paid well below their MRPs in the reserve clause period (defined in the next section). This is understandable since the reserve clause prevented the movement of players to new teams by limiting free agency. The standard monopsony model of industry structure predicts that the wage rate paid to players will be well below their MRPs when there is only a single buyer of talent. We do not refute Scully’s results. However, subsequent analyses using more recent salary and performance data after the abolition of the reserve clause suggest that the situation has become reversed for many players, but in particular, for highly talented players. One can justify this anomaly by pointing to the greatly increased bargaining power of these players after the fall of the reserve clause, however it is not clear what this bargaining power actually is.

6 Source: http://www.inflationdata.com/inflation/Consumer_Price_Index/ taken on February 8, 2017.

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5

We attempt to clarify the process of bargaining by introducing the concept of real options. A player and an owner who wish to agree on a multi-year contract each give up valuable options in comparison to a series of one-year contracts. Players give up the option to move to another team if more attractive ones become available. Owners give up the option to leave the player un-signed in future years if the player’s performance diminishes and his MRP falls. Salary negotiations then involve each party placing values on these options and agreeing on their net value. If the net value favors the player, such as a younger player moving into the prime of his career, the player will demand and receive a salary greater than his expected MRP. If the net value favors the owner, such as an older player whose skills and MRP could diminish, the owner will demand and pay a salary less than the player’s expected MRP. Hence our explanation for the apparent salary–MRP anomalies in multi-year contracts. In singleyear contracts, the player and owner do not have options of any value, so players should be paid a salary equal to their expected MRP. The remainder of this chapter provides brief histories of salaries and multi-year contracts of more notable players, and a brief review of the Scully (1974) approach to estimating MRPs that is essential to finding evidence for the real options approach. We develop a technique to estimate free-agent player MRPs and estimate them in Chapter 2. Our findings confirm the salary–MRP anomaly for a recent sample period and motivate the real options model that follows in Chapter 3. Chapter 4 provides extensions to the real options model and Chapter 5 provides concluding remarks.

1.2 A Brief History of Multi-year Contracts: Early Years (1876–1975) The history of the labor market in MLB can be divided into three distinct periods that progressed from a system of indentured servitude for players to the lucrative market that exists today in which players have tremendous bargaining power. These divisions mark a century and a half of contract history: the reserve clause period from 1876 to 1975, the early years of free agency from 1976 to 2000, and the years since 2001 when television and media rights fees exploded. The first period of contract history spanned almost a century. The inception of the National League (NL) of Baseball in 1876 created a closed league with only eight teams operating in some of the largest cities

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in the eastern United States. Amateur leagues quickly dissolved as a consequence of the higher quality of baseball played in the NL. Players in the NL were full-time employees during the playing season, meaning they did not need to hold other jobs to earn a living, and they could devote their time to honing their baseball skills. The NL also saw bargaining power for salaries transferred from the players to the owners with the inclusion of a reserve clause in the standard playing contract (fully implemented in 1879) and a salary cap of $2000 when annual earnings of non-farm employees was $403.7 . The reserve clause generally stated that if a player and an owner could not agree on a salary for the coming MLB season, the owner had the right to “reserve” the player at the salary paid in the season just ended. The owner could then invoke the reserve clause at the end of each season that the owner wished to retain the player, effectively tying the player to one team for the length of his playing career. If the owner chose not to retain the player’s services, the player was a free agent able to sign a contract with any team that would have him. Contracts were for only a single season in the early years of baseball—multi-year contracts were unheard of—however, the players did not complain as most were happy to earn a good living playing baseball. A player would receive his contract in the mail at the end of the playing season, sign it, and mail it back to the team owner without question. Players were not represented by agents, instead contract negotiations were conducted between the player and the team owner, as owners refused to negotiate with player agents. Team owners were allowed to release a player from his contract at any time during the playing season in exchange for a small compensation payment. Thus players had very little job security. Cash sales of players were allowed as well with the player receiving none of the proceeds. In this way, team owners kept the surplus value of the player’s services among themselves. Connie Mack used this strategy twice during his tenure with the Philadelphia Athletics (now operating in Oakland) during years in which his team struggled financially. Mack sold many players during the 1914–1916 seasons, the most notable of which were Eddie Collins, sold for $50,000 to the Chicago White Sox

7 Table Ba4280-4282 in Historical statistics of the United States, earliest times to the present: Millennial edition, edited by Susan B. Carter, Scott Sigmund Gartner, Michael R. Haines, Alan L. Olmstead, Richard Sutch, and Gavin Wright. New York: Cambridge University Press, 2006. http://dx.doi.org/10.1017/ISBN-9780511132971.Ba4214-454 410.1017/ISBN-9780511132971.Ba4214-4544.

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in 1914, and Home Run Baker, sold to the New York Yankees in 1916 for $37,500. Even a World Series appearance in 1931 could not keep the team afloat, subsequently, Mack sold Mickey Cochrane for $100,000 to the Detroit Tigers, Lefty Grove for $125,000 to the Boston Red Sox, and Al Simmons, Jimmy Dykes and Mule Haas to the Chicago White Sox for $100,000. These cash sales effectively moved the Athletics out of contention by the 1934 season. The reserve clause effectively eliminated the need for multi-year contracts, even for the best players. However, there were a few exceptions. Data on player contracts is sparse for the early years of baseball all the way up to the 1960s, and generally, the data that are available are for the star players. Ty Cobb negotiated a three-year contract with the Detroit Tigers in 1910 for an annual salary of $9000, significantly more than the average player salary of $3000. Cobb did not report to spring training for the 1913 season and missed a number of games while holding out but received a one-year contract for what is thought to have been the first five-figure salary in MLB history ($12,000). He negotiated a twoyear contract with Detroit in 1914 for annual salaries of $15,000 and $20,000, and inked multi-year contracts thereafter until becoming the player-manager of the Tigers in 1921. Cobb was arguably the top player in MLB over the 1910–1920 seasons, achieving a weight-average8 batting, on-base percentage and slugging percentage (weighted by at bats) of 0.382, 0.453, and 0.462, respectively, and was the American League (AL) MVP in 1911.9 Cobb led the AL in batting average in nine of those seasons and led in total hits in five. After being released by the Tigers in 1927, Cobb signed a one-year contract for an MLB record salary of $85,000 with the Philadelphia Athletics.10 His investments in real estate and the stock market made Cobb a very wealthy man, far beyond his wealth from baseball. Yankee Stadium is still known as the “house that Ruth built,” despite not being the original stadium in which Ruth played. That “house” was in the Bronx, built in 1923, renovated in 1976, and closed in 2008. Ruth’s legacy lives on through his amazing playing statistics and his financial 8 Each season’s batting average weighted by the number of at bats to form an overall batting average for the period. 9 All playing statistics hereafter taken from http://www.baseball-reference.com. 10 To put this salary in perspective, the Dodger’s great Sandy Koufax earned the same

salary in his 1965 season, some 38 years after Cobb’s.

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rewards. Ruth signed a string of one-year contracts with the Boston Red Sox and New York Yankees up to the 1922 season, at which point he negotiated a three-year contract at $52,000 per year (40% of the Yankee’s team payroll). A two-year contract followed in the 1925 season for the same salary, followed by a three-year contract in the 1927 season for $70,000 per season. Ruth played another four seasons for the Yankees, each a one-year contract, until he retired. Ruth’s playing statistics over the 1922–1930 seasons are phenomenal: a weight-average batting, onbase percentage, and slugging percentage (weighted by at bats) of 0.351, 0.479, and 0.714, respectively, His season average of 46 home runs would be impressive today, however Ruth played when the playing rules dictated that hits that cleared the fences but curve outside the foul pole did not count as home runs. He earned AL MVP honors in 1923 and the Yankees won three World Series championships (appearing in six) over 1922–1930. At the time of Babe Ruth, the Yankees “murderer’s row” lineup also included Lou Gehrig. Over the 1926–1937 seasons, Gehrig averaged 37 home runs per season (weighted by each season’s at bats) and featured a weight-average batting, on-base percentage, and slugging percentage of 0.348, 0.457, and 0.651, respectively. He was AL MVP in 1927 and 1936 and won World Series titles in four of these seasons. Gehrig was truly the ironman of MLB in his playing days, playing in almost every regular season game. Despite these statistical accolades that are, in many ways, comparable to Ruth, Gehrig was paid far less than Ruth and only once negotiated a multi-year contract—a three-year deal in 1928 paying him $25,000 per season. This was a significant increase in salary compared to the $8000 he was paid in the 1927 season. Gehrig’s annual salary was consistently in the $25,000–$30,000 range over much of his career with the Yankees, suggesting he was severely underpaid. Jimmie Foxx began his playing career with the Philadelphia Athletics in 1925 and quickly established himself as one of the elite players in baseball. Foxx batted 0.354 in 1929, slugged 33 home runs and contributed 118 runs batted in (RBI). He was rewarded with a three-year contract paying a total of $50,000 by Connie Mack, manager, treasurer, and part owner of the Athletics. The team won World Series championships in 1929 and 1930 and Foxx won MVP titles in 1932, 1933, and 1938. His career statistics compare very favorably to Cobb, Ruth, and Gehrig in many respects, yet his annual salary averaged far less, likely due to the financial difficulties constantly plaguing Mack and the Athletics.

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Many other star players toiled in the major leagues until the 1960s, perhaps most notably Joe DiMaggio, Ted Williams, and Willie Mays. DiMaggio (the “Yankee Clipper”) played for the New York Yankees for the 1936–1942 and 1946–1951 seasons, with three years of military service during World War II. Although an excellent player throughout his career, DiMaggio’s prewar statistics are impressive: a 0.339 batting average (weighted by at bats), 0.403 on-base percentage, and 0.606 slugging average, earning MVP titles in 1939 and 1941.11 In salary history, DiMaggio is best known as the first six-figure player in MLB history, earning $100,000 for the 1949 and 1950 seasons. He is also known for holding out at the start of the 1939 season, demanding a one-year contract at $40,000 when the Yankees offered $25,000. With nowhere else to play, DiMaggio accepted the Yankees offer with Yankees owner, Colonel Jacob Ruppert, quipping “I hope the young man has learned his lesson.”12 Despite having an outstanding career and being a tough negotiator, DiMaggio never negotiated a multi-year contract. Ted Williams is generally thought to be the highest paid player in MLB during 1951 to 1960 seasons, consistently earning $100,000 or more per season. One of the greatest hitters to have ever played, Williams played his entire career with the Boston Red Sox and negotiated a number of short multi-year contracts toward the end of his career. Beginning in 1951, Willie Mays played his entire 22-year career with the New York/San Francisco Giants, winning MVP honors in the 1954 and 1965 seasons. Mays 0.345 batting average and 41 home runs helped power the Giants to a World Series title in 1954, but the team achieved few other successes during his lengthy playing career. In his best season (1954), Mays earned $12,500 and was severely underpaid afterward with a series of one-year contracts. A threeyear contract was agreed in 1966 that paid Mays $105,000 per season. This contract set the standard for the famous dual contract hold outs of Sandy Koufax and Don Drysdale in 1966. Believing that they could negotiate more effectively as a pair, Koufax and Drysdale demanded threeyear contracts totaling $500,000 each, but ultimately capitulated to the

11 In 1941 DiMaggio also hit in 56 straight games, a record that still stands. 12 D. Gaffney, “DiMaggio’s contract hold-out”. https://www.pbs.org/wgbh/americane

xperience/features/dimaggio-contract-hold-out/.

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Dodgers and accepted one-year contracts of $125,000 and $110,000, respectively.13 Data for average salaries by season are not available prior to 1967, the year in which the MLB Player’s Association began publishing salary figures. However, Haupert (2012) has used a number of sources to compile the highest salary for each season. It is unreasonable to assume that the average salary increased as quickly as the highest salary, nevertheless the highest salaries are instructive. Albert Spalding earned $4000 in 1876 playing for the Chicago White Stockings of the NL (later to form the Spalding sporting goods company) when the average salary was approximately $1700 (Kahn, 2000). By 1920, the aforementioned Ty Cobb topped the salary list at $20,000, while the average salary was approximately $5000. Jumping forward, Willie Mays’ $125,000 was the highest salary in 1967, an increase of $105,000, or 525% since 1920. The average salary in 1967 was only $19,000, an increase of $14,000, or 280%, however not really a king’s ransom. With prices increasing by 67% over the same period,14 the net increase in the average salary was 213%, roughly doubling in 57 years. Multi-year contracts were rare up to 1976 and were only awarded to the very best players. The presence of the reserve clause in the standard MLB contract eliminated the need for multi-year contracts since players had no options to move to other teams except by the decision of the team owner to either trade or release the player. Owners could minimize their risk of injured players, or players with declining skills, by signing players to a series of one-year contracts. The very best star players could hold out by not reporting to spring training if they had other lucrative opportunities outside of baseball. Ty Cobb, Babe Ruth, and Ted Williams were well-known celebrities, often appearing on magazine and newspaper covers, and sometimes in movies and radio. They may have convinced team owners of available opportunities in corporate boardrooms or politics. If this were a credible threat to leave the team, it was in the best interest of the owner to retain the player’s services in a multi-year contract. However, for all other players, multi-year contracts were not even a remote consideration. 13 The Dodgers negotiated wisely with Koufax as he retired following the 1966 season due to arm injuries. 14 https://www.usinflationcalculator.com/inflation/consumer-price-index-and-annualpercent-changes-from-1913-to-2008/.

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11

Early Years of Free Agency

The road to free agency in MLB began with the 1970 collective bargaining agreement (CBA) that allowed for a binding arbitration dispute settlement mechanism.15 Player’s Association (MLBPA) President Marvin Miller convinced pitchers Andy Messersmith and Dave McNally to play the 1975 season without signing their new one-year contracts. Immediately following the end of the 1975 season, the MLBPA launched a challenge, arguing that the reserve clause did not apply to Messersmith and McNally since the players could not be reserved for the 1976 season having not signed their contracts from the previous season. The arbitration panel decided in favor of the players and deemed the two were free agents. The owners failed to have the decision overturned in subsequent courts, hence the 1976 CBA included provisions for free agency (minimum six years of MLB service). This case set the stage for a multitude of lucrative multi-year contracts for many players, 32 before the 1977 season and 50 the year after. Four star players left the Oakland Athletics after winning three World Series championships: Reggie Jackson inked a four-year contract with the New York Yankees for $525,000 per season (including bonuses and incentives) in 1977; Joe Rudi signed a fiveyear contract with the California Angels for $400,000 per season; Rollie Fingers signed a six-year contract with the San Diego Padres for $266,667 per season (including bonuses and incentives) in 1977; Bert Campaneris signed a five-year contract with the Texas Rangers for $190,000 per season. Free agency allowed for a quick reshuffling of star players to the teams that valued them the most. The average salary in MLB increased from $44,676 in 1975 to $1895, 630 by 2000, or 4143% in just 25 seasons.16 However moving players to new teams via cash sales was effectively eliminated, although not formally banned. Following the 1975 season, Oakland owner Charlie Finley reached an agreement with the Boston Red Sox to sell Rollie Fingers and Joe Rudi for $1 million each. On the same day, Finley sold Vida Blue to the New York Yankees for $1.5 million. Commissioner

15 The 1970 CBA also established the 10 and 5 rule. Players with at least ten years of MLB service and the last five years with the same club could veto any trade. This rule was put in place in response to the Curt Flood legal challenge. Although unsuccessful, Flood’s challenge to the reserve clause brought attention to the contract strictures. 16 https://www.latimes.com/sports/mlb/la-sp-mlb-salaries-chart-20160329-story.html.

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Bowie Kuhn vetoed the deals arguing that the cash sales violated Article 1, Section 4 of the 1921 Major League Agreement that granted the Commissioner powers to protect the interests and morale of the game. In response to Kuhn’s decision, Finley refused to play his three star players but eventually yielded to a threat by the team not to play any games until the three players were reintroduced to the lineup. Significant cash sales have been discouraged since the Kuhn decision and none have taken place.

1.4

Free Agency Since 2000

The 2001 MLB season was a landmark year for media rights. MLB agreed to grant the FOX network exclusive rights to broadcast MLB games nationally for six seasons in exchange for $2.5 billion, the largest national television contract in MLB history. The previous rights deals signed in 1996 paid MLB a total just under $1 billion. In 2006, FOX and TBS paid MLB $3 billion for television rights to 2012, after which, FOX and TBS paid MLB just over $6.8 billion for the national television rights for through the 2021 season. The monies each team received from these rights deals fueled an accelerated period of free-agent salaries and contract lengths. The average salary in MLB increased from $1.99 million in 2000 to $4.1 million in 2018, or 106% in 18 years. However, the salaries for the star players increased much more dramatically. Kevin Brown’s six-year contract with the Los Angeles Dodgers at a $15.7 million annual salary topped the list in 2000. Most pundits at the time were shocked at the total value of the contract, however they did not foresee the even more lucrative contracts to follow. Alex Rodriguez set the standard in 2001 when he signed a ten-year $252 million contract with the Texas Rangers—the first ten-year contract in MLB history. After being traded to the New York Yankees, Rodriguez opted out of his contract in 2007 and re-signed with the Yankees for another ten years at $275 million. Nolan Arenado’s eight-year contract signed in 2019 with the Colorado Rockies will pay him $260 million. Mike Trout set the record for any player contract in North America, negotiating a 12-year $426 million contract with the Los Angeles Angels of Anaheim at the age of 27.

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1.5 Multi-year Contracts in Basketball, Football, and Hockey Prior to the formal striking down of the reserve clause in baseball in 1976, the National Football League (NFL), National Basketball Association (NBA), and the National Hockey League (NHL) each had a variation of the reserve clause in its standard player contract. Like MLB, one-year contracts were the norm and multi-year contracts a rarity. However, there were some exceptions for star players. Historical data for the details of player contracts are scarce outside of baseball, so we provide only a few examples. Multi-year contracts were almost nonexistent in the NFL prior to the 1950s. From the league’s inception in 1922 to the 1960s, the NFL paled in popularity compared to college football. Players needed to find second jobs in the off-season due to the low salaries in the NFL. Star players in college typically found it more lucrative to use their popularity to find employment in business or government, hence the opportunity cost for playing in the NFL was high. In 1936, only 24 of 81 players drafted by NFL teams signed contracts. The rules of the game and the playing schedules were not very formalized, and franchise turnover was frequent. This resulted in low salaries and a predominance of short-term player contracts, many players being paid by the game. Harold “Red” Grange, a star college player at the University of Illinois, was paid a share of the gate receipts by the Chicago Bears in the late 1920s, thus limiting his income to the games he played in. Number one draft pick in 1936, Jay Berwanger took a job as a foam rubber salesman instead of signing a contract to pay him $150 per game. The merger with the All-American Football Conference (AAFC) in 1950 solidified the NFL into a set number of teams that lasted until its merger with American Football League (AFL) in 1970. Star players, such as Frank Gifford, Johnny Unitas, and others, typically earned in the $20,000 per year range, but only negotiated one-year contracts.17 NFL teams avoided multi-year contracts due to the high probability of injury that could limit a player’s playing career.18 The salary landscape changed dramatically with the signing of Joe Namath, from the University of Alabama, by the New York Jets (AFL). Namath’s three-year 17 Average annual income in the United States was about $4000 in 1960. 18 Currently the average playing life is 3.3 years in the NFL. https://careertrend.com/

how-long-is-the-average-career-of-an-nfl-player-3032896.html Accessed May 4, 2020.

