The Run to the Pennant: A Multiple Equilibria Approach to Professional Sports Leagues

77 Pages·2014·3.186 MB·English

by  Duane W Rockerbie, Stephen T Easton (auth.)

Sports Economics, Management and Policy
Series Editor: Dennis Coates
Duane W. Rockerbie
Stephen T. Easton
The Run to the
Pennant
A Multiple Equilibria Approach to
Professional Sports Leagues
Sports Economics, Management and Policy
Series Editor
Dennis Coates
For further volumes:
http://www.springer.com/series/8343
http://avaxhome.ws/blogs/ChrisRedfield
Duane W. Rockerbie · Stephen T. Easton
The Run to the Pennant
A Multiple Equilibria Approach to
Professional Sports Leagues
1 3
Duane W. Rockerbie Stephen T. Easton
Department of Economics Department of Economics
University of Lethbridge Simon Fraser University
Lethbridge, AB Burnaby, BC
Canada Canada
ISSN 2191-298X ISSN 2191-2998 (electronic)
ISBN 978-1-4614-7884-3 ISBN 978-1-4614-7885-0 (eBook)
DOI 10.1007/978-1-4614-7885-0
Springer New York Heidelberg Dordrecht London
Library of Congress Control Number: 2013941543
© Springer Science+Business Media New York 2014
This work is subject to copyright. All rights are reserved 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. Exempted from this legal reservation are brief excerpts
in connection with reviews or scholarly analysis or material supplied specifically for the purpose of
being entered and executed on a computer system, for exclusive use by the purchaser of the work.
Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright
Law of the Publisher’s location, in its current version, and permission for use must always be obtained
from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance
Center. Violations are liable to prosecution under the respective Copyright Law.
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.
While the advice and information in this book are believed to be true and accurate at the date of
publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for
any errors or omissions that may be made. The publisher makes no warranty, express or implied, with
respect to the material contained herein.
Printed on acid-free paper
Springer is part of Springer Science+Business Media (www.springer.com)
Contents
1 Introducing Unsustainable Runs ............................... 1
1.1 Introduction ............................................ 1
1.2 Unsustainable Runs in Sports Leagues: Some Examples ......... 2
1.2.1 The 2008–2011 Tampa Bay Rays (MLB) ............... 3
1.2.2 The 1997 and 2003 Florida Marlins (MLB) .............. 4
1.2.3 The 1992–1993 Toronto Blue Jays (MLB) .............. 5
1.2.4 Leeds United 1999–2004, Portsmouth
FC 2002–2009 (English Premier League) ............... 6
1.3 The Rest of the Book ..................................... 8
2 Casual Evidence of Unsustainable Runs ......................... 9
2.1 Cyclical Winning Percentages .............................. 9
2.2 Time-Series Evidence ..................................... 14
3 A Model of a Professional Sports League ........................ 21
3.1 The Standard Model: A Profit Maximizer ..................... 21
3.2 The Impossibility of Multiple Equilibria in the Standard Model .... 23
3.3 The Standard Model: A Win Maximizer ...................... 25
3.4 The Standard Model: A Utility Maximizer .................... 27
4 A Professional League Model with Unsustainable Runs ............ 29
4.1 Introduction ............................................ 29
4.2 Setup of the Model ....................................... 30
4.3 