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deal totaled $427,000 (with a signing bonus, a new car, and other incentives), a pro football record at the time. This contract set the stage for other star players to sign lucrative multi-year contracts in the years leading up to the NFL–AFL merger. Heisman Trophy winner O. J. Simpson signed a five-year deal with the Buffalo Bills for a total of $650,000 in 1969. Competition for players between the NFL and AFL drove up salaries, particularly for rookie players who also received large signing bonuses. After the merger in 1970, salary growth and contract lengths were reduced until the abolishment of the reserve clause in the late 1970s. The longest contract in NFL history is Donovan McNabb’s 12-year deal with the Philadelphia Eagles in 2002 for a total of $115 million, and 8- to 10-year deals are not uncommon today for the league’s best star players. However, NFL contracts are not guaranteed unless a player negotiates guarantees in the contract. Prior to the start of the NBA, George Mikan signed a five-year contract with the Chicago American Gears of the National Basketball League (NBL) for an annual salary of $12,000, a record at that time for a professional basketball player. Mikan’s 6-foot 10-inch height made him a dominant player in the NBL. The NBL morphed into the Basketball Association of America (BAA) that morphed into the NBA. The NBA played its first season in 1949, making it the youngest of the four major professional sports leagues in North America. The 1950s witnessed unstable franchises and low attendances for most teams. Like the NFL, the NBA competed with the college game and was a distant second in popularity. Bob Cousy of the Boston Celtics was one of the best players in the young league, but only negotiated a one-year deal for $26,000 in 1959. Bill Russell and Wilt Chamberlain each earned $100,000 for the 1966 season, but only on one-year contracts. It was not until competition with the upstart American Basketball Association (ABA) in 1968 that contracts increased in value and length, despite the reserve clause. The move to the new league started with the case of Rick Barry who signed a three-year contract with the ABA Oakland Oaks worth $500,000 plus a 15% ownership share and 5% of gate revenue. Other new players followed to the new league for lucrative multi-year contracts, including Julius Erving (4 years, $500,000), Artis Gilmore (10 years, $2.5 million) and David Thompson (3 years, $1.45 million). Salaries and contract lengths continued to climb after the NBA–ABA merger in 1979. Kobe Bryant, Shaquille O’Neal, Tim Duncan, and Chris Webber all share the longest contracts in NBA history at seven years. Bryant’s deal

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with the Los Angeles Lakers paid a total of $136.4 million commencing in 2004, with O’Neal’s contract with the Lakers totaling $120 million in 1996. Tim Duncan signed a seven-year deal worth $122 million in 2003 with the San Antonio Spurs. The Sacramento Kings inked Chris Webber to a deal worth $123 million in 2001. However, like the NFL, the NBA is not friendly to longer-term contracts, perhaps due to the uncertainty of injury and the small roster size for each team (17 players) relative to the number of available players in college to be drafted. Many NBA star players negotiate four- and five-year deals, but few longer than that. The NHL (incepted in 1917) has a better-documented history than the NFL or NBA. Again, one-year contracts were the norm in the league, with a few exceptions for star players. Maurice Richard signed a twoyear contract with the Montreal Canadiens in 1943 worth $5000 per season (with performance bonuses) and signed two-year deals until the mid-1950s. The Montreal Canadiens also signed Jean Beliveau in 1953 to a three-year contract worth a total of $100,000, a large amount for its times. Beliveau had a strong business relationship with Molson Breweries in Montreal and could have left the Canadiens to assume an executive position, hence his opportunity cost to play hockey was significant and the Canadiens knew it. Bobby Hull negotiated a five-year contract with the Chicago Black Hawks (NHL) in 1960 for $20,000 per season. The Detroit Red Wings signed Doug Harvey to a three-year contract as a player-coach for $27,000 per season. Bobby Orr, one of hockey’s greatest players, signed a three-year with the Boston Bruins in 1968 for $50,000 per season. The establishment of the rival World Hockey Association (WHA) in 1972 created a higher level of competition for star players that increased salaries and contract lengths rapidly. The most notable of these being the ten-year, $1 million contract signed by Guy Lafleur with the Montreal Canadiens, the largest NHL contract up to that time, and the ten-year $2.75 million contract signed by Bobby Hull with the WHA Winnipeg Jets. The longest multi-year contracts we could find in the four professional sports leagues in North America were the 15-year NHL contracts signed by Rick DiPietro of the New York Islanders in 2006 and Ilya Kovalchuk with the New Jersey Devils in 2010. DiPietro was to receive $4.5 million per season, however the Islanders bought out his contract in 2013 due to his frequent injuries. Under the terms of his buyout, DiPietro will receive $1.5 million per year until 2026. Kovalchuk turned down a 12year $101 million contract with the Atlanta Thrashers to sign with the

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D. W. ROCKERBIE AND S. T. EASTON

Devils for a total of $100 million. The Devils initially agreed to a 17-year contract, but the terms of the deal violated the NHL collective bargaining agreement and was disallowed. Just three years into the deal, Kovalchuk retired from the NHL to play hockey in his native Russia.

1.6 Player Salaries and Marginal Revenue Products: the Scully Method The workhorse method to estimate MRPs of professional athletes paid on a salary basis is Scully (1974), hereafter referred to as the “Scully method.” The method requires estimation of a revenue function and a team production function for the team the player is employed by. These can be specified in general form as Ri = R(wi , Ai ) and wi = w(X i ), where Ri is local revenue for team i, wi is the team winning percentage, Ai is a vector of market-specific variables, and X i is a vector of team performance measures that are proxies for the stock of team talent ti . These two functions should have the characteristics ∂ Ri /wi > 0, ∂ 2 Ri /∂wi2 < 0, ∂wi /∂ X i > 0 and ∂ 2 wi /∂ X i2 < 0 for concavity. The reserve clause was still in place at the time of Scully (1974) therefore a monopsony model of talent acquisition was quite appropriate. The monopsonist is the only buyer of talent and will acquire talent up to the point where the increase in team payroll (the marginal resource cost [MRC]) is just equal to the marginal revenue product. Note that the owner is buying units of talent that are continuous, not discrete numbers of players since MLB teams have fixed roster sizes of 25 players. An owner cannot buy additional players but can acquire a fixed roster of players that possess a greater stock of talent. The supply curve of talent is assumed to be upward sloping due to talent scarcity, so the MRC is above the supply curve of talent in Fig. 1.2. Technically, the profit maximization problem in general form is M AX Ri = R(wi (ti ), Ai ) − Z i (ti )ti − FCi

(1.1)

The wage rate per unit of talent is Z i and fixed costs are FCi . Maximizing profit with respect to stock of team talent gives the first-order condition   ∂ Ri ∂wi d Zi (1.2) − ti + Z i (ti ) = 0 ∂wi ∂ti dti

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ON THE RISE: PLAYER COMPENSATION AND MULTI-YEAR CONTRACTS

17

Fig. 1.2 Monopsony model of talent acquisition (Source Author’s creation)

The first term in (1.2) is the MRP of talent and the bracketed term is the MRC that includes the wage rate per unit of talent plus the increase in the wage rate paid to all units of talent when one more unit of talent is acquired (the total being the MRC). Figure 1.2 demonstrates that a profit-maximizing owner will page a wage rate per unit of talent Z i when acquiring a team stock of talent Ti , much less than the MRP, hence players are “exploited.” It is important to note that it is a mistake to conclude that each player will be paid his MRP in the absence of monopsony power. Each player contributes a different MRP of each unit of talent, but the wage rate per unit of talent is determined by the last unit of talent acquired. The player’s salary is then the profit-maximizing value of Z i multiplied by the amount of talent units ti j that player j contributes to the team stock of talent. More talented players will earn higher salaries, but in equilibrium, the MRP is the same for all units of talent and thus players. If all players earned their MRPs, there would be no surplus left for the owner, however in the case of the monopsonist, the owner earns an additional area given by (M R Pi − Z i )Ti . Assuming specific functional forms and estimating slope coefficients for the independent variables allows for the computation of the MRP for each player on the roster. The first step is to estimate the team revenue function. This is straightforward given the availability of data. Unfortunately,

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comprehensive revenue data was difficult to obtain 50 years ago, and the Forbes magazine estimates were not produced at that time. Scully (1974) computed gate revenue by multiplying an average ticket price by attendance for each team, then added the share of national broadcast revenue. This introduces two problems. First, the average ticket price should be a weighted average of ticket prices, the weights being the share of seats in each seating section. It is not clear if the original Scully (1974) study used weighted average ticket prices or just some sort of other average. Second, Scully admits that his revenue data were not post-revenue sharing. Up to the late 1990s, visiting clubs received a fixed share of gate revenue in the American League and a fixed price per ticket sold in the National League. Team revenues that are available to the owner to pay players will be overestimated for teams above the average team revenue and underestimated for teams that fall below. This is true whether the revenue sharing formula is the current pooled system, or the old gate-sharing system (Rockerbie 2009a), however in the latter system, the ranking of each team in the league revenue hierarchy can change using team revenue after sharing. Scully specified a revenue function and a winning percentage function that are each linear in their components. This could be an issue if one is concerned with concavity of the revenue function (diminishing marginal revenue), however if the winning percentage function is nonlinear and concave, a downward MRP schedule is still assured. The A-vector in the Scully method is composed of the same independent variables that we employ in Chapter 2 and summarized in an appendix.19 Scully found that a one percentage point increase in the team winning percentage was estimated to increase team revenue by $10,330 and the regression model fit reasonably well with an adjusted R2 of 0.75. The winning percentage function is also linear in its components with the same independent variables that we employ in Chapter 2 and summarized in an appendix. The fit was quite good with an adjusted R2 of 0.88 and slope coefficients for the team slugging average and team strikeout to walk ratio of 0.92 and 0.90, respectively. The linearity of the revenue and winning percentage functions result in a perfectly elastic MRP schedule, a problem that has been corrected in later studies described in Chapter 2.20

19 In addition to the independent variables used in Scully (1974), we include dummy variables for new television contracts. 20 We specify a logistic winning percentage function in Chapter 2.

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19

Each player’s contribution to the team winning percentage is computed in a simple way. For hitters, each player’s slugging percentage (total bases/total at bats) is multiplied by 0.0833 since Scully assumed 12 positional players on a roster. In this way, each player contributes to the team slugging average with an equal weight. In reality, the team slugging average that is computed by MLB and reported in statistical services is the total team bases/total team at bats, so the Scully method is not accurate unless Scully computed his own team slugging average (he did not discuss this point). The appropriate weighting is the share of team at bats that we use in Chapter 2. The Scully method computes the contribution of each starting pitcher by assuming eight starters on the team roster and then multiplying each pitcher’s strikeout to walk ratio by 0.125, on the basis that this is the contribution to the team average strikeout to walk ratio. This method suffers from the same weighting issue as for hitters. A better weight is the number of innings pitched or the number of batters faced. When the marginal value of a win is $10,330, for a hitter with a good 0.350 slugging average, the contribution to the team revenue (the MRP) is 0.0833(350)(0.92)($10,330) = $277,077.45. A starting pitcher with a good strikeout to walk ratio of 2 contributes an MRP equal to 0.125(2)(0.90)($10,330) = $232,425. Scully (1974) estimated the MRP of every positional player and starting pitcher in MLB for the 1968 and 1969 seasons. Unfortunately, salary data for only 88 players in the sample were available so Scully estimated a log salary regression model with past performance statistics as independent variables. This allowed for the comparison of estimated net MRPs with estimated salaries. The Scully method deducts estimates of player development costs (10% of gross MRP) from the gross MRP figure to arrive at a net MRP. Rather than present results for each player, Scully grouped players into performance categories (mediocre, average, and star) using arbitrary hitting and pitching criteria. As one would expect, mediocre players were the most exploited, while the star players were paid estimated salaries close to their MRPs.

1.7

Real Options

Scully (1974) found that all MLB players were paid a salary below their estimated MRP during the reserve clause era. Free agency appears to have changed the salary–MRP relationship so much so that recent studies described in Chapter 2 suggest that many players are paid a salary

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above their estimated MRP. This does not fit with the standard monopsony model. One explanation is that some star players bring more to a team than just their on-field performance. Acquiring a superstar player could result in higher local media revenue, apparel revenue, promotion revenue, or even result in a team developing a world brand. In other sports, there are players who bring a sort of cachet to an organization to which fans respond. Christiano Ronaldo and Neymar’s move to Juventus and Paris-St. Germain in European football came with record transfer fees (112 million euros and 222 million euros) that give an indication of their worth to their clubs beyond their performance on the field. David Beckham’s move from Real Madrid to LA Galaxy brought tremendous exposure to a previously mediocre Major League Soccer in North America. The top European clubs can earn large bonus revenues from competing deep into the annual Champion’s League competition. Shirt sales often garner enough revenue to recover a significant portion of salaries for these superstars. Today there are few examples in MLB of these players whose popularity extends well beyond their performance on the field. Babe Ruth, Joe DiMaggio, and Ted Williams are players from the distant past now. The skew in the salary–MRP relationship is more systematic in MLB, suggesting that there is an important feature of bargaining that did not exist in the reserve clause period. One factor at the aggregate level is that the talent market cannot be characterized as a monopsony for freeagent players. Competitive bidding between clubs drives a player’s salary much closer to their expected MRP and could drive it above that if owners are willing to bid away some or all of their expected surplus (Rockerbie 2009b). This sort of “winner’s curse” argument could hold for the very best free agents, but not likely for the large number of free agents observed to be “overpaid” in Chapter 2.

References Haupert, M. (2012). MLB’s annual salary leaders since 1874. Society for American Baseball Research (SABR) Newsletter. https://sabr.org/research/mlbsannual-salary-leaders-1874-2012. Kahn, L. (2000). The sports business as a labor market laboratory. Journal of Economic Perspectives, 14(3), 75–94. Rockerbie, D. (2009a). Free agent auctions and revenue sharing: A simple exposition. Journal of Sport Management, 23(1), 87–98.

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Rockerbie, D. (2009b). Strategic free agency in baseball. Journal of Sports Economics, 10(4), 278–291. Scully, G. (1974). Pay and performance in major league baseball. American Economic Review, 64(5), 915–930. Zimbalist, A. (2011). Circling the bases: Essays on the challenges and prospects of the sports industry. Philadelphia: Temple University Press.

CHAPTER 2

The Puzzle of Overpaid and Underpaid Players

Abstract To use real options theory to explain the salary anomaly in Major League Baseball, it is necessary to estimate a player’s marginal revenue product (MRP). In this chapter, we specify a team revenue model and winning percentage function to specify a player’s MRP in theory. We then estimate an MRP for a large sample of free-agent players over the 2000–2012 baseball seasons. Our method is novel in that it utilizes features not found in previous published studies. The empirical estimates of player surpluses confirm the salary anomaly result for comparisons relative to the league average salary and by single- or multi-year contracts. Keywords Marginal revenue product · Surplus · Logistic · Monopsony

2.1

Introduction

One of the important issues in the sports economics literature is whether players are paid according to what economic theory predicts: profitmaximizing firms pay a salary equal to a player’s marginal revenue product (MRP). Scully (1974) tackled the problem decades ago during the last remnants of the reserve clause era in MLB. His method and results are reviewed in the last chapter, and his paper sparked a burgeoning literature

© The Author(s) 2020 D. W. Rockerbie and S. T. Easton, Contract Options for Buyers and Sellers of Talent in Professional Sports, Palgrave Pivots in Sports Economics, https://doi.org/10.1007/978-3-030-49513-8_2

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on the subject. More recent contributions include Scully (1989), Bruggink and Rose (1990), Fort (1992), Zimbalist (1992), MacDonald and Reynolds (1994), Leeds and Kowalewski (2001), Bradbury (2007), and Berri et al. (2015). Each of these papers utilizes a two-equation regression model to estimate the appropriate salary given an individual player’s production on the field by looking first at the relationship between team performance and revenue, and then estimating the relationship between player performance and team performance. The method places strains on the data, although it is not computationally burdensome. Krautmann (1999) developed a simpler, more direct approach that requires less data and utilizes only a single regression equation. This has become the method of choice over the last few years (Krautmann and Ciecka 2009; Brown and Jepsen 2009, to name a few), however it does not provide an estimate of a player’s MRP, rather it is a method to predict a player’s salary assuming that the MRP rule holds (see Bradbury [2013] for a critique of the method). Previous studies have estimated MRP in an ex ante sense, that is, they attempt to estimate how a club owner forms an expectation of a player’s future MRP from past performance data. Utilizing the Scully method, this MRP expectation for a particular season is then compared to the actual salary a player earned to determine if this is consistent with the expectation. The method does not compare the negotiated salary (which assumedly is the expectation the owner has formed plus any monopsony rent plus any additional surplus the player has been able to negotiate from the owner) with the realization of the player’s future MRP. Abstracting from player injuries, the ability to accurately forecast player MRPs is an ex post test of the MRP rule. An innovation in our analysis is to compare the negotiated salary for free agents with their subsequent discounted MRP in the following seasons of the contract period. By doing so we discover an anomaly. Future MRP as traditionally estimated is not well indicated by future salary. In the subsequent chapter we explore why this may occur. The purpose of this chapter is to revisit the question of whether baseball players are paid their MRP in an ex post sense, by improving on past studies. Our method follows Scully (1974) in flavor but introduces several improvements. Accurate and reliable financial data for MLB clubs is more available in 2020 than it was in the 1980s, and a consistent time series

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THE PUZZLE OF OVERPAID AND UNDERPAID PLAYERS

25

of estimates has been provided by Financial World and Forbes magazine since 1990.1 Data limitations for other variables in our approach, however, constrain us to begin our analysis in 2000. Nonetheless, we use a longer sample period than has been used in previous studies and utilize average ticket prices in our revenue function. We estimate our winning percentage function using a logistic regression, rather than the standard linear probability model used in the past. Finally, rather than estimate MRPs for every player, we estimate MRPs only for players who signed contracts with new clubs after free agency. In this way, we isolate the effect that the expectation of future performance has on the negotiated salary. We compare the newly negotiated (average) annual salary of each free-agent position player (excluding pitchers) to an estimate of the (average) present value of the marginal revenue products over the lifetime of the new contract. More broadly, we explore how workers are paid in long-term contracts by focusing on an industry in which MRP’s can be estimated and compared to actual salaries: professional baseball players. Although a traditional labor market demand-supply approach (Rosen and Sanderson 2001) results in the MRP = salary profit-maximizing condition, the approach does not account for observed systematic failures in the condition for specific players other than to resort to untested monopsony models or vague discussions of the bargaining power of players. Our sample includes 678 free agents (excluding pitchers) who were signed to MLB contracts over the 2000–2012 MLB seasons. The free-agent market was more active in some seasons than others. Summary statistics of free-agent activity by fielding position appear in Table 2.1. When a player played in multiple fielding positions during the season immediately following their free-agent signing, the most frequently played position was used in the table.2 Our results in this chapter suggest that significant changes have occurred in the MRP = salary relationship since the 1980s. We find 1 These revenue data are not without their limitations. See Zimbalist (2010) for an in-depth analysis of salary and revenue data. Forbes revenue estimates are net of revenue sharing of local revenues and net of debt payments on stadiums paid by the teams. See Ouzanian and Badenhausen (2020) for a brief description of the methodology of revenue calculations and team valuations. 2 The Designated Hitter (DH) position for American League teams was not used since most teams did not employ a full-time DH, rather they split time among several players at different fielding positions with the DH position.

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Table 2.1 Free-agent fielding players by playing position, 2000–2012 Season

Catcher

1B

2B

3B

SS

OF

Total

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Total

8 7 6 7 12 11 8 9 7 7 12 15 9 118

3 5 5 7 9 7 9 9 3 8 11 8 9 93

6 4 5 6 9 6 7 14 4 5 8 4 9 87

3 5 4 5 8 5 5 10 5 4 7 6 3 70

5 4 5 3 7 9 6 3 3 7 7 6 7 72

9 13 21 14 32 19 16 25 14 17 19 19 20 238

34 38 46 42 77 57 51 70 36 48 64 58 57 678

Source Author’s research

that higher-priced free agents, defined as those paid above the league average salary for all players, tend to be overpaid (or their expected MRP overestimated) while other free agents are underpaid or paid appropriately. Berri et al. (2015) found that NBA players were overpaid over the 2001–2011 sample period, resulting in negative surpluses for team owners. They suggest that the MRP rule works to some extent and that players earn part of the owner’s surplus that arises from fixed revenues through a bargaining process. Krautmann and Solow (2018) found that most MLB free agents were overpaid using a different methodology to estimate player MRPs. These results contrast sharply with the belief that the player’s market is a monopsony (Humphreys and Pyun 2017; Leeds and Leeds 2017). Krautmann et al. (2009) found that players with low bargaining power tend to be underpaid in the National Football League, the National Basketball Association, and MLB. Our empirical results in this paper substantiate this claim and provide a number of further insights, the most important being that free agents signing multi-year contracts are overpaid relative to those signing one-year contracts. In Chapter 4 we provide a theoretical structure to help explain this apparent anomaly.

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2.2

27

A Revenue Model

The essence of the Scully (1974) method is that an improvement in player performance increases a club’s winning percentage at the expense of other clubs, which in turn draws more fans to their games and increases the club’s revenue. In our specification, the revenue function for a single club is given by: R = X α (W P)β

(2.1)

where R WP X

= attendance revenue + television revenue + all other revenues = season winning percentage = a vector of independent variables that affect revenue

Total revenue includes revenue that is specific to each club (attendance, local television, concessions, etc.) and revenue that is shared by all clubs (national television, apparel, etc.). Although some of these revenues may not be a function of local player talent directly (such as national television revenue), increases in these revenue sources can increase the MRP of talent by shifting the MRP schedule for each club. This is the breakdown of team revenues provided by Forbes Magazine. The only way to obtain more detailed (and accurate) revenue figures is to take them from the team accounting statements. However, these are generally unavailable with a few exceptions and include only a few seasons.3 The vector X includes per capita income (total metropolitan income/metropolitan population) Y , a state unemployment rate U , a weighted average real ticket price P, a dummy variable, NEWSTA, taking on the value one for a period of five seasons after a new stadium is opened4 (Coffin 1996; Clapp and Hakes 2005; Coates and Humphreys 3 Some of these are the Blue Ribbon Report and follow-up report commissioned by MLB in 1999 and 2000. Deadspin leaked financial statements for several MLB teams for specific seasons but not for long enough periods of time to be used in our study. See https://sites.google.com/site/rodswebpages/codes for all of the Deadspin releases. 4 New or extensively renovated stadiums since 2001–2012 included Cincinnati, Miami, Milwaukee, New York (NL), New York (AL), Philadelphia, Pittsburgh, San Diego, St. Louis, Kansas City, and Minnesota. New stadiums opened before the start of the 2000 season were not included, even though the 5-year period extended into the sample period.

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2005), and three dummy variables (TV1, TV2, and TV3) that take on the value one in each season during or after a new national television contract (2001, 2007, and 2012, respectively). Finally, team revenue, per capita income, and the average ticket price were deflated by an individual state consumer price index (2000 = 100). A list of sources for all variables is contained in Table 2.2. The revenue function in (2.1) is a departure from typical linear revenue functions utilized in the literature, however we see it as an improvement. Revenue functions that are linear in the winning percentage assume strong separability and a completely elastic marginal revenue schedule. The more general revenue function in (2.1) allows for a downward sloping marginal revenue schedule that shifts with changes in the independent variables. Since market conditions can differ between cities and can change over time, it is reasonable to assume that the MRP schedule is not constant. The function relating team winning percentage to player performance is given by the logistical function: ln[W P/(1 − W P)] =δ + θ O P S + μ(K /B B) + π E R A+ ρC O N T + ωOU T + ε

(2.2)

where OPS K/BB ERA CONT OUT ε

= team slugging percentage (total bases/total at bats) + team on-base percentage = team strikeout–walk ratio = earned run average (earned runs surrendered by a pitcher/9 innings pitched) = a dummy variable equal to one if a team finishes within five games of the wild-card winner = a dummy variable equal to one if a team finishes twenty or more games behind the wild-card winner = a normal error

These stadiums included Detroit, Houston, San Francisco, and Seattle. It was thought best not to include these as the variable would not capture what their revenues were prior to the new stadium opening.

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Table 2.2 Estimates of the (natural logarithm of the) revenue function R = MLB club revenue from all sources P = Average ticket price WP = Club winning percentage Y = Metropolitan area income per capita

U = State-wide unemployment rate CPI = State-wide consumer price index (2000 = 100) NEWSTA = dummy variable = 1 for a new stadium SA = Team slugging average (total bases/at bats) K/BB = team strikeout to walk ratio CONT = a dummy variable = 1 if a club finished the season within five games of the wild-card winner in each league. OUT = a dummy variable = 1 if a club finished the season within twenty or more games behind the wild-card winner in each league TV1, TV2, TV3 = 1 for the seasons covered by a new national television contract (2001, 2007, and 2012, respectively)

Taken from http://www.rodneyfort.com which is data compiled from Forbes magazine and Financial World magazine Taken from http://www.rodneyfort.com which is data compiled from Team Marketing Report Taken from Sports Reference, LLC http://www.sports-reference.com Local metropolitan area personal income and population taken from Bureau of Economic Analysis, Regional Accounts, http://www.bea.gov/regional/reis/ Taken from Bureau of Labor Statistics, http://www.bls.gov/schedule/archives/ metro_nr.htm

Determined from http://www.ballparks. com/ Taken from Sports Reference, LLC http://www.sports-reference.com Taken from Sports Reference, LLC http://www.sports-reference.com Determined from Sports Reference, LLC http://www.sports-reference.com Determined from Sports Reference, LLC http://www.sports-reference.com

Source For data in regression models

The independent variables OPS, K/BB, and ERA are measures of hitting and pitching quality that have been justified by Scully (1974) and others elsewhere. The independent variables CONT and OUT were also used by Scully (1974) and others as proxies for team morale or perhaps managerial ability. They represent a shift in the team production function based on factors other than player performance. We have retained their use to allow for comparison of our results to previous work. An earlier version of the model also included fielding percentage (outs per fielding attempt)

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D. W. ROCKERBIE AND S. T. EASTON

as an independent variable in (2.2). It was omitted here as it lacked statistical significance in any of the formulations. The sabermetric literature suggests many different measures of player performance, such as Wins After Replacement (WAR) and Wins After Replacement Plus (WARP), among others.5 One could argue that some of these should be included as independent variables in (2.2). We think otherwise for two reasons. First, many of these variables are measures of a player’s output from a team production function, instead of being an input into a team production function. Using an independent variable like WAR would imply regressing a team’s winning percentage on a measure of the contribution to wins from each player, suggesting that some sort of adding up property should apply across the members of the team. We view WAR as an intermediate output, rather than an input. Second, it is difficult to judge the marginal effect on winning percentage from a change in a sabermetric composite statistic. The marginal change in OPS is well understood and the derivative to calculate a player’s MRP is straightforward. Although imperfect, the contribution to the team is also easily calculated. Many of the sabermetric statistics are measured in units that are not easily translated to a team contribution, making the calculation of MRP difficult. The fact that winning percentage is bounded between zero and one justifies the use of the logistic function. Previous studies have relied on a linear probability model for winning percentage. The predictions for the marginal effect on winning percentage require estimation of the parameters and the choice of a baseline winning percentage (∂ W P/∂ O P S = θ W P(1 − W P)). Teams with a 0.500 winning percentage will show the largest marginal effect, holding player performance and team morale constant. We chose to use the fitted value for the current season’s winning percentage for each team as the baseline winning percentage. This places each team on a logistic function at different positions with different marginal effects. This could not be done with a linear probability model and we think it is an improvement. Taking the natural logarithm of (2.1), the calculation for MRP is straightforward once (2.1) and (2.2) have been estimated. For a specific hitter denoted as player i playing on team j, MRP is given by (where AB denotes at bats): 

M R Pi = (∂ Ri /∂ W Pi )(∂ W Pi /∂ O P Si )d O P Si j 5 A useful reference is Baumer and Zimbalist (2013).

(2.3)

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Totally differentiating (2.1) gives α β 1 dR = dX + dW P R X WP The vector X is not a function of WP by assumption so dX = 0. Multiplying by R and dividing by dOPS gives the first required derivative in (2.3), d Od RP S = R WβP ddOWPPS . Totally differentiating (2.2) and focusing only on the OPS term gives    1 1−WP dW P = θ d O P S WP (1 − W P)2   1 dW P = θ d O P S W P(1 − W P) dW P = W P(1 − W P)θ dOPS Inserting the necessary derivatives into (2.3) gives     ABi M R Pi j = β θ R j 1 − W P j O P Si j AB j 

(2.4)

The contribution to the team OPS by a specific hitter is calculated using the hitter’s total at bats as a share of total team at bats multiplied by the hitter’s OPS for a season.6 If a hitter has an OPS of 0.750 and accounts for 10% of the team’s total at bats, his contribution to the team OPS is 0.075. This differs from the method used by Scully (1974) and others where the player’s contribution to the team OPS is the team OPS multiplied by the share of team at bats of the individual player. That measure might not be reflective of the player’s performance so we use the player’s OPS since it provides individual information of performance.7 The method assumes that the team performance is simply the 6 OPS is on-base percentage plus slugging percentage. The former is based on total plate appearances, while the latter is based on total at bats. Total plate appearances includes walks, while total at bats does not. We chose to use total at bats for the player contribution to the team OPS, although we admit the choice is arbitrary.  7 Since the team OPS is calculated by T eam O P S =  N (AB /T eam AB) × O P S i i i=1 we use the right-hand side value for each player as the player’s contribution. The Scully

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D. W. ROCKERBIE AND S. T. EASTON

linear summation of the individual player performances and ignores other aspects of team production such as complementarities. We found that the estimates for gross MRP for pitchers were very unreliable when compared to actual salaries, so we do not report them. Pitchers can be divided into three categories: starters, middle relievers, and relievers. Starting pitchers are paid far less per inning pitched than relief pitchers and this makes the results very hard to interpret. If the samples of free agents were evenly divided between starters and relievers, the differences might cancel out in the overall average gross MRP, however our sample years of free agents were typically heavily weighted toward starting pitchers or relief pitchers. Zimbalist (1992) also excluded gross MRP estimates for pitchers on similar grounds. We also discovered that a large proportion of free-agent pitchers spent a considerable amount of time on the 60-day disabled list in the first season of their new contract. Consequently, their gross MRP was smaller than expected, but not due to their own performance or the mistake of the owner.

2.3 Estimates of the Revenue and Winning Percentage Functions The revenue function in (2.1) was estimated in natural log form using data collected from the 2000 through 2012 MLB seasons, providing a total pooled sample size of 364 observations per variable. The Montreal Expos and Washington Nationals were excluded from the sample. It was thought that the franchise move from Montreal to Washington for the 2005 season could distort the regression results. The Toronto Blue Jays were also excluded since there were substantial swings in the CanadianU.S. Dollar exchange rate that affected the club’s revenues measured in U.S. Dollars. Total revenue for each club was taken from Forbes magazine and includes revenue from all sources including net revenue sharing from national media rights and revenue sharing of local revenues. Although it would not be difficult to reverse the effects of revenue sharing on team revenues using the revenue sharing formula for each season, it was method uses (ABi /T eam AB) × T eam O P S which does not utilize any information about the individual player and is not reflective of how the team OPS is calculated. The original Scully (1974) paper used team batting average, not team OPS, but the team calculation is the same.

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33

left in place on the reasoning that each owner can more or less predict team revenues after revenue sharing fairly accurately and base their talent acquisition and payroll decisions on available revenues after sharing. Team fixed effects were included to account for variations in team revenue not explained by the independent variables in (2.1). Team fixed effects were included, but year fixed effects were not.8 A weighted least squares method was used to account for heteroskedasticity across teams. Although Scully (1974) included a dummy variable to distinguish between National League and American League teams, we did not. The National and American League used the same revenue sharing formula over our sample, so we see little reason to include the dummy variable in (2.1). After testing for and rejecting nonlinearity, we report the linear regression results (tratios appear in parentheses) in Table 2.3. To test for robustness of the team revenue model, results are also reported for the 2000–2008 and 2004–2012 subsamples. The team fixed effects coefficient estimates are omitted from Table 2.3 for the sake of brevity. The high significance of the F-statistic and the very acceptable adjusted R2 suggests that the log-linear model is appropriate for explaining variations in team revenue. All the regression coefficients are statistically significant at 95% confidence with the exception of the state unemployment rate. The unemployment rate is a proxy for economic conditions and the results suggest that MLB team revenues are not sensitive (a-cyclical) to the business cycle. The team winning percentage is the key variable in the marginal revenue calculation and its elasticity estimate of 0.523 suggests that a ten percent increase in winning percentage (say from 0.5 to 0.55) raises team revenue by about 5.23% indicating that revenue is quite inelastic with respect to winning percentage. Given that approximately 90% of teams in any given season fell within winning percentages of 0.4 and 0.6, large revenue swings due to team performance are not a frequent occurrence in MLB. A new stadium has no significant effect on team revenue, but has a significantly negative effect on revenue in the 2004–2012 seasons. This result is counter to the short-run effects on attendance found by Coffin (1996), Clapp and Hakes (2005), and Coates and Humphreys (2005). 8 The inclusion of year fixed effects created vectors of zeroes and ones whose combination was perfectly correlated with the combination of vectors from the NEWSTA, TV1, TV2, and TV3 independent variables. Rather than omit one of these variables, it was thought best to omit the year fixed effects.

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D. W. ROCKERBIE AND S. T. EASTON

Table 2.3 Estimates of the (natural logarithm of the) revenue function (2.1)

Constant WP Y U P NEWSTAD TV1 TV2 TV3 Adjusted R2 F N

2000–2012

2000–2008

2004–2012

13.755 (16.51)∗ 0.523 (6.82)∗ 0.873 (3.79)∗ 0.252 (0.61) 0.457 (14.75)∗ −0.009 (0.65) 0.147 (6.89)∗ 0.292 (11.74)∗ 0.364 (17.44)∗ 0.923 125.88∗ 364

13.136 (12.53)∗ 0.565 (7.21)∗ 1.023 (3.46)∗ 0.348 (0.25) 0.476 (16.59)∗ 0.037 (1.29) 0.137 (4.64)∗ 0.277 (7.75)∗

15.727 (30.01)∗ 0.256 (6.01)∗ 0.493 (3.73)∗ 0.267 (1.05) 0.368 (10.47)∗ 0.025 (2.24)*

0.922 88.46∗ 252

0.101 (4.76)∗ 0.175 (9.02)∗ 0.946 130.29∗ 252

Note t-statistics appear in parentheses ∗ denotes statistical significance at 95% confidence Source Author’s creation

However, Rockerbie and Easton (2019) find the same result on team performance using a much longer sample period and a model that incorporates the availability of talent. The lack of statistical significance is likely due to the inclusion of the real average ticket price in the team revenue function. The previously cited papers did not include the real average ticket price. A regression of the real ticket price on the opening of a new stadium suggests that the average real ticket price increased by an average of 20.8% (p-value = 0.001) in the first season. If ticket demand is inelastic, the revenue increases noted by the previously cited papers will show up as an increase in the average ticket price. Removing the real average ticket price from the regression of (2.1) reveals a coefficient for NEWSTA of 0.088 with a t-statistic of 4.15, suggesting that real team revenue increased by 9.2% following the construction of a new stadium. We chose to include the real average ticket price since it provides a useful elasticity estimate.

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Real per capita income has the largest positive effect on revenue with an estimated elasticity 0.873, confirming that baseball’s composite commodity is a normal good. Ticket price has a positive effect on revenue that is inelastic (0.457), confirming that marginal revenue is less than the ticket price. Each new national television contract increased team revenue independently of the other variables, with percentage increases of 0.158, 0.339, and 0.439, respectively.9 The coefficients for the 2004–2012 subsample are all smaller than those for the 2000–2008 subsample, although the statistical significance is virtually unchanged. This can be explained by the declining annual real revenue growth that occurred over the 2000–2012 seasons. Revenues grew by an annual average of 7.3% in 2000–2008 but fell to 5.6% in 2004–2012. With the weighted average ticket price (P ) held constant, revenue growth could have slowed from a decrease in attendance growth and/or decreases in the growth of other revenue sources (concessions and other local revenues). The winning percentage function (2.2) was also estimated using fixed effects and weighted least squares to account for heteroskedasticity. The model was estimated separately for the National and American Leagues owing to the use of the designated hitter in the American League. Team hitting statistics are somewhat higher and pitching statistics are somewhat lower for the American League relative to the National League where pitchers are required to hit. The results for each league are given in Table 2.4. Again, the fixed effects estimates are omitted for the sake of brevity. The degree of fit was quite high for both leagues and the F-statistic for each regression suggests that the model specification is appropriate.10 All of the coefficients carried the expected signs and all of the coefficients were statistically significant with the exception of the strikeout–walk ratio for the National League. The marginal effects can be found dividing each coefficient by 4 since the linear marginal effect is given by βi W P(1 − W P) and W P = 0.5 over the entire sample. Since we focus on the performance of hitters, the OPS variable is of key interest. A 100 point increase in team OPS is predicted to increase the team winning percentage by 9 The effect on revenue expressed as a percentage change when using a dummy variable is eb − 1 where b is the slope coefficient. 10 This measures the degree of fit for the nonlinear dependent variable, but not for the predicted winning percentages themselves.

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D. W. ROCKERBIE AND S. T. EASTON

Table 2.4 Estimates of the logistic winning percentage function in (2.2)

Coefficient CONSTANT OPS K/BB ERA CONT OUT Adjusted R2 F N

National League

American League

−1.520 (4.78)∗ 3.161 (6.65)∗ 0.041 (1.58) −0.226 (6.57)* 0.172 (6.20)∗ −0.175 (4.26)∗ 0.870 69.26∗ 195

−1.850 (6.19)∗ 3.459 (7.40)∗ 0.073 (1.96)∗∗ −0.202 (5.64)* 0.147 (6.39)∗ −0.180 (6.58)∗ 0.903 92.78∗ 169

Note t-statistics appear in parentheses ∗ denotes statistical significance at 95% confidence. ∗∗ denotes statistical significance at 90% confidence Source Author’s creation

(3.149/4)∗0.1 = 0.0787 for the National League and (3.459/4)∗0.1 = 0.0865 for the American League.11 A 100 point increase in the team OPS is considerable given that the sample standard deviation for team OPS was just 0.0393. As expected, pitching is a larger contributor to winning in the National League based on its larger t-ratio for ERA, while hitting is a bigger contributor in the American League based on its larger t-ratio for OPS.

2.4

Calculating a Player’s Net MRP

Each of the 678 free-agent players’ gross MRP was calculated using (2.4) for the first four seasons or less of their new contract. For multi-year contracts, the estimate gross MRP in seasons 2 and 3 were discounted using a discount rate of 5%, then an average MRP was computed in order to make a comparison with the player’s annual salary. Any player who

11 The team OPS was divided by 1000 in the regression model to make it comparable with the team winning percentage.

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37

was placed on the 60-day disabled list in the season following their freeagent signing was excluded from the sample as this would be the result of a serious injury that likely reduced the player’s performance. The freeagent market was more active in some seasons than others. The 2004 season featured 77 free agents signed in the 2003–2004 off-season, while the 2000 season featured only 34 free agents signed in the 1999–2000 off-season. Summary statistics of free-agent activity by fielding position appear in Table 2.1. Where a player played in multiple fielding positions during the season immediately following their free-agent signing, the most frequently played position was used.12 Having calculated gross MRP estimates, Scully (1974) and others obtain a net MRP estimate by subtracting an estimate of payments to other factors of production and player training and development costs. Different studies have used different conventions to estimate these costs. The important point is that these should only be costs that vary with the team stock of talent and should not include fixed costs. Many of the costs that major league teams face are fixed costs, such as stadium financing and maintenance costs, promotional costs, transportation costs, and equipment costs. Scully (1974) included many costs that appear to be fixed costs and these figures were subsequently adjusted for inflation and used by Macdonald and Reynolds (1994). Zimbalist (1992) simply assumes that the appropriate costs are 10% of the estimated gross MRP, but this ignores the fact that most of these costs will be similar regardless of the player being considered (except perhaps when signing a highly valued free agent). One can always debate what sorts of costs make up the difference between gross MRP, where MRP = MRC , and net MRP, where MRP = W S (the wage rate per unit of talent given by the talent supply curve), in a monopsony model. Ideally calculating net MRP from  gross MRP is accomplished by recog. The supply elasticity of talent, ε S , can nizing that W S = M R P/ 1 + ε−1 S be estimated using the log of actual player salaries and performance indicators that are consistent with the estimation of gross MRP: SA for hitters and K/BB for pitchers. Attention would need to be paid to the proper identification of the talent supply function. A reduced-form approach

12 The Designated Hitter (DH) position for American League teams was not used since most teams did not employ a full-time DH, rather they split time among several players at different fielding positions with the DH position.

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D. W. ROCKERBIE AND S. T. EASTON

cannot be used because the competitive wage rate (where MRP = S) is not observed in a monopsony, so a disequilibrium modeling approach would be necessary. Ideally calculating net MRP

fromgross MRP is accomplished by recogin a monopsony market for talent, nizing that W S = M R P/ 1 + ε−1 S where the supply elasticity of talent is ε S . Rockerbie and Easton (2019) used a model of a profit-maximizing team owner that chooses a team budget and estimated a long-run talent supply elasticity between 2 and 3 using a sample period of 25 years, suggesting that the salary depressing effect of a league monopsony is almost nonexistent. Of course, the time horizon the team owner faces in this paper is a single off-season, so the talent supply elasticity will be much smaller and the ability of free-agent players to capture a portion of their surplus through bargaining is greater. The 10% approximation used by Zimbalist (1992) implies a talent supply elasticity equal to 9, a value we feel is too elastic. We computed each freeagent player’s net average MRP using a value of 2, which we then used to compare with the actual average annual salary over the contract. Our estimates of net MRP are calculated by inserting the estimated coefficients into (2.4) and using the fitted team winning percentages and fitted revenues for the subsequent seasons of the free-agent player’s new contract. A net MRP was estimated for every freeagent hitter over the 2000 through 2012 MLB seasons.13 Players who spent at least one period during a season on the 60-day disabled list were excluded from that sample.14 Generally, players who experience periods on the 60-day disabled list possessed large negative net MRPs, due largely to their injuries. Some large variations in net MRP and actual salaries were apparent for individual players, however these often occur due to injuries (net MRP— salary < 0) or an unexpectedly good season (net MRP—salary > 0).

13 These estimates can be viewed in an Excel spreadsheet file by emailing one of the authors. 14 Players who are assigned to the 60-day disabled list (DL) typically have serious injuries that require rehabilitation. They may not return to the major league roster before the 60-day period has expired, however they may be replaced on the team roster by another player. Clubs can apply for reimbursement of salary for players on the 60-day DL through insurance policies they purchase on their players, hence the player’s MRP is zero while on the DL, but the club suffers no salary expense. Historical transactions for the 60-day DL can be found at the MLB website http://mlb.mlb.com/mlb/transactions/.

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They might also occur due to positive or negative externalities in team production that we do not model. An example of the calculation of the net MRP is the case of Albert Pujols. Pujols signed a ten-year contract with the Los Angeles Angels of Anaheim in 2012 after 11 years of full-time MLB service with the St. Louis Cardinals. Pujols was a very productive player with the Cardinals, a three-time National League MVP and nine-time All Star. His contract with the Angels featured an average yearly salary of $25.4 million. Our calculations of Pujols’ net MRP covered only the first four seasons of his contract with the Angels. The gross MRP calculations are given below. Note that the team revenue is divided by the state CPI (2000 = 100).     ABi E(M R P2012 ) =β θ R j 1 − W P j O P Si j AB j     $239m 607 =0.523(3.459) (1 − 0.549)(859) 1.3791 5536 =$11, 834, 732 



   $253m 391 (0.481)(1 − 0.481)(767) 1.3940 5558



   $304m 633 − 0.605)(790) (0.605)(1 1.4128 5652

E(M R P2013 ) =0.523(3.459) =$8, 850, 944 E(M R P2014 ) =0.523(3.459) =$12, 538, 555 

   $312m 602 E(M R P2015 ) =0.523(3.459) (0.525)(1 − 0.525)(787) 1.4128 5417 =$14, 681, 193 To compute Pujols’ net MRP, we assumed a talent supply elasticity of 2 for each of the first four seasons of his contract with the  Angels. Each gross MRP figure given above is multiplied by 1/ 1 + ε−1 to arrive S at the net MRP figure for each season: $7.89 million, $5.90 million, $8.36 million, and $9.79 million. We then discounted these net MRP figures (at a discount rate of 5%) to the start of the 2012 season and took their average, coming to $7.39 million. The final step is to subtract

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D. W. ROCKERBIE AND S. T. EASTON

the deflated value of Pujols’ annual salary to arrive at a final figure of −$11.03 million. The results suggest that Pujols was dramatically overpaid relative to his net MRP over the first four years of his contract with the Angels. It is quite likely that this was the case since Pujols’ OPS was a respectable 0.859 in the first year of his Angel’s contract, but then declined each season thereafter. There are bargains to be had if astute owners look hard. Bernie Williams signed a one-year contract with the New York Yankees for the 2006 season for $1.5 million. This was the last season of his career and not much was expected of Williams at the plate. However, with an OPS of 768, 420 at bats, and playing for the high revenue Yankees, Williams earned a net surplus to the Yankees of $6.15 million for a single season. This is the largest positive average net MRP calculated over the entire 768 players in the 2000–2012 sample period. Unfortunately, bad deals seem to be much worse than the good deals are better. The largest negative annual average surplus is the staggering −$14.29 million of Alex Rodriguez who signed with the Texas Rangers in 2001 (more about Rodriguez below) after six productive seasons with the Seattle Mariners. Estimating the degree of uncertainty in our estimates of each player’s surplus is possible by taking the variance of the MRP in (2.4). However we wish to compute aggregated measures of the surplus by taking the average surplus for groups of players above and below the MLB average salary, and the average surplus for players with single-year and multi-year contracts. Computing the variance of the sample mean for each category is a simple matter if one can assume that each player’s surplus is drawn from the same population distribution of player surpluses. The average variance from the sample of player surplus variances for each category could serve as a measure of the unknown population variance, σ 2 . The variance of the sample mean surplus in each category is then just σ 2 /N , where N is the number of players in the specific category. This method to compute a confidence interval for the average surplus relies on knowing the density function for the population distribution of player surpluses. Our estimated surpluses displayed distributions that were skewed and non-normal, making the computation of confidence intervals difficult. Bootstrapping is a relatively simple method developed in Efron (1979) to compute a confidence interval when the population distribution of observations is not known. The estimated surpluses in each category are sampled repeatedly with replacement 1000 times to produce 1000 new samples that are the same sample size as the original sample of surpluses.

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The average surplus in each sample is computed and then the lot is sorted in ascending order. The 95% confidence interval is bounded by the 25th and 975th values. These confidence intervals are presented in Tables 2.4 and 2.5. The confidence intervals are not symmetric and are wider the smaller the number of estimated surpluses in a particular category. Free-agent players earning a salary below the league average consistently generate positive surpluses over the 2000–2012 seasons, ranging from an average of $900,000 in 2001 to $1,981,000 in 2012. These are average annual surpluses, hence for a player who just signed a threeyear contract, the total discounted surplus to the owner is three times the average in Tables 2.5 and 2.6. It is not hard to see that these lesser talented players generate significant surpluses when the contract Table 2.5 Estimated surpluses for MLB free agents, 2006–2012, (η S = 2) Surplus to Team Owner ($ millions)

2012

2011

2010

2009

2008

2007

2006

Average Upper bound Lower bound Average Upper bound Lower bound Average Upper bound Lower bound Average Upper bound Lower bound Average Upper bound Lower bound Average Upper bound Lower bound Average Upper bound Lower bound

Source Author’s creation

Below average salary

Above average salary

One-year contracts

Multiyear contracts

1.981 2.704 1.416 0.917 1.448 0.462 1.397 1.818 0.965 1.445 1.950 0.926 0.981 1.590 0.348 1.650 2.200 1.064 1.894 2.402 1.443

−1.286 −0.267 −3.377 −0.889 0.524 −2.234 0.310 1.494 −1.029 −1.408 0.648 −4.114 −2.575 −0.695 −4.723 −1.121 −0.158 −2.304 −0.514 0.427 −1.556

1.533 2.438 0.653 0.606 1.101 0.166 1.092 1.574 0.615 0.707 1.571 −0.397 −0.152 0.849 −1.540 0.948 1.560 0.272 1.813 2.292 1.341

−3.837 0.538 −2.512 −0.592 1.196 −2.401 0.803 2.143 −0.759 0.181 1.832 −1.570 −1.558 0.402 −4.114 −0.966 −0.234 −2.716 −0.635 0.341 −1.729

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D. W. ROCKERBIE AND S. T. EASTON

Table 2.6 Estimated surpluses for MLB free agents, 2000–2006, (η S = 2) Surplus to Team Owner ($ millions)

2005

2004

2003

2002

2001

2000

Average Upper bound Lower bound Average Upper bound Lower bound Average Upper bound Lower bound Average Upper bound Lower bound Average Upper bound Lower bound Average Upper bound Lower bound

Below average salary

Above average salary

One-year contracts

Multiyear contracts

1.890 2.217 1.546 1.785 2.225 1.376 1.723 2.224 1.281 1.484 1.924 1.076 0.900 1.373 0.427 1.435 1.992 1.007

−0.106 0.876 −1.154 −0.352 0.669 −1.562 −1.444 −0.034 −2.954 −1.127 0.793 −3.108 −1.900 −0.308 −4.088 0.804 1.679 −0.308

1.673 2.157 1.186 1.715 2.132 1.347 1.260 1.846 0.534 1.161 1.892 0.272 0.493 1.087 −0.183 1.461 2.052 0.968

0.322 1.210 −0.549 −0.626 0.762 −2.001 −0.324 1.455 −2.371 −0.443 1.143 −1.661 −1.718 0.487 −4.309 0.856 1.737 −0.188

Source Author’s creation

lengths are factored in (although most of these players signed one-year contracts). This is clear evidence of monopsony power for lesser talented players. The average annual surplus is largely negative for free agents earning above the league average salary, the only exceptions being the 2000 and 2010 seasons. These losses for the team owner ranged from $2,575,000 in 2008, to a modest positive surplus of $310,000 in 2010. Free agents signing one-year contracts consistently generated positive annual surpluses, with the exception of 2008, with the positive surpluses ranging from $606,000 in 2011 to $1,813,000 in 2006. Without giving up any options in a one-year contract, these players had little bargaining power and suffered from monopsony exploitation. This contrasts sharply with players signing multi-year contracts. By giving up valuable options to leave, these free agents extracted annual surpluses from the team owner, ranging from an annual average of $324,000 in 2003 to $3,837,000 in 2012. These estimates suggest these free agents were paid salaries far

2

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above their expected MRP, particularly when the length of the contract is factored into the calculation. It is easier to place the estimated player surpluses in context by using a relative measure of exploitation. Table 2.7 presents what we call the “exploitation rate” defined below, and the MLB average salary for all players for each season in the sample. n (net M R Pi − salar yi ) (2.5) ex ploitationrate = i=1 n i=1 salar yi A negative exploitation rate indicates an overpayment of salary relative to net MRP and a positive value indicates an underpayment. This calculation suggests that free agents who are paid above the major league average salary are overpaid in each year of the sample. Owners tend to earn a surplus for players paid below the major league average. The results suggest that free agents are overpaid relative to their net or gross MRP in each year of the sample if they are paid above the major league average salary. Owners tend to earn a surplus for players paid below the major league average, however the overall average across all free Table 2.7 Exploitation rates for MLB free agents versus salary, 2000–2012, (η S = 2) Exploitation Rate Season

MLB average salary

Free agents above average salary

Free agents below average salary

All free agents

2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000

$3,440,000 $3,305,393 $3,297,828 $3,240,206 $3,154,845 $2,820,000 $2,699,292 $2,632,655 $2,486,609 $2,555,416 $2,340,920 $2,138,896 $1,895,630

−0.191 −0.114 0.031 −0.141 −0.290 −0.165 −0.094 −0.030 −0.020 −0.257 −0.215 −0.348 0.167

1.168 0.544 0.906 0.951 0.563 1.080 1.491 1.673 2.002 1.991 1.242 0.964 1.836

0.115 0.037 0.281 0.147 −0.145 0.050 0.285 0.398 0.576 0.360 0.186 −0.109 1.137

Source Author’s creation

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D. W. ROCKERBIE AND S. T. EASTON

agents is negative. The 2001 season also saw MLB negotiate a new television contract with the FOX broadcasting network, a six-year package totaling $2.5 billion. This television package paid each club 2.5 times their previous annual television royalty. Although this revenue increase is included in the revenue data used here, it would appear that some club owners greatly overpaid their free-agent acquisitions in anticipation of these higher revenues. The same might have happened after the new television contract in the 2007 season. Some special cases of free-agent signings in the sample help to understand some of the results in Table 2.7. Alex Rodriguez signed a free-agent ten-year contract with the Texas Rangers before the 2001 season that paid him approximately $22 million per season, at that time, the largest salary in baseball history. The 2001 season saw the Rangers finish with a winning percentage of only 0.4506, last in the American League west division. The Rodriguez contract consumed just over 16% of estimated total revenue for the 2001 season and approximately one-quarter of the total payroll of $88.9 million. Rodriguez had a good season, producing an OPS of 1.021 in 632 at bats. However, with the poor performance of the Rangers and their revenues only slightly above the major league average, the Rangers realized a gross annual average MRP of only $11.7 million from Rodriguez. After playing three seasons in Texas, Rodriguez was traded to the New York Yankees for the 2004 season for fellow shortstop Alfonso Soriano. The Yankees appeared to be much smarter than the Rangers since they insisted that the Rangers continue to pay a sizeable portion of Rodriguez’s salary. Barry Bonds had set the major league record with 73 home runs in the 2001 season and had proven to be a major contributor to the San Francisco Giants playoff run during that season. He subsequently declared free agency prior to the 2002 season and re-signed with the Giants for three seasons for an annual salary of $16.17 million. Like the Alex Rodriguez contract, the Giants may have greatly overestimated his monetary value to the club. Bonds accumulated an impressive OPS of 1.321 for the 2002 season, but only in 406 at bats (slightly under two-thirds the number of at bats for a full-time player). The Giants total revenue of $159 million placed them in the upper half of the league revenue distribution, but not high enough to justify the large salary paid to Bonds. The Giants winning percentage of 0.5741 insured another playoff appearance in 2002, however adding Bonds to an already good team lowered his MRP below what it would have been on a slightly lesser team. The

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estimated average annual net MRP for Bonds was just $3.43 million, resulting in an average annual surplus of −$11.7 million. For comparison, Bond’s estimated MRP if he played with the New York Yankees for the 2002 season with 600 at bats would have been close to $14 million. The best bargain players are typically not big-name free agents. Dave Dellucci signed a one-year contract with the Texas Rangers before the 2005 season for a salary of $850,000. Prior to that season, Dellucci was a rather light-hitting outfielder who mostly played for the Arizona Diamondbacks. Dellucci accumulated an OPS of 0.879 for the 2005 season (the team average was 0.798) in 435 at bats, the most at bats in his career. Rather unexpectedly, Dellucci had the third-highest OPS on the team and played regularly in the outfield. The Rangers did not fare well in the standings winning only 79 games and their total revenue of only $153 million was slightly below the league average. Despite the lack of marginal revenue, Dellucci’s estimated annual average net MRP was $3.75 million, making his $850,000 salary an unexpected bargain. The exploitation rates in Table 2.7 could be sensitive to the talent supply elasticity value.15 To test this, we computed the exploitation rates with η S = ∞, an open talent market with constant marginal cost of talent.16 These results are given in Table 2.8. The choice of talent supply elasticity increases the exploitation rate for free agents above the average salary by an average of 0.359, indicating that these players exploit owners by a smaller amount in an open talent market. An open talent market also increases the exploitation rate for free agents below the average salary by an average of 1.064. All free agents are worse off in the open talent market assumption by an average increase in the exploitation rate equal to 0.491. However, the choice of talent supply elasticity does not affect the qualitative result that free agents who are paid above the league average salary exploit owners, while those paid below the league average salary are exploited by owners. We compared the exploitation rates for one-year versus multi-year contracts in Table 2.9. The results are striking. For every season in our sample, excepting the 2011 season, players on single-year contracts are 1 15 Take the derivative ∂ N M R P =

2 G M R P > 0. An increase in the elasticity ∂η S η2S 1+η−1 S

of talent supply will increase the net MRP for any player. 16 It is a simple matter to specify a different talent supply elasticity in our spreadsheet

file.

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Table 2.8 Exploitation rates for MLB free agents versus salary, 2000–2012, (η S = ∞) Exploitation Rate Season

MLB average salary

Free agents above average salary

Free agents below average salary

All free agents

2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000

$3,440,000 $3,305,393 $3,297,828 $3,240,206 $3,154,845 $2,820,000 $2,699,292 $2,632,655 $2,486,609 $2,555,416 $2,340,920 $2,138,896 $1,895,630

0.089 0.215 0.425 0.180 −0.042 0.166 0.278 0.391 0.420 0.057 0.152 −0.037 0.706

2.128 1.199 1.770 1.828 1.240 2.034 2.668 2.949 3.455 3.450 2.340 1.928 3.253

0.547 0.441 0.809 0.615 0.175 0.488 0.845 1.033 1.315 0.989 0.753 0.321 1.375

Source Author’s creation

paid a salary below their estimated MRP, while players on multi-year contracts are paid a salary above their estimated MRP for every season. A small number of free agents were excluded from the calculations in Table 2.9 due to the anomalous nature of their one-year contracts.17 These are listed in the notes to Table 2.9. Each note also includes the value of the exploitation rate if the player was included in the calculation in a bracket. The result for players with multi-year contracts runs contrary to the monopsony model of the talent market and agrees with the results found in Krautmann and Solow (2018) for MLB. The choice of talent supply elasticity affects the values of the exploitation rates in the same way as before, but the qualitative result is robust. In the next chapter, we develop a simple model of real options to explain this key result.

17 These players capture enormous amounts of surplus and are good examples of the “superstar” effect developed by Rosen (1981).

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Table 2.9 Exploitation rates of free-agent players by contract length, 2000– 2012, (η S = 2) Exploitation Rate Season

Free agents with multi-year contracts

Free agents with one-year contracts

All free agents

2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000

−0.191 −0.099 0.031 0.054 −0.059 −0.154 −0.122 0.051 −0.048 −0.082 −0.077 −0.391 0.248

0.747a 0.192 0.906 0.479b 0.129c 0.308 0.934 0.874 1.340 1.418d 1.119e 0.317f 1.137

0.146 0.033 0.281 0.249 −0.094 0.050 0.285 0.398 0.576 0.477 0.267 −0.083 0.669

Source Author’s creation a Excludes Jose Reyes, Miami Marlins, $17.7 million (0.547) b Excludes Manny Ramirez, Los Angeles Dodgers, $22.5 million (0.231) c Excludes Andruw Jones, Los Angeles Dodgers, $18.1 million (−0.199) d Excludes Ivan Rodriguez, Florida Marlins, $10 million (0.919) e Excludes Juan Gonzalez, Texas Rangers, $11 million (0.670) f Excludes Juan Gonzalez, Cleveland Indians, $10 million (0.190)

2.5

A Linear Probability Model

The logistic model for team winning percentage is not commonly used in the sports economics literature even though econometric theory supports its use. Scully (1974) and others that followed have used a linear probability model, based largely on the argument that team winning percentages do not approach extreme values close to zero or one very often, if at all. The linear probability model also makes the interpretation of the slope coefficients easier, if that is the purpose of the research. Our results suggest that star players tend to be overpaid relative to the net MRP and that lesser talented players are underpaid. This could be the result of the logistic functional form, rather than any lack of relationship between the player’s net MRP and salary. As the tails of the logistic curve

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D. W. ROCKERBIE AND S. T. EASTON

flatten out, the marginal contribution to the team winning percentage decreases, affecting the MRP of high and low performing players.18 Fortunately, it is a simple matter to convert the net MRP’s computed using the logistic winning percentage function to a linear winning percentage function without the need to reestimate. In its general form, the team revenue function in (2.1) for team j is ln R j = αln X j + βlnW P j + ei . Taking the derivative with respect to WP gives R1j d R j = R

β W1P j dW P j , or d R j = β W Pj j dW P j . Substituting the change in the winning percentage for a change in team OPS from a linear winning R percentage function19 gives d R j = β W Pj j θ L d O P S (the superscript R

L denotes linear) or M R P jL = β W Pj j θ L . The logistic function for WP

the team winning percentage in (2.2) is given by ln 1−W Pj j = δ + θ N L O P S + μ(K /B B) + π E R A + ρC O N T + ωOU T (the superscript NL denotes nonlinear). Taking the derivativewith respect to OPS gives WP 1 N L d O P S, or dln 1−W Pj j = θ N L d O P S, or W1P j + 1−W P j dW P j = θ   dW P j = θ N L 1 − W P j d O P S. The MRP using the logistic function for team winning percentage is given in (2.5) and repeated below with the substitution of the MRP with the linear winning percentage function.       ABi NL N L = 4M R PiL W P j 1 − W P j M R Pi = β θ R j 1 − W P j O P Si j AB j (2.6) 



 

NL ≈ θ 4 . To The MRP in (2.6) makes use of the approximation obtain the estimated net MRP from a linear winning percentage function, it is only necessary to perform a simple division.

θL

M R PiL =

M R PiN L   4W P j 1 − W P j

(2.7)

The exploitation rates for our 678 free agents are computed in Table 2.10 for players above and below the league average salary. The 18 We thank Young Hoon Lee for this important suggestion. 19 The linear winning percentage function being W P = δ + θ L O P S + μ(K /B B) + j

π E R A + ρC O N T + ωOU T .

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Table 2.10 Exploitation rates for MLB free agents versus salary using linear probability model, 2000–2012, (η S = 2) Exploitation Rate Season

MLB average salary

Free agents above average salary

Free agents below average salary

All free agents

2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000

$3,440,000 $3,305,393 $3,297,828 $3,240,206 $3,154,845 $2,820,000 $2,699,292 $2,632,655 $2,486,609 $2,555,416 $2,340,920 $2,138,896 $1,895,630

−0.181 −0.102 0.047 −0.156 −0.279 −0.157 −0.078 −0.016 −0.062 −0.238 −0.175 −0.311 0.198

1.213 0.571 0.936 0.984 0.583 1.107 1.535 1.717 2.091 2.045 1.393 1.012 1.892

0.133 0.052 0.301 0.145 −0.133 0.061 0.308 0.419 0.573 0.389 0.256 −0.070 0.643

Source Author’s creation

exploitation rates for players with one-year and multi-year contracts are computed in Table 2.11 with the same players excluded as in Table 2.9.

2.6

Summary

This chapter developed a simple model of a profit-maximizing club owner to determine the MRP of a potential free-agent acquisition. The profitmaximizing rule of setting salary equal to net MRP was tested and found to be wanting. The study followed Scully (1974, 1989) in spirit but introduced a number of useful innovations. First, only free-agent players were considered since players in the middle of long-term contracts may not be expected to provide a net MRP equal to their salary that was negotiated several seasons ago. This suggestion was first made by Krautmann (1999) and we employed it here. Second, our club revenue data is the most up to date we could find and includes all revenue sources, whereas Scully (1974, 1989) estimates revenue from gate attendance and average ticket price. The importance of using all revenue sources can be noted in our results for the 2001 season when television revenues increased substantially. Third, our regression equation to predict winning percentage used

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Table 2.11 Exploitation rates of free-agent players by contract length, 2000– 2012, (η S = 2) Exploitation Rate Season

Free agents with multi-year contracts

Free agents with one-year contracts

All free agents

2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000

−0.113 −0.086 0.180 0.029 −0.188 −0.143 −0.106 0.063 −0.112 −0.063 −0.010 −0.357 0.295

0.778a 0.209 0.370 0.500b 0.146c 0.320 0.968 0.908 1.412 1.471d 1.219e 0.370f 1.169

0.164 0.048 0.296 0.246 −0.081 0.061 0.308 0.419 0.573 0.510 0.344 −0.040 0.710

Source Author’s creation a Excludes Jose Reyes, Miami Marlins, $17.7 million (0.575) b Excludes Manny Ramirez, Los Angeles Dodgers, $22.5 million (0.249) c Excludes Andruw Jones, Los Angeles Dodgers, $18.1 million (−0.046) d Excludes Ivan Rodriguez, Florida Marlins, $10 million (0.960) e Excludes Juan Gonzalez, Texas Rangers, $11 million (0.746) f Excludes Juan Gonzalez, Cleveland Indians, $10 million (0.235)

a logistic function instead of the linear probability function, making the estimated marginal effect of slugging percentage dependent upon the overall performance of the club. Finally, we estimated the net surplus (positive or negative) for every free-agent player over a much longer sample period than the one or two season samples of previous studies. We believe it is important to consider longer samples in order to avoid implying that the results for a single season are representative of many seasons. We also excluded players who spent time on the 60-day disabled list since their net MRPs are expected to be unusually low and their salaries are not paid by club owners during their time on the disabled list. Two tentative results emerge from our results. First, the salary equals net MRP rule does not hold up well in our sample, suggesting that team

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owners are utilizing their monopsony power. As often suspected by baseball fans, our results suggest that higher-priced free agents are overpaid, but bargains can be had with lesser-paid free agents. If some clubs are able to exploit this result consistently, we did not detect them in our sample. Second, free agents who negotiate multi-year contracts are able to demand salaries above the monopsony salary offer, usually acquiring salaries that are equal to, or above, their revealed MRPs. In the next chapter, we develop a simple option model that explains this result.

References Baumer, B., & Zimbalist, A. (2013). The sabermetric revolution: Assessing the growth of analytics in baseball. Pennsylvania: University of Pennsylvania Press. Berri, D., Leeds, M., & von Allmen, P. (2015). Salary determination in the presence of fixed revenues. International Journal of Sport Finance, 10, 5–25. Bradbury, J. C. (2007). Does the baseball player market properly value pitchers? Journal of Sports Economics, 8(6), 616–632. ———. (2013). What is right with Scully estimates of a player’s marginal revenue product. Journal of Sports Economics, 14(1), 87–96. Brown, K., & Jepsen, L. (2009). The impact of team revenues on MLS salaries. Journal of Sports Economics, 10(2), 192–203. Bruggink, T., & Rose, D. (1990). Financial restraint in the free agent labor market for major league baseball: Players look at strike three. Southern Economic Journal, 57 (4), 1029–1043. Clapp, C., & Hakes, J. (2005). How long a honeymoon? The effect of new stadiums on attendance in Major League Baseball. Journal of Sports Economics, 6(3), 37–63. Coates, D., & Humphreys, B. (2005). Novelty effects of new facilities on attendance at professional sporting events. Contemporary Economic Policy, 23(3), 436–455. Coffin, D. A. (1996). If you build it, will they come? Attendance and new stadium construction. In J. Fizel, E. Gustafson, & L. Hadley (Eds.), Baseball economics: Current research. Westport, CO and London: Greenwood, Praeger, 33–46. Efron, B. (1979). Bootstrap methods: Another look at the jackknife. Annals of Statistics, 7 (1), 1–26. Fort, R. (1992). Pay and performance: Is the field of dreams barren? In P. Sommers (Ed.), Diamonds are forever: The business of baseball. Washington, DC: The Brookings Institution, 134–160.

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Humphreys, B., & Pyun, H. (2017). Monopsony exploitation in professional sport: Evidence from Major League Baseball position players, 2000–2011. Managerial and Decision Economics, 38(5), 676–688. Krautmann, A. (1999). What is wrong with Scully’s estimates of a player’s marginal revenue product? Economic Inquiry, 37 (2), 369–381. Krautmann, A., & Ciecka, J. (2009). The post season value of an elite player to a contending team. Journal of Sports Economics, 10(2), 168–179. Krautmann, A., & Solow, J. (2018). The economics of long-term contracts in Major League Baseball. Unpublished working paper, DePaul University. Krautmann, A., von Allmen, P., & Berri, D. (2009). The underpayment of restricted players in North American sports leagues. International Journal of Sport Finance, 4(3), 161–175. Leeds, M., & Kowalewski, S. (2001). Winner take all in the NFL: The effect of the salary cap and free agency on the compensation of skill position players. Journal of Sports Economics, 2(3), 244–256. Leeds, E., & Leeds, M. (2017). Monopsony power in the labor market of nippon professional baseball. Managerial and Decision Economics, 38(5), 689–696. Ouzanian, M., & Badenhausen, K. (2020). Despite lockdown, MLB teams gain value in 2020. https://www.forbes.com/sites/mikeozanian/2020/04/09/ despite-lockdown-mlb-teams-gain-value-in-2020/#3b497d462010. Taken on June 6, 2020. MacDonald, D., & Reynolds, M. (1994). Are baseball players paid their marginal products? Managerial and Decision Economics, 15, 443–457. Rockerbie, D., & Easton, S. (2019). Of bricks and bats: New stadiums, talent supply and team performance in Major League Baseball. Journal of Sports Economics, 20(1), 3–24. Rosen, S. (1981). The economics of superstars. American Economic Review, 71(5), 845–858. Rosen, S., & Sanderson, A. (2001). Labor market in professional sports. Economic Journal, 111(February), F47–F68. Scully, G. (1974). Pay and performance in major league baseball. American Economic Review, 64(5), 915–930. ———. (1989). The business of major league baseball. Chicago, IL: University of Chicago Press. Zimbalist, A. (1992). Salaries and performance: Beyond the Scully model. In P. Sommers (Ed.), Diamonds are forever: The business of baseball (pp. 109–133). Washington, DC: The Brookings Institution. ———. (2010). Reflections on salary shares and salary caps. Journal of Sports Economics, 11(1), 17–28.

CHAPTER 3

Contract Options for Buyers and Sellers of Talent

Abstract Simple present value calculations of how a team owner values multi-year player contracts ignore the value of options to defer signing players or release players in subsequent years of the contract. Salary demands for players who use present value calculations of their expected future productivity ignore their valuable options to move to another team over the duration of the contract. Bargaining is then based on the expected future productivity of the player and the net value of the options to the owner and player. In this chapter, we provide a real option model of salary negotiations over two-year contracts. We also identify different conditions that influence the values of the options attached to player contracts. Keywords Real options · Baseball contracts

3.1

Introduction

Classical economic theory suggests that a profit-maximizing firm will hire labor up to the point where the marginal revenue product (MRP) of labor just equals the wage rate: the contribution to revenue by the last unit of labor hired just equals what all labor is paid. The profit from hiring labor to the employer is the surplus revenue over and above what all units © The Author(s) 2020 D. W. Rockerbie and S. T. Easton, Contract Options for Buyers and Sellers of Talent in Professional Sports, Palgrave Pivots in Sports Economics, https://doi.org/10.1007/978-3-030-49513-8_3

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of labor are paid (the payroll). This is a rather static approach since it assumes that fluctuations in product demand, and thus labor demand, do not exist, workers will all accept the same wage rate per unit of labor and employers have perfect foresight. The reality is that employers face many uncertainties when negotiating fixed-wage labor contracts that are not piece-rate contracts. The productivity of individual workers is difficult to measure in most industries as well as the future state of demand for the products that workers produce. More recently, it has been recognized by economists that employment contracts can include many features beyond the wage = MRP rule to mitigate risk and uncertainty that provide mutual advantages for the employer and worker. Although originally developed in contracts for investment projects, real options can also be capitalized into employment contracts to mitigate risk and uncertainty and recoup any loss in future flexibility to each party to the contract. It is with real options theory that economics can explain the apparent systematic nonoptimizing behavior in professional sports labor contracts.

3.2 Employment Contracts that Include Real Options Multi-year or long-term labor contracts are characterized by a rigid wage and employment schedule that cannot be broken in the event of economic fluctuations except under extraordinary circumstances that are agreed to in the contract. Of course, the contract is null and void if the employer goes out of business, but failing that, long-term contracts are quite rigid. Given that economic fluctuations are unpredictable, the agreement by both parties to the contract to sacrifice flexibility is puzzling. The standard economic approach to explaining the rigidity of long-term labor contracts assumes a risk-neutral employer offering such a contract to riskaverse workers who value stability in their wages. By being risk-neutral, the employer only considers the expected value of the worker’s productivity and ignores any variability. Risk-averse workers experience a loss in utility when their wage and hours of work become variable. Early contributors to this approach were Baily (1974) and Azariadis (1975). Rudanko (2009) is a more recent example. Labor productivity generally behaves procyclically (Romer 2012) due to technology shocks, imperfect competition and increasing returns to labor, changes in how labor is utilized in production, and resource reallocations (Basu and Fernald 2000). Consequently, workers experience periods where their MRP can

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fall above or below a normally contracted wage. Employers will then maximize profit by displaying pro-cyclical employment. These implicit contracting models suggest that risk-averse workers will accept a longterm contract with employment stability in exchange for a wage below their MRP and risk-neutral employers will be happy to agree to such contracts. The lower wage capitalizes the utility value that workers place on employment stability, resulting in an efficient contract. Unfortunately, this standard approach fails to take into account the possible options that an unexpectedly high productivity worker might have to move to a higher paying job during the contract, and the options that an employer foregoes by laying off an unexpectedly low productivity worker. Yamaguchi (2010) estimates that the real option value to workers increased wages by 15% in the first five years of employment in a large sample of U.S. workers. It is easier to place the discussion of real options in labor contracts by first considering the decision to undertake long-term investment projects by firms. In the simplest case, the decision to undertake an investment project is governed by the annual cash return, the number of periods the capital yields a cash return, the initial cost of the project, and the opportunity cost of the funds invested in capital. The decision-maker compares the net present value (NPV) of the future cash returns with the initial cost of the capital investment (CC). If NPV > CC, the investment project may go ahead as long as there do not exist other investment projects with a higher net return. If NPV < CC, the project is not profitable and will not go ahead. The discount factor is typically a market rate of return that the firm could earn instead of investing in the capital project. This simplistic approach typically underestimates the NPV calculation in a world of uncertainty and risk. The firm may choose to defer the project before all of the capital is in place if the expected cash flows or the opportunity cost of funds is more favorable in a future time horizon. The firm could abandon the project (selling it) at a future time if economic conditions change for the worse. Instead of relying on present value calculations alone, real options theory has become increasingly popular to model investment decisions by firms.1 Present value calculations do not account for the flexibility provided by deferring, restarting, or altogether dropping investment project decisions. If this flexibility is valuable to decision-makers, real

1 A good reference is Copeland and Antikarov (2003).

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options will have a positive value and may increase the likelihood of undertaking an investment project. Real options differ from financial options, such as stock or commodity options, in that the holder of the real option can affect its value, whereas the holder of a financial option is one of potentially millions of holders of the same option and has no influence on the value of the option. In an employer–employee relationship, a worker can certainly affect the value of his or her productivity and thus the value of a real option to stay with the employer over the life of a long-term contract. A rational employer knows this and will place a value on the real option to release the worker in the event of low productivity, rather than commit to a long-term contract. We employ a simple real options approach to model the decisions by professional sports team owners and players to agree to multi-year player contracts. For the player, flexibility is the option to leave the team to move to another team at the end of any year excepting for the last year of the contract. The player could do so if available salary offers in midcontract are higher than the currently contracted salary. The team owner values flexibility if he or she can release the player from the contract at the end of any year, excepting for the last year of the contract. He or she could do so if the expected revenue gained from keeping the player (expected MRP) is less than the contracted salary owing. The positive value of real options to the player and team owner may help explain the puzzling empirical result in the previous chapter that highly paid (and skilled) players are generally overpaid,2 while lesser players are generally underpaid, as compared to their estimated MRPs.

2 A recent example is the 10-year, $300 million contract signed by Manny Machado

with the San Diego Padres in 2019, the third largest total value contract in MLB history. This contract effectively takes the now 26-year-old Machado through the bulk of his remaining playing years, capturing the financial value of most of his remaining options, but not all. The contract includes an option for Machado to leave the team after five seasons.

3

3.3

CONTRACT OPTIONS FOR BUYERS AND SELLERS OF TALENT

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Setup of the Real Options Model

We begin our exposition of contract options and how they influence player salaries with a simple example. Consider a risk-averse team owner who is considering signing a free-agent player to a 2-year contract.3 Two years keeps the option problem as simple as possible. Assume the risk-free rate of interest is 5%. The owner considers the risk-free rate of interest (rf ) as the rate of return on an alternative market investment, instead of investing in risky player talent. The player’s financial performance for the owner is modeled as only three possible states at the end of each of the two seasons. In the good state, the player’s MRP is $5 million, based on the player’s marginal physical product and the team owner’s marginal revenue. In the bad state, the MRP is only $1 million due to an unexpectedly low marginal physical product. In the neutral state, the player’s MRP is just equal to the expected MRP of $3 million. Each state has a probability of 1/3 of occurring and the team owner and player agree on this knowledge. We denote the probability of each state as pG , p N and p B . The possible states of the return to the team owner over the 2-year contract are shown in Fig. 3.1. What total (or annual) salary will the risk-averse team owner offer? A rational team owner will first compute the present value of the future expected MRP’s to determine the total value of player j’s contract. The player’s output is uncertain in each season, hence the owner will not use the risk-free4 interest rate, rf , as a discount rate. Instead the owner will implicitly calculate a risk spread to add to the risk-free rate. In the stock market literature, the value of the Beta coefficient is used for this calculation. The Beta (β) coefficient is the measure of the stock’s return variability relative to the market average return (rm ). If β > 1, the stock is riskier than the market average. Formally, each  player could have a  unique value for Beta given by β j = C O V r j , rm /V A R(rm ). This would measure the player’s variability in MRP relative to the average player MRP in the entire league or on the owner’s team, perhaps even at the same 3 We assume a single team owner although that is often not the case in professional sports leagues. Nevertheless, most leagues require that a single owner be identified if there is a group of owners. 4 Or more precisely, a rate of return that is uncorrelated with the baseball player market, and when there is risk-free borrowing and lending, is equal to the risk-free rate. If there is no risk-free rate, then the relationship of Beta to the return on the market remains intact although the portfolio cannot be shown to be efficient (Fama and French 1994).

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Fig. 3.1 Possible states during the two-year player contract (Source Author’s creation)

playing position, or some other player grouping that the team owner and player both implicitly agree to use. If measured on the owner’s team only, each player’s beta coefficient would reflect differences in variability of marginal physical product. Since a player’s past performance statistics are easily available, we assume the team owner and player could potentially agree on the player’s beta coefficient. The present value of the player’s expected MRP over the two-year contract is calculated using 3.1 where rp is the risk-adjusted discount rate equal  to the risk-free rate plus the risk premium described by r p =  rm − r f β j .     E M R P j,2 E M R P j,1  +  PV =  2  1 + r f + rm − r f β j 1 + r f + rm − r f β j     E M R P j,1 E M R P j,2 = +  (3.1) 2 1 + rp 1 + rp

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For the team owner, the present value, PV , is just equal to the player’s total salary offer (assuming the owner has no monopsony power). The rate of return rm can be thought of as the average rate of return for all players in the league, calculated as the surplus to the owners as a percentage of the salary. We will assume for this exercise that the risk-adjusted rate of return is 10% based on (3.1) and the player’s Beta coefficient.5 In this way, the owner sets a team budget based on the perceived riskfree rate of return and the risk-adjusted rate of return for players. The owner’s problem is how much to invest in the team. The expected return to the owner’s portfolio is E(Rt ) = α R f + (1 − α)R pt where R pt is the return from the players on the team and α is the share of his or her portfolio allocated to the risk-free asset. The separation theorem suggests that any investor (owner), regardless of utility function, will invest the same shares of his or her portfolio in the capital market and the player market when facing the same relative rates of return. In contrast, the general manager’s problem is how much to invest in the contract, in which the options are other players since the team must have a roster to compete in the league. Choosing a team budget, instead of choosing a stock of player talent, has received recent support in the sports economics literature (Rockerbie and Easton 2019; Madden 2011; Szymanski 2004). How much talent a team budget will purchase will depend upon the talent supply market. Choosing a stock of talent implicitly assumes a completely elastic supply of talent, whereas choosing a team budget allows for a broad range of talent supply elasticities.6 Calculating the present value of the player’s expected MRP described in Fig. 3.1 is straightforward using (3.1). The condition in (3.2) will hold when the present value of known payments to the player, salary S i , evaluated at the risk-free rate of 5% is equal to the (assumed) 10% discounted expected value of the player’s risky MRP. The annual salaries in year 1 and

5 We imagine a world in which players are like highly variable individual stocks. The risk-adjusted rate might differ from 5% in that case and βi j would differ as well if the portfolio is for all players rather than the capital market. The beta coefficient for the entire league of players (the “market risk”) is equal to one. If we had the MRP for each player and their salary, we could calculate the market risk and then the beta for each “stock” player and the consequent “portfolio” contribution of a team. 6 Rockerbie and Easton (2019) show how to estimate the talent supply elasticity.

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year 2 are denoted S1 and S2 , respectively.   1 1  1 S1 S2 3 $5m + 3 $3m 3 $1m = + 1 + 0.05 (1 + 0.05)2 1 + 0.1   1 1  1 3 $5m + 3 $3m 3 $1m + (1 + 0.1)2

(3.2)

Assume S 1 = S 2 = S in a player contract, (and we assume no performance incentives) so the player’s expected MRP (M R P jC ) for his current team of $3 million in each season can be factored out and 3.2 simplified. ⎞ ⎛ 1 1 1+0.1 + (1+0.1)2 ⎠ = $3m(0.9334) = $2.8m (3.3) S = $3m ⎝ 1 1 + 2 1+0.05 (1+0.05)

With equal salaries in each season, we can label the net discount factor in the bracket as δ2 , the subscript referring to the length of the contract. Because he or she is risk-averse, the team owner offers less than $3 million per year, offering $3 million only if he or she were risk-neutral.

3.4

The Player’s European Put Option

Suppose the player is considering signing the two-year deal in Fig. 3.1 or signing a one-year deal with the same owner to maintain a flexible position. Perhaps in one year’s time, the player could sign with a large market team that will pay a higher salary even if the marginal physical product of the player is unchanged. What is the value to the player of this flexibility? This is the value of the purchase of a European put option for the player that permits him to opt out of the two-year deal at the end of one season. Of course, the team owner also has an option to sign the player to a one-year deal to avoid the uncertainty of the second year and maintain a flexible position—a valuable put option. That exercise is considered in the next section. To proceed, we need to specify who the possible suitor teams will be at the end of the first year of the contract. For simplicity, we assume there are only two suitors. We will assume that there is a probability of p L = 0.5 that a large market team could be interested in signing the player to a two-year deal and (the team) receives $10 million for his MRP in the good state, $2 million for his MRP in the bad state, and $6 million in the

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neutral state, each with a probability of 1/3. In all three states, the value to the large market team is higher than tothe team the player will leave L after one year, and his expected MRP is E M R P j = $6 million. There is also a probability of 0.5 that a small market team could be the only team interested in signing the player. The player’s MRP is just $4 million in the good state, $0.75 million in the bad state, and $2.375 million in the state, each with a probability of 1/3. His expected MRP  neutral S is E M R P j = $2.375 million. All three states are lower in MRP than those for the (original) team the player would leave. We can compute the salary each of the two new risk-averse owners would offer by computing the present value of the player’s MRP for each, assuming that the owner of each of the suitor teams faces the same risk-free and risk-adjusted interest rate as the current team owner. For the large market team, this is ⎞ ⎛ 1 1 1+0.1 + (1+0.1)2 ⎠ = $6m(0.9334) = δ2 $6m = $5.6m (3.4) S = $6m ⎝ 1 1 2 1+0.05 + (1+0.05)

For the small market team, the annual salary offer is S = $2.375mδ2 = $2.22m

(3.5)

The player has already received his $2.8 million salary from his original team for the first year of his two-year contract. He faces the decision whether to leave.7 He will only exercise his option if he can sign with the large market team. We assume that the large market team will only show interest in the player if the player does not have a bad first season with his current team, that is, his actual MRP exceeded or equaled his expected MRP. We follow this rule for the examples that follow. This eliminates the lower branch of the lattice in Fig. 3.2 from the calculations and the player will only accept a new contract from the large market team in the branches in bold. We now compute the option value in the top node in Fig. 3.2, after the player has had a good season. The large market team will offer an annual salary of $5.6 million based on its present value calculation in (3.3). The 7 For simplicity, we are assuming that players are only forward-looking to their next contract in our model. That is, they do not consider the put option to leave the new team they sign with at the end of year one at any point in their new two-year contract.

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Fig. 3.2 Options available to the player after one season (Source Author’s creation)

player’s current team is paying him $2.8 million per season, so the return from the option is $5.6 million−$2.8 million = $2.8 million at the start of the second year if the large market team is willing to sign the player. If only the small market team is interested, the player does not exercise the option and it has zero value since the player is receiving an amount greater than the small market team is willing to pay from (3.5). Since there is an equal chance of either  team showing interest, the expected value of the option is then 13 (0.5 $2.8m + 0.5(0)) = $0.467 million. However, he faces this decision when negotiating his current two-year contract. This suggests there may be an expansion of options for each kind and duration of contracts. Already it is becoming more common in professional sports leagues in North America that some contracts include one or more option years at the end of the contract that the player or owner can exercise if they choose. This is one way to recover the value of the option without explicitly including its value in the player’s salary in the initial contract (with obvious tax advantages.)

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We can compute the present value to the player of the put option value. This is done using the discount rate adjusted for risk since the player does not know his revealed productivity in advance of season one.8 Since the player faces the same market in the middle node in Fig. 3.2, his option value is the same as the top node. Thus the present value of the option to the player is $0.934 million/1.1 = $0.849 million. Possibly the player may choose to demand this option value be included in his salary offer from the team owner at the start of the lattice in Fig. 3.1, to agree to give up his flexibility and sign a two-year contract. Since the player is a free agent (by assumption) at the end of the second year, the option value can only be captured in the first year of the player contract. If so, the value of the contract is $2.8m + $2.8m + $0.849m = $3.65 million or $3.118 million per year, greater than the average expected MRP of $2.8 million. The option value drives a wedge between the return to the owner and what the owner must pay the player. Note that this is not due to any assumption of a monopsony or bargaining power. It is simply an efficient contract outcome. We can express the annual option value (OV) algebraically as ⎤ ⎡   E M R P jL (3.6) − E M R P jC ⎦ O V = ( pG + p N )δ2 p L ⎣ 1 + rp The option value, OV, is the difference between the player’s expected marginal revenue product of the large team and the current team discounted by the probability, p L , of the large market team showing δ2 . The annual interest, bringing the value to the start of year one, 1+r ( p)   1 1 $6m option value is 3 + 3 0.9334(0.5) 1+0.10 − $3m = $0.849 million. Several factors could increase the value of the player’s put option and increase his salary above his average expected MRP. 1. The probability of a large market team being available at the end of the first year of the contract increases. 2. The expected MRP of the player for the large market team increases due to an increase in market size (big media contract). 8 We are assuming he does not manipulate his productivity. Rather it is a random outcome of a process with at least two moments.

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3. The physical productivity of the player increases at the end of the first year of the contract, and the large market team is available. This could be the case for a younger player who is still on the upside of his career. 4. The length of the contract increases from two years to three or more years. This would add more complexity to the lattice and give the player more flexible options that are valuable. These “compound options” are options on options and will be explored in the next chapter. 5. The variance of the player’s MRP decreases relative to the average across all players. This would be reflected in a decrease in the player’s Beta coefficient. 6. A decrease in risk-free interest rates.

3.5

The Owner’s European Put Option

Based on the model of the previous section, it is apparent that players who are later in their playing careers whose expected MRP is declining due to declining skills will have put options to leave the current team that have no value. This is because there will be a low probability that a larger market suitor team will be interested in signing the player at the end of each season of the current contract. With no option values, these players should be paid a salary equal to their expected MRP only, but in fact, they will be paid less than that if they demand a multi-year contract. A team owner will demand that the player compensate the owner for the lack of flexibility in signing the player to only a one-year contract. Essentially this is giving up the right to release the player at the end of each season in a multi-year contract, although players cannot be released in this way (except in the NFL). The option value to the owner is computed as if the owner could do this. This option model does not rely on any assumption of a monopsony that gives the same salary–MRP result. We use essentially the same model that was outlined in the previous section of the player’s put option. In a two-year contract, the team owner faces the same two-year horizon as the player in Fig. 3.1. He or she faces the decision whether to sign the player to a two-year guaranteed contract or a one-year contract that provides flexibility. Unlike the player, the team owner receives no gain if the player bolts to a large market team at the end of the first year—although he or she does have the opportunity to

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sign a new player. Hence Fig. 3.1 contains all of the information relevant to the contract decision. The decision to sign the player to a one-year deal can be modeled as equivalent to exercise a European put option on the player’s two-year contract at the end of the first year.9 If this put option has value, we can assume the owner will deduct its purchase price from the player’s two-year total compensation as payment by the player to compensate the owner for giving up this flexibility. This could push the player’s contracted salary below his MRP, ignoring the value, if any, of the player’s put option determined in the previous section. The two-year contract annual salary will still be the $2.8 million computed in (3.3). We assume that the owner wishes to avoid any losses over the life of the contract, that is, where the total discounted expected MRP is less than the total two-year compensation.10 This can occur only in the lowest two nodes of the lattice in Fig. 3.1: the neutral and bad states. The option value for each node is computed below  2   $3m $1m 1 + − $5.6m = −$334, 031 3 1.1 1.12  2   $1m $3m 1 + = − $5.6m = −$245, 730 3 1.1 1.12  2   $1m $1m 1 + = − $5.6m = −$429, 385 3 1.1 1.12

O VN B = O VB N O VB B

The total put option value is $1.00915 million. This is what the owner must receive in order to relinquish the option of “releasing” the player at the end of the first season of the two-year contract. The present value of the total compensation to the player under a two-year contract is $2.8m + $2.8m−$1.00915m = $4.59085m or $2.2954m per year. The put option 9 Although the player has a valuable put option to leave the team to sign with a more lucrative team, we assume that the team owner does not face the decision of releasing the player at the end of one season and signing a more valuable player (in terms of expected MRP). This keeps the exposition simple although it would be an interesting strategy game for team owners to anticipate the future availability of valuable players. 10 This would be consistent with the assumption that the team owner is an expected profit maximizer. In the upper branch of Fig. 3.1, the owner earns a windfall profit, however the owner experiences an unexpected loss in the lower branch. In the two middle branches, the owner just pays the player his expected MRP over the life of the contract.

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value reduces the value of the player contract by approximately 18%. The player pays for the certainty of a two-year contract by accepting a salary offer less than his expected MRP, but not by much since the team owner incurs losing states in only three out of ten possible states. This gives the owner’s put option a low value. Several factors could increase the value of the owner’s put option and reduce the player’s salary below his average expected MRP. 1. The physical productivity of the player is expected to decrease at the end of the first year of the contract. This could be the case for an older player who is in the downside of his career. 2. The length of the contract increases from two years to 3 or more years. This would add more complexity to the lattice and increase the number of really bad states for the owner. 3. A decrease in risk-free interest rates. 4. An increase in the variance of the player’s MRP relative to the league average, increasing the player’s Beta coefficient.

References Azariadis, C. (1975). Implicit contracts and underemployment equilibria. Journal of Political Economy, 83(6), 1183–1202. Baily, M. (1974). Wages and employment under uncertain demand. Review of Economic Studies, 41(1), 37–50. Basu, S., & Fernald, J. (2000). Why is productivity procyclical? Why do we care? NBER Working Paper No. 7590. https://www.nber.org/papers/w7940. Copeland, T., & Antikarov, V. (2003). Real options: A practitioner’s guide. New York: Thomson. Fama, E., & French, K. (1994). The capital asset pricing model: Theory and evidence. Journal of Economic Perspectives, 18(3), 25–46. Madden, P. (2011). Game theoretic analysis of basic team sports leagues. Journal of Sports Economics, 12(4), 407–431. Rockerbie, D., & Easton, S. (2019). Of bricks and bats: New stadiums, talent supply and team performance in Major League Baseball. Journal of Sports Economics, 20(1), 3–24. Romer, D. (2012). Advanced macroeconomics (4th ed.). New York: McGraw-Hill Irwin. Rudanko, L. (2009). Labor market dynamics under long-term wage contracting. Journal of Monetary Economics, 56(2), 170–183.

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Szymanski, S. (2004). Professional team sports are only a game: The Walrasian fixed-supply conjecture model, contest-nash equilibrium, and the invariance principle. Journal of Sports Economics, 5(2), 111–126. Yamaguchi, S. (2010). Job search, bargaining and wage dynamics. Journal of Labor Economics, 28(3), 595–631.

CHAPTER 4

Extensions to the Put Option Model

Abstract In this chapter, we extend the real options model of player contracts to include three-year contracts. A longer contract adds greater complexity to a salary negotiation, however the model suggests that the option values decline in later years due to higher uncertainty of the available choices for players and team owners. Options have higher value for players whose productivity is expected to increase over the length of the contract, typically players at earlier stages of their careers. Veteran players closer to the end of their career have low option values and might find it difficult to negotiate a multi-year contract. We also explore the effects of no-trade clauses on negotiated salaries. Keywords Real options · Player contracts · Risk · Uncertainty

The two-year contract model of Chapter 3 lays the groundwork for the real options approach but lacks many of the features of professional sports contracts. In this chapter, we explore a number of additional features including: a three-year player contract, different player career profiles, the model when players and owners have put options, an option year in the final year of a multi-year contract, and a no-trade clause. The real options approach does a good job in explaining why these features are efficient extensions of the simple two-year contract. © The Author(s) 2020 D. W. Rockerbie and S. T. Easton, Contract Options for Buyers and Sellers of Talent in Professional Sports, Palgrave Pivots in Sports Economics, https://doi.org/10.1007/978-3-030-49513-8_4

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4.1 The Player’s Option Value in a Three-Year Contract Adding more years to a player contract will enhance the option value to the annual salary the player negotiates, but quantifying the effect is made difficult by the increased uncertainty of the player’s performance and the uncertainty of the available opportunities from other suitor teams in future years. Here we consider adding only an extra year to the twoyear contract to keep the exposition tractable, however the insights we gain are naturally extended to longer-term contracts. Figure 4.1 provides a lattice for the three-year contract decision for the player. Each of the upper, middle, and lower branches starting at the end of the second

Fig. 4.1 Possible states during the three-year player contract (Source Author’s creation)

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season and finishing at the end of the third season have probabilities pG , p N , and p B , respectively. The branches in the third year are only relevant for computing the player’s expected MRP over the life of the three-year contract, and thus his salary. For simplicity, the player’s expected MRP is not expected to change, hence the annual salary will be $2.74 million, less than the $2.8 million in the two-year contract due to discounting. This can be calculated as ⎞ ⎛ 1 1 1 1+0.1 + (1+0.1)2 + (1+0.1)3 ⎠ = $3m (0.931) S =$3m ⎝ 1 1 1 + + 2 3 1+0.05 (1+0.05)

=$3mδ3 = $2.74m

(1+0.05)

(4.1)

The third year is otherwise not relevant for computing option values since the player has given up any options by committing to play for the current team in the last year of his contract. The available options to leave the team at the end of the second year are illustrated in Fig. 4.2. Each node at the end of the second year of the current contract represents the expected value of the player’s MRP for the current team over the branches that have led to each node. All but two of the nodes have two different paths to reach the node. The expected value of the total MRP over two seasons (without discounting) for each node is given in Fig. 4.2. The player must have had no interest from a large market team at the end of the first season in order to have an option available at the end of the second contract year. For the paths where a large market team could be interested at the end of the second year, this will occur with a probability of either pG (1 − p L ) or p N (1 − p L ) after the first year of the contract. A large market team will not be interested in the player after two seasons in the bottom two nodes in Fig. 4.2, so they are excluded from any further consideration. We assume that the player faces the option of leaving his current team and signing a new three-year contract with a new team at the end of the first or second season. The large and small market teams will each offer a three-year contract with an annual salary of δ3 $6 million = $5.586 million and δ3 $2.375 million = $2.211 million, respectively. Since the player can earn $2.74 million annually by signing the current contract, he will never sign with the small market team during the three-year contract period.

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Fig. 4.2 Possible paths for the player after two seasons (Source Author’s creation)

Option values for each node are not difficult to compute and many of them replicate. Consider the top node denoted GG. The option value is the probability of reaching the GG node multiplied by the difference in the present values of the expected salaries from the large market team and the current team. The small market team does not enter the calculation since its contract offer will be refused. The annual value of the option to leave the team at the GG node is ⎤ ⎡   E M R P jL 2 (4.2) − E M R P jC ⎦ O V = pG (1 − p L )δ3 p L ⎣ 1 + rp Using our assumed values of pG = 1/3,  p L = 0.5, δ3 = 0.931, r p = 0.1, E M R P jL = $6 million and E M R P jC = $3 million, the annual option value is $68,181. This does not appear to be very high, however we must also compute the option values at the next two nodes

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moving down in Fig. 4.2 and add these to the figure from (4.2). The option value at the second node (GN, NG) is given by ⎤ ⎡   E M R P jL (4.3) − E M R P jC ⎦ O V = 2 pG p N (1 − p L )δ3 p L ⎣ 1 + rp The annual option value for this node is $136,362.1 The option value for the third node (NN, GB, BG) is given by ⎤ ⎡    E M R P jL − E M R P jC ⎦ O V = 2 pG p N + p 2N (1 − p L )δ3 p L ⎣ 1 + rp (4.4) The annual option value for this node is $268,015. Neither of the two nodes below the third node has any option value. The total option value for signing with the large market team at the end of the second year of the three-year contract is $472,558. The option value to leave at the end of the first season is a simple modification of (3.5) for discounting. ⎤ ⎡   E M R P jL (4.5) − E M R P jC ⎦ O V = ( pG + p N )δ3 p L ⎣ 1 + rp The option value in (4.5) is $761,727, bringing the total annual option value of the three-year player contract to $1.234 million. Coupled with the salary offer of $2.74 million per year, the player could ask to receive the full value of two put options and demand $3.357 million for the first two years of the contract and $2.74 million for the third year, or an annual average value of $3.151 million. This is well above his expected MRP, but slightly less than the average salary demand in the two-year contract of $3.65 million due to the uncertainty of the player’s performance and the availability of a large market team at the end of the second season. The option value at the end of the second year only exists if the option is not exercised at the end of the first year, resulting in a much lower option value at the end of the second year. 1 If p = p then this option value is just double the option value in (4.2). G N

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The upshot of the option model is the rather surprising result that player options decline greatly in value for additional years of the contract. This could be expressed diagrammatically as a downward sloping concave function. The two-year contract gives the highest average annual salary, determined as the player’s annual average expected MRP plus annual average option value. This is because the option to leave the team at the end of the second year of a three-year contract is a compound option, that is, an option in which the value relies upon the non-exercising of a previous option. Compound options add little value to the contract due to the uncertainty that they will be exercised.

4.2 The Owner’s Option Value in a Three-Year Contract Extending the contract to a three-year term can increase the value of the owner’s put option and, subsequently, lower the salary offer the owner is willing to make. This is because the put option value is zero in the good and neutral states where the player’s actual MRP is greater than or just equal to the expected MRP, and thus the player is not overpaid relative to his salary. A greater number of possible bad states result in which the put option has positive value to the owner. Figure 4.3 demonstrates the lattice for the three-year player contract on the part of the team owner. The end of any branch that occurs at or above the annual salary has no put option value since the player is generating an MRP above or just equal to the expected MRP. In those cases, the owner is earning a windfall profit or just maximizing expected profit. The three bottom nodes in Fig. 4.3 isolate the paths to the repeated bad states. To calculate the put option values, consider the GBB path first. In the first year, the player generates an actual MRP equal to $5 million which discounted by one year with the risky interest rate is $4.55 million. This is followed by an actual MRP of only $1 million in year two, or $826,446 when discounted twice. The third year also experiences an actual MRP of only $1 million, or $751,315. The total discounted actual MRP is $6.128 million and the player is paid $8.22 million over the three seasons of the three-year contract (in present value). This gives a loss of $2.092 million, which weighted by the probability of reaching the GBB node of 1/27, gives a put option value of $77,659. The computation of the put option value is not the same for the BBG path due to differences

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Fig. 4.3 Player paths that give positive put option value for the owner (Source Author’s creation)

 1 $1m $1m $5m in discounting: O V = 27 + + − $8.22m = $101, 033. The 2 3 1.1 1.1 1.1 task is to calculate option values for all of the possible paths in three bottom nodes of Fig. 4.3 and sum them. The total put option value is $1.2023 million. The team owner will then offer a contract of $2.74 + $2.74 + $2.74 − $1.2023 = $7.0177 million or $2.34 million per year, less than the expected MRP of $2.74 million per year. The put option value reduces the value of the player contract by approximately 14.6%.

4.3 Option Values with Different Career Profiles The previous example suggests that the largest put option value for the player is in moving from a one-year to a two-year contract. However, adding a third year can add a positive option value to the annual salary if the player’s opportunities improve dramatically at the end of the second year. This could be the case of a younger player whose career takes

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an unexpected upswing or who hopes for changing market conditions to make his MRP greater for other teams as enumerated below. These changes could result in an increase in the offer that a suitor team makes at the end of the first and second years, or an increase in the probability that a large market team is available and makes an offer. Suppose at the end of each of the first two years of a new three-year contract, a large market team is available with probability p L = 0.8 whose expected annual MRP from the player is $10 million, instead of p L = 0.5 and $6 million as before. Using (4.2) through (4.5), the option values in each node are  2  1 $10m − $3m = $50, 155 OV = (1 − 0.8)(0.931)0.8 3 1 + 0.10   1 1 $10m OV = 2 − $3m = $100, 310 (1 − 0.8)(0.931)0.8 3 3 1 + 0.10     1 1 2 1 $10m + − $3m OV = 2 (1 − 0.8)(0.931)0.8 3 3 3 1 + 0.10 =$302, 434 OV =

  1 1 $10m + − $3m = $3, 024, 339 (0.931)0.8 3 3 1 + 0.10

This gives a total option value of $3,477,238, for the first two years of the contract, more than the annual salary offer of $2.74 million of the current team, but less than the salary offer of the large market team. The current team will have to offer an annual salary of $3.9 million to retain the player’s services, perhaps much more than the team is willing to pay. In that event, the team may decide to pass on the player. The expected MRP of any suitor team reflects where the suitor falls in the distribution of team revenues in the league. For instance, a player considering signing a three-year contract with the New York Yankees (or Los Angeles Dodgers if you prefer) has very few opportunities to sign with a larger market team at the end of the first and second years of the contract. Although the player will receive an attractive salary offer based on his expected MRP, the options to leave in the future will have little to no value. The model then predicts that the Yankees will not overpay a player above his expected MRP. The most likely teams to do so are

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perhaps those in the middle to lower positions of the league revenue distribution. A player considering signing a three-year contract could think of the option values in (4.2) through (4.5) as being determined by L an average value of p L and E M R P j for all of the teams who fall above the current team in the league revenue distribution. For all of the teams below the current team in the league revenue distribution, the options have no value. The option model suggests a testable hypothesis: that large market teams tend not to pay a player a salary above his expected MRP and that middle to lower market size teams tend to overpay. This is difficult to test because smaller market teams will have to compensate players for considerable option values in their player contracts and may decide to leave those players for the larger market teams. Data are generally not available for players that negotiate with teams on salaries but do not agree on a contract. All of this is made uncertain due to difficulty in forming an expectation of a player’s future MRP and who the available suitors might be. The Yankees might not be interested in signing the player if the team does not have a position to fill that suits the player, even though the player’s expected MRP is attractive. The value of the owner’s put options will increase if the player’s performance is expected to fall over the lifetime of the three-year contract. Suppose that the player’s MRP is expected to fall to $4 million in the good state, $2.5 million in the neutral state and remain at $1 million in the bad state in year 2 of the contract, falling further to $3 million, $1.5 million, and $1 million in year 3 of the contract. The discounted expected MRP, divided by three years, is just the new annual salary offer, equal to $2.266 million. ⎛ ⎜ S =⎝

1 3

($5m )+ 13 ($3m ) 13 ($1m )

=$2.266m

1+0.1

+

1 3

($4m )+ 13 ($2.5m ) 13 ($1m ) (1+0.1)2

1 1.05

+

1 1.052

+

1 1.053

+

1 3

($3m )+ 13 ($1.5m ) 13 ($1m ) (1+0.1)3

⎞ ⎟ ⎠ (4.6)

If the team owner’s expectations are correct, the total value of the owner’s put options will not change much from before since the annual salary offer is lower, and therefore the owner is somewhat compensated in the bad states. Nevertheless, the put option value increases to $8.111 million or $2.937 million annually after computing the put option

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value at each of the bottom three nodes and summing in Fig. 4.3. The team owner needs to offer an annual salary of −$670,920, that is, the player must pay the owner to play for the team. In this case, the uncertainty of the player’s MRP over three years makes it infeasible to offer a three-year contract.

4.4

Contract Values with Player and Owner Put Options

Professional players can possess valuable put options that are bargaining chips in the salary negotiations for multi-year contracts. These options can have particularly high values if the player’s performance is expected to improve over the life of the contract. Team owners also can possess valuable put options since the flexibility to “release” the player is foregone when offering a multi-contract. The “give and take” of contract negotiations can be interpreted to be the effort by each party to capture the value of their put options. In the simplest case, the negotiated salary package is the sum of the present value of the player’s expected MRP and the present value of the player’s put options, less the present value of the owner’s put options. Players who are on the upside of their careers have put options that are much more valuable than the put options of the team owner and they will be paid more than their expected MRP. Multiyear contracts will be difficult to acquire for players on the downside of their careers since there is a high value to the owner’s put options in a multi-year deal. Young players whose performance is expected to improve cannot capture their put option values in MLB due to the restriction that players must complete six years of major league service before being eligible for unrestricted free agency, unless they are released outright. It is not until these players reach their late twenty’s that they can capture the value of their put options in a new contract (probably with a new team). Three years of service are required in the NBA, four years in the NFL, and seven years in the NHL (unless over 27 years old) for unrestricted free agency. However, once eligible for unrestricted free agency, multi-year contracts for these players can come at significant costs for team owners with little room for bargaining. Consider the following case study. Billy Batts has just completed six seasons of MLB service and is an unrestricted free agent. He has serious interest from the owner of mid-level market team who would like to

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sign Billy to a three-year contract. The owner expects Billy’s MRP to be $12 million, $14 million, and $16 million over the three-year contract in the good state, $10 million in each season in the neutral state, and $6 million, $7 million, and $8 million in the bad states. The probabilities of each state are 0.5, 0.25, and 0.25 in each season. The team owner will offer Billy an annual salary of $10.201 million. ⎛ ⎜ S =⎝

1 2

($12m )+ 14 ($10m ) 41 ($6m ) 1+0.1

+

1 2

($14m )+ 41 ($10m )+ 14 ($7m ) (1+0.1)2

1 1.05

+

1 1.052

+

+

1 2

($16m )+ 41 ($10m ) 14 ($8m ) (1+0.1)3

1 1.053

=$10.201m

⎞ ⎟ ⎠

(4.7)

At the end of each of the first two seasons of the contract, a larger market team is willing to sign Billy to a three-year contract with an annual salary of $18 million with a probability of 0.8. Unfortunately, this team is not willing to make an offer today since it already has a player at Billy’s playing position that it prefers. Other teams are also interested in signing Billy in each of the first two years of his potential contract, but will not offer a salary higher than his current offer of $10.201 million. The values of Billy’s put options can be computed using the top four nodes in Fig. 4.3. The total value is $4.245 million.   2 $18m 1 − $10.201m = $229, 497 (1 − 0.8)(0.931)0.8 2 1 + 0.10   1 1 $18m OV = 2 − $10.201m = $229, 497 (1 − 0.8)(0.931)0.8 2 4 1 + 0.10     1 1 2 1 $18m + − $10.201m OV = 2 (1 − 0.8)(0.931)0.8 2 4 4 1 + 0.10 OV =

=$344, 245 OV =

  1 1 $18m + − $10.201m = $3.442m (0.931)0.8 2 4 1 + 0.10

Billy will demand an annual salary of $10.201 + $1.415 = $11.616 million based on his expected MRP and put options. The team owner is also committing to retaining Billy for three seasons without the possibility of releasing him (only signing him to a one-year contract) and

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these put options might have value, but in this case, not much. These put options only have value in the bottom three nodes of Fig. 4.3. The calculations are made more complicated by the fact that few of the possible paths have identical MRP outcomes after three seasons. For instance, the GBB path has a total expected MRP (without discounting) of $27 million while the BGB path has a total expected MRP of $28 million and the BBG path equal to $29 million. Nevertheless, the owner’s put options total $1.865 million. His preferred annual salary offer is just $9.58 million. This results in a bargaining zone of an annual salary of $9.58 million–$11.616 million that more heavily favors Billy. Older players on the downside of their careers will not fare as well. Phil Walkman is an aging pitcher who is an unrestricted free agent. He wishes to sign a three-year contract with a mid-level market club, realizing that his days of playing for a large market team are over. He has serious interest from the owner of a mid-level market team who might sign Phil to a three-year contract if the price is right. The owner expects Phil’s MRP to be $7 million, $6 million, and $5 million over the three-year contract in the good state, $4 million in each season in the neutral state, and $3 million, $2 million, and $2 million in the bad states. The probabilities of each state are 1/3 in each season. The team owner will offer Phil an annual salary of $3.783 million. ⎛ ⎜ S =⎝

1 3

($7m )+ 13 ($4m ) 13 ($3m )

=$3.783m

1+0.1

+

1 3

($6m )+ 13 ($4m )+ 13 ($2m ) (1+0.1)2 1 1 1 + + 1.05 3 1.05 1.052

+

1 3

($5m )+ 13 ($4m ) 13 ($2m ) (1+0.1)3

⎞ ⎟ ⎠ (4.8)

Phil has no options to leave the team at the end of the first or second year of the three-year contract since the only interested teams operate in smaller markets and will not offer an annual salary higher than $3.783 million. The team owner’s put options only have value in the bottom three nodes of Fig. 4.3. The total value of these put options is $1.229 million, resulting in an annual salary offer of $3.373 million, less than Phil’s annual expected MRP. Unfortunately, Phil has no put options with value to bargain with.

4

4.5

EXTENSIONS TO THE PUT OPTION MODEL

81

Multi-year Contracts with Option Years

It is becoming more commonplace for owners and players to include an option year in the last year of a multi-year contract. The option year gives the player the right to finish the final year of the contract at an agreed salary or leave the team as an unrestricted free agent. This is advantageous to the player in two situations: if he anticipates that a large market suitor team will be interested in his services and offer a contract prior to the last year of the current contract, or; the player’s skills are diminishing and he cannot expect to negotiate a better one-year contract with a new team.2 A team owner can also hold an option year that gives the owner the right to retain the player for the final year of the contract, or release the player (typically with a small fixed payment to the player that is a fraction of the contracted annual salary). This is advantageous to the owner if he or she anticipates the player will generate an MRP that is less than the contracted salary in the final year. It is possible that the player and the owner can hold an option year in the same contract. In that event, the owner and player must agree to exercise their options in a way that generates a mutually advantageous outcome. Option years are also a strategic method for a player to defer entering free agency in a year in which there is a relatively large supply of similar free-agent players that could depress the player’s negotiated salary with a new team (see Rockerbie 2009). Vesting options are a common feature of MLB contracts in which the player will be retained in the option year of his contract if he meets certain performance incentive thresholds, such as appearing in a minimum number of games. For a player whose career is moving upwards (expected MRP is increasing), it is a good strategy to negotiate an option year as the final year of a multi-year contract. The previous numerical examples have demonstrated that the total value of a player’s put options is small at the end of the second, and subsequent, years of a multi-year contract, so an option year comes at a small price. The player is willing to forego the total value of the put options in the final year of the current contract if an option year is included, reducing the annual salary of the current contract,

2 Marc Gasol entered the option year of his contract with the Toronto Raptors (NBA) in 2019. He chose to stay with the Raptors for his final season at a salary of $25.6 million after finding no interest for a similar salary with another team. This was advantageous for Gasol, but perhaps not for the Raptors.

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but possibly paying large returns to the player. As already demonstrated, a player on the downside of his playing career (expected MRP is decreasing) must forego salary in order to negotiate a multi-year contract with an owner. If the player agrees to grant the owner an option year (in which the owner can release the player at a small cost), he could negotiate a higher annual salary since the owner will not capitalize the total value of the final year put options in the contract. Of course, the other strategy for player and owner is to agree to a shorter-term contract, perhaps only a single year, in order to hold an option at the end of one year without “paying” for it.

4.6

No-Trade Clauses in Multi-year Contracts

A no-trade clause is a contractual clause that allows players to veto trades to certain teams. Sometimes players will waive their no-trade clauses if they receive agreeable compensation. In MLB, players who have atleast ten years of MLB and service and have spent the last five years with the same team are automatically granted a no-trade clause (so-called 10 and 5 players). The Chicago Cub’s Ron Santo was the first player to utilize the 10 and 5 rule when he vetoed a trade to the California Angels in 1973. No-trade clauses are rare in the NBA due to the restrictive conditions under which they can appear in player contracts. Players must have eight seasons of NBA service and have been with their current team for the last four seasons. An exception is a player signing a one-year contract with his current team, or a two-year contract in which the second year is a team/player option year. Trades are uncommon in the NFL, negating the need for no-trade clauses, hence they are rare.3 No-trade clauses are common for star players in the NHL, however the player must have seven years of NHL service or be over 27 years old. A no-trade clause does not require that a player will never be traded, only that the player must agree to any trade. So-called 10 and 5 players in MLB may be reluctant to accept a trade, even to a contending team, since they will give up their 10 and 5 rights by accepting a trade. No-trade clauses do not make sense in a one-year contract, however they do in a 3 Signing bonuses paid to players up front are amortized over the length of the contract for the purposes of monies toward the team salary cap in the NFL. Any team trading for a player must claim the remaining portion of the amortized signing bonus toward their salary cap, even the bonus money was already paid by the previous team.

4

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83

multi-year contract if the player prefers to live in a certain city or simply wishes to avoid the uncertainty of moving to a new team. The player must compensate the team owner for the value of the owner’s put options in a multi-year contract. The inclusion of a no-trade clause could introduce additional put options if the player has value to the owner of another team over and above the value to the owner of the current team. This would be reflected in a lower salary for a given level of performance in a multi-year contract with a stronger negative effect the longer the length of the contract, since more put options are being set aside by the team owner. Pedace and Hall (2012) find supportive evidence for this using a sample of MLB players over the 2003–2008 seasons. As in international trade, trades of players must be mutually beneficial in the perceptions of the trading parties. For each team owner, the discounted expected MRP from the acquired player’s potential services should be larger than the same for the player traded away. Each owner may have differing values for each player due to market sizes and how well the acquired player will “fit” into the team production function for wins. Our model suggests that each team owner forms an expectation of this trading value that is weighted by the probability that a trade becomes the most profitable outcome, given who the potential trading partners might be. It might not be possible to form any sort of accurate expectation of the owner’s put option to trade the player over the length of the contract given the high degree of uncertainty. This could be why notrade (or partial no-trade) clauses are used to lure the free-agent player to a specific team when the player faces the same offers from competing teams otherwise.

References Pedace, R., & Hall, C. (2012). Home safe: No-trade clauses and player salaries in Major League Baseball. Industrial Relations, 51(3), 627–644. Rockerbie, D. (2009). Free agent auctions and revenue sharing: A simple exposition. Journal of Sport Management, 23(1), 87–98.

CHAPTER 5

Concluding Remarks

Abstract This chapter concludes our development of the real options approach to salary negotiations and the salary anomaly in professional sports. We begin with a simple empirical test that relates player surpluses to contract lengths and find supporting evidence. We close the book by pointing out shortcomings in our real options model that can be addressed by future research. Keywords Surplus value · Regression model · Winner’s curse

Our real options approach to player contracts is not without its shortcomings and we discuss these in this chapter. Some sports economists have questioned the use of the Scully method to estimate MRPs, instead recommending an approach that estimates a salary regression on the assumption that players are always paid their MRPs. We explain why this approach is not workable in our econometric work in Chapter 2 since it cannot estimate a player’s expected MRP over the life of a playing contract, only his actual MRP in any season of a contract, although we acknowledge that the salary regression method does have other applications in other areas.

© The Author(s) 2020 D. W. Rockerbie and S. T. Easton, Contract Options for Buyers and Sellers of Talent in Professional Sports, Palgrave Pivots in Sports Economics, https://doi.org/10.1007/978-3-030-49513-8_5

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The incorporation of real options in professional sports labor contracts has not been addressed in the sports economics literature to our knowledge. It should open up avenues for future research and we suggest a number of those here. However, we begin this concluding chapter with a simple empirical test to suggest evidence for the real options approach to player contracts.

5.1

An Empirical Test

Real options can enhance or diminish the value of multi-year free-agent contracts. It would be ideal to develop a theoretical formula to estimate the value of these options, such as the Black–Scholes model for stock options. Unfortunately, the complexity of the model prevents this. Any formula would require some expectation of what the future suitors would be willing to offer the player, the probabilities of future suitors being available, and the length of the current contract offer. Stock options pricing models work well because there are millions of traders in very atomistic markets. Free-agent contracts are determined by only two “traders,” the player and the team owner, who trade very infrequently and can form expectations with potentially large degrees of error. We offer an empirical test to lend support to our real options approach. The positive and negative surpluses that were estimated from our sample of 676 free-agent players in Chapter 2 are regressed on the number of years of the new contract for each player. Our model predicts that the longer the term of the contract for player i, years ij , the smaller the surplus, surplus ij , that is captured by the owner of team j, so we should find a negative and statistically significant association. Figure 5.1 provides a scatter plot of the estimated surplus to the team owner versus the number of years of the player contract. The plot suggests that a negative association is evident, although the discrete nature of the contract years makes the plot difficult to interpret. The regression model was estimated using a weighted least squares procedure to account for heteroskedasticity and fixed effects for each season in the sample period.1 The estimated model is summarized in Table 5.1 from the EViews output.

1 A White heteroskedasticity test rejected the null hypothesis of no heteroskedasticity at a very high level of confidence. The 2000 season is excluded as a fixed effect variable.

5

CONCLUDING REMARKS

87

10000000

Surplus ($)

5000000 0 -5000000 -10000000 -15000000 -20000000 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Years Fig. 5.1 Scatter plot of surplus to team owner versus number of years of player contract (Source Author’s creation)

The average surplus to the team owner in any season for players on single-year contracts is estimated to be $3,593,289 + −$1,335,928 = $2,257,361 holding the factors that affect team revenue and player performance constant. These one-season players do not possess any put options of value allowing the owner to extract surplus. However, the estimated model suggests significant differences between some of the seasons. For instance, the surplus to owner for the most recent season in the sample, 2012, is estimated to be ($3,593,289−$1,014,529) + −$1,335,928 = $1,242,832. Each additional contract year reduces the surplus to the owner by $1,335,928. A free agent receiving a four-year contract earns an estimated average surplus of $1,750,423 (in any season). The adjusted R-squared of 0.252 suggests that there are still other factors not accounted for in the model that are associated with the surplus to the team owner. These include intangibles, such as management skills, the ability to forecast a player’s MRP, and the cross-subsidization of team revenues from other business ventures.

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Table 5.1 Weighted least squares estimate of surplus model Coefficient

Std. Error

t-Statistic

Prob.

C(1) 3,593,289.0 490,066.5 7.332,247 0.0000 C(2) −2331936.0 632,734.1 −3.685,492 0.0002 C(3) −1,094,962.0 595,948.3 −1.837,344 0.0666 C(4) −650,155.8 621,716.6 −1.045,743 0.2961 C(5) −497,603.0 556,227.9 −0.894,603 0.3713 C(6) 397,153.1 560,413.9 0.708,678 0.4788 C(7) −657,215.5 579,989.3 −1.133,151 0.2576 C(8) −1,379,026.0 548,638.6 −2.513,542 0.0122 C(9) −2,238,597.0 613,427.7 −3.649,326 0.0003 C(10) −872,680.1 599,735.4 −1.455,109 0.1461 C(11) −760,448.5 571,347.0 −1.330,975 0.1837 C(12) −1,276,509.0 570,529.5 −2.237,411 0.0256 C(13) −1,014,529.0 564,984.1 −1.795,676 0.0730 C(14) −1,335,928.0 97,327.49 −13.72,611 0.0000 Weighted statistics R2 0.266,479 Mean dependent var 340,634.9 0.252,074 S.D. dependent var 3047954.0 Adjusted R2 S.E. of 2652258.0 Akaike info criterion 32.44,021 regression Sum squared 4.66E + 15 Schwarz criterion 32.53,374 resid Log likelihood −10,950.79 Hannan–Quinn criter. 32.47,643 F -statistic 18.49,968 Durbin–Watson stat 2.110,390 Prob(F 0.000000 Weighted mean dep. 30,307.30 statistic) Dependent Variable: SURPLUS Method: Least Squares (Gauss–Newton/Marquardt steps) Sample: 1 676 Included observations: 676 Weighting series: YEARS Weight type: Inverse variance (average scaling) SURPLUS = C(1) + C(2)∗DUMMY01 + C(3)∗DUMMY02 + C(4)∗DUMMY03 + C(5)∗DUMMY04 + C(6)∗DUMMY05 + C(7)∗DUMMY06 + C(8)*DUMMY07 + C(9)∗DUMMY08 + C(10)∗DUMMY09 + C(11)∗DUMMY10 + C(12)∗DUMMY11 + C(13)∗DUMMY12 + C(14)∗YEARS Source Author’s creation

5

5.2

CONCLUDING REMARKS

89

Extensions to the Real Options Model

The real put options held by free-agent players and team owners are easy to describe, but more difficult to model. The player’s put option is the right to move to another team after having signed a multi-year contract. Since the player gives up this right, he will demand to be compensated for the value of the option. The team owner’s put option is the right to release the player at the end of each season of the multi-year contract. The owner is giving up this right, so he or she will demand to be compensated for the value of the option. The final negotiated salary in a multi-year contract is then ideally the player’s expected MRP plus the net value of the two put options. Unfortunately, there is no reasonable calculation to determine these option values. There are simply too many unknown variables. The player must form an expectation, when negotiating the initial contract, of whom the possible suitor teams could be with attached probabilities and what their salary offers would be at the end of season of the contract. The team owner must form an expectation of the trajectory of the player’s expected MRP over the life of the contract, as well as the expected MRP in each of the possible states that could be revealed each season. In the last chapter we demonstrated, with a few stylized examples, how free-agent players and team owners can arrive at an agreed contract value that includes the net value of the real put options based on the assumption that the player and team owner can form these expectations. The real option approach deals with uncertainty by assigning probabilities to future states of the player’s performance, but it does not deal with risk. The variance of the player’s past performance could be a good measure of risk and will likely be reflected in the negotiated salary in some way. If risk changes over the life of the contract in a deterministic way, it can be modeled by adjusting the structure of the lattice to add more branches, however this though feasible will greatly increase the complexity of the calculations. It is likely that a smart team owner learns valuable information about the player over the course of the contract. This information concerns the likelihood of good or bad performance each season, the likelihood of injuries, the availability of rival suitors for the player, the availability of other free-agent players, etc. Unfortunately, the owner must form expectations for all of these factors when negotiating the initial contract. Since this future information has a value, the owner will be willing to pay for the option to obtain it, but he or she can only do that by deferring on

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the contract. This further reduces the amount the owner is willing to pay the free-agent player. The real option approach developed here does not deal with the value of future information. We assume in our model that there is no competitive bidding for the free-agent player—we consider only a single owner negotiating with the player with no concern for other bidders. In reality, owners must consider the possible offers being made by other teams, giving rise to the winner’s curse. In a sealed-bid auction (an auction in which teams cannot view each other’s bids), team owners have the incentive to “shade” their bids (increase them) in order to increase the odds of winning the auction. This is particularly evident between rival teams whose team performance greatly affects the bottom line of the other team. This could also push up the free-agent player’s salary offer in seasons where there are few other free-agent players available (Rockerbie 2009). An alternative, but perhaps, complementary argument for why star players are overpaid is that team owners treat their teams as components in a profit-maximizing portfolio of investments (Zimbalist 2011). Owners are willing to cross-subsidize losses if it increases the overall profit of the portfolio, particularly if the baseball operations are only a small portion of the overall portfolio. This might be especially true for the wealthier teams that operate in large markets. While corporate ownership of sports teams is either not allowed, or discouraged, in North American professional sports leagues, a single owner or limited liability partnership (LLC) could be wealthy enough to be a win-maximizer instead of a profit maximizer. A related concept is that team owners who are winmaximizers and face a “soft” budget constraint will overbid for players of a given quality (Andreff 2013). This results in a disequilibrium in the labor market that can persist if there are constraints on salary adjustments, such as league-imposed salary caps. It was also suggested to us that the sports labor market could be characterized by a dual labor market for quality and lesser-quality players.2 If these types of players are not substitutes, then there could be a market segmentation effect that determines a unique wage in each market. Our approach does not treat the labor market at any level of aggregation, rather it treats each player with heterogeneous skills and models the contracting process for a unique salary. Players are paid a salary based

2 We thank Wladimir Andreff for this idea.

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91

on their own MRP that might be related to some sort of market wage, but not specifically in our model. The real options model we develop in this monograph is a useful tool to explain the empirical anomaly that players are consistently overpaid or underpaid relative to their estimated MRPs. It is not the only approach, but we place less value on the alternative explanations of monopsony power for the owner or bargaining power for the player. The real options model offers an explicit description of the salary negotiation process that incorporates expectations over the life of the contract. It also explains very well why owners and players will negotiate single-year contracts instead of multi-year contracts. We see this as a valuable contribution to the sports economics literature and hope that it leads to useful extensions in the future.

References Andreff, W. (2013). Building blocks for a disequilibrium model of a European team sports league. International Journal of Sport Finance, 9, 20–38. Rockerbie, D. (2009). Strategic free agency in baseball. Journal of Sports Economics, 10(4), 278–291. Zimbalist, A. (2011). Circling the bases: Essays on the challenges and prospects of the sports industry. Philadelphia: Temple University Press.

Index

A All-American Football Conference (AAFC), 13 American Basketball Association (ABA), 14 American Football League (AFL), 13 American League (AL), 7, 18, 25, 33, 35–37, 44 Antikarov, V., 55 Arenado, Nolan, 12 Arizona Diamondbacks, 45 attendance, 2, 3, 18, 27, 33, 35, 49 average salary, 10–12, 26, 40, 42, 43, 45, 46, 48, 49, 73 Azariadis, C., 54

B Badenhausen, K., 25 Baily, M., 54 Baker, Home Run, 7 bargaining power, vi, 4–6, 25, 26, 42, 63, 91

Barry, Rick, 14 Basketball Association of America (BAA), 14 Basu, S., 54 Beckham, David, 20 Beliveau, Jean, 15 Berwanger, Jay, 13 Beta, 57, 59, 64, 66 Blue Ribbon Report, 27 Bonds, Barry, 44 Boston Red Sox, 7–9, 11 Bradbury, J.C., 24 Brown, K., 24 Brown, Kevin, 12 Bruggink, T., 24 Bryant, Kobe, 14

C California Angels, 11, 82 Campaneris, Bert, 11 Chamberlain, Wilt, 14 Champion’s League, 20

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020 D. W. Rockerbie and S. T. Easton, Contract Options for Buyers and Sellers of Talent in Professional Sports, Palgrave Pivots in Sports Economics, https://doi.org/10.1007/978-3-030-49513-8

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94

INDEX

Chicago Bears, 13 Chicago Cub, 82 Chicago White Sox, 6 Chicago White Stockings, 10 Ciecka, J., 24 Clapp, C., 27, 33 Cleveland Indians, 47, 50 Coates, D., 27, 33 Cobb, Ty, 7, 10 Cochrane, Mickey, 7 Coffin, Donald A., 27, 33 Collective Bargaining Agreement (CBA), 11 Collins, Eddie, 6 Colorado Rockies, 12 competitive balance tax, 3 compound option, 64, 74 confidence interval, 40 Copeland, T., 55 Cousy, Bob, 14

D Deadspin, 27 Dellucci, Dave, 45 Detroit Tigers, 7 DiMaggio, Joe, 9, 20 DiPietro, Rick, 15 discount factor, 55, 60 Drysdale, Don, 9 Duncan, Tim, 14 Dykes, Jimmy, 7

E Easton, S., 34, 38, 59 efficient contract, 55, 63 Efron, B., 40 Erving, Julius, 14 exploitation/exploited, vi, 17, 19, 45 exploitation rate, 43, 45, 46

F Fama, E., 57 Fernald, J., 54 Financial World, 2, 3, 25, 29 Fingers, Rollie, 11 Finley, Charlie, 11 flexibility, 54–56, 60, 63, 64, 78 Flood, Curt, 11 Florida Marlins, 47, 50 Forbes , 2, 3, 18, 25, 27, 29, 32 Fort, R., 24 FOX, 12, 44 Foxx, Jimmie, 8 free agency, 4, 5, 11, 25, 44, 78, 81 free agents, 11, 20, 24–26, 32, 37, 41–43, 45–51 French, K., 57

G Gartner, Scott Sigmund, 6 Gasol, Marc, 81 gate revenue, 3, 18 Gehrig, Lou, 8 Gifford, Frank, 13 Gilmore, Artis, 14 Gonzalez, Juan, 47, 50 Grange, Harold “Red”, 13 Grove, Lefty, 7

H Haas, Mule, 7 Haines, Michael R., 6 Hakes, J., 27, 33 Hall, C., 83 Hoon Lee, Young, 48 Hull, Bobby, 15 Humphreys, B., 26, 27, 33

I inflation, 2–4, 10, 37

INDEX

J Jackson, Reggie, 11 Jepsen, L., 24 Jones, Andruw, 47, 50 Juventus, 20

K Kahn, L., 10 Koufax, Sandy, 7, 9 Kovalchuk, Ilya, 15 Kowalewski, S., 24 Krautmann, A., vi, 24, 26, 46, 49 Kuhn, Bowie, 12

L labor contracts, 54, 55, 86 Lafleur, Guy, 15 LA Galaxy, 20 Leeds, E., 26 Leeds, M., 24 length of the contract, 43, 60, 64, 66, 82, 83 linearity, 18, 33 linear probability, 25, 30, 47, 49, 50 logistic, 18, 25, 30, 36, 47, 48, 50 Los Angeles Dodgers, 12, 47, 50, 76

M MacDonald, D., 24 Mack, Connie, 6, 8 Madden, P., 59 Major League Baseball (MLB), 2, 4–12, 16, 19, 20, 23–27, 29, 32, 33, 38–44, 46, 49, 56, 78, 81, 82 Major League Player’s Association (MLBPA), 11 Major League Soccer, 20 Marginal Resource Cost (MRC), 16, 17, 37

95

Marginal Revenue Product (MRP), vi, 4, 5, 16–20, 23–25, 27, 28, 30, 32, 36–40, 43–50, 53, 54, 56–61, 63–66, 71, 73, 74, 76–81, 83, 85, 87, 89, 91 Mays, Willie, 9, 10 McNabb, Donovan, 14 McNally, Dave, 11 mean, 40, 82, 88 Messersmith, Andy, 11 Miami Marlins, 47, 50 Mikan, George, 14 Miller, Marvin, 11 monopsony, 4, 16, 17, 20, 24–26, 37, 38, 42, 46, 51, 59, 63, 64, 91 Montreal Canadiens, 15 multi-year, 5, 8–11, 26, 36, 40, 42, 45, 47, 49–51, 56, 64, 69, 78, 81–83, 86, 89, 91 multi-year contract, 5, 8–10, 64, 69, 81, 83, 89 N Namath, Joe, 13 National Basketball Association (NBA), 3, 4, 26, 78, 81, 82 National Basketball League (NBL), 14 National Football League (NFL), 3, 4, 64, 78, 82 National Hockey League (NHL), 3, 4, 78, 82 National League (NL), 5, 6, 10, 18, 33, 35, 36, 39 New York Yankees, 7–9, 11, 12, 40, 44, 45, 76 Neymar, 20 no-trade clause, 82 O Oakland Athletics, 11 Olmstead, Alan L., 6

96

INDEX

on-base percentage, 7, 8 O’Neal, Shaquille, 14 OPS, 28, 29, 31, 35, 36, 40, 44, 45, 48 Option Value (OV), 55, 61, 63–65, 70, 72–77 Orr, Bobby, 15 Ouzanian, M., 25 P Paris-St. Germain, 20 payroll, 2, 8, 16, 33, 44, 54 Pedace, R., 83 Philadelphia Athletics, 6–8 Philadelphia Eagles, 14 present value, 25, 55, 57–59, 61–63, 65, 74, 78 productivity, 54, 56, 63, 64, 66 Pujols, Albert, 39 put option, 60, 61, 63–66, 74, 75, 77, 78, 83, 89 Pyun, H., 26 R Ramirez, Manny, 47, 50 real options, 5, 46, 54–57, 69, 85, 86, 89, 91 real options model, 5, 57, 89, 91 reserve clause, 4–7, 10, 11, 16, 19, 20, 23 revenue function, 16–18, 25, 27, 28, 32, 34, 48 revenue sharing, v, 3, 18, 32 Reyes, Jose, 47, 50 Reynolds, M., 24, 37 Richard, Maurice, 15 risk, v, 10, 54, 55, 57–61, 63, 64, 66, 89 risk-averse, 54, 61 risk-free, 57–59, 61, 64, 66 risk-neutral, 54

Rockerbie, D., 18, 20, 34, 38, 59, 81, 90 Rodriguez, Alex, 12, 40, 44 Rodriguez, Ivan, 47, 50 Romer, D., 54 Ronaldo, Christiano, 20 Rose, D., 24 Rosen, S., 25, 46 Rudanko, L., 54 Rudi, Joe, 11 10 and 5 rule, 11, 82 Ruppert, Jacob, 9 Russell, Bill, 14 Ruth, Babe, 7, 8, 10, 20 S salary cap, 3, 6, 82 Sanderson, A., 25 San Diego Padres, 11, 56 San Francisco Giants, 9, 44 Santo, Ron, 82 Scully, G., 4, 5, 16, 18, 19, 23, 24, 27, 29, 31, 33, 37, 47, 49, 85 separation theorem, 59 Simmons, Al, 7 Simpson, O.J., 14 slugging average, 9, 18, 19, 29 slugging percentage, 7, 8, 19, 28, 50 Solow, J., 26, 46 Spalding, Albert, 10 St. Louis Cardinals, 39 strikeout to walk, 18, 19, 29 supply elasticity, 37–39, 45, 46, 59 surplus, 4, 6, 17, 20, 24, 26, 38, 40, 41, 43, 45, 46, 50, 53, 59, 86–88 Sutch, Richard, 6 Szymanski, S., 59 T TBS, 12

INDEX

team budget, 38, 59 team revenue, 2, 17–19, 28, 33, 39, 48, 87 team values, 3 Texas Rangers, 11, 12, 40, 44, 45, 47, 50 Thompson, David, 14 ticket price, 18, 27, 29, 35, 49 Trout, Mike, 12 U uncertainty, 40, 54, 55, 60, 70, 73, 74, 78, 83, 89 Unitas, Johnny, 13 V variance, 40, 64, 66, 88, 89 Vida Blue, 11

97

von Allmen, P., 26 W Webber, Chris, 14 Williams, Bernie, 40 Williams, Ted, 9, 10, 20 winner’s curse, 20, 90 winning percentage, 16, 18, 19, 25, 27–30, 32, 33, 35, 36, 44, 47–49 World Hockey Association (WHA), 15 Wright, Gavin, 6 Y Yamaguchi, S., 55 Z Zimbalist, A., 24, 25, 32, 37, 38, 90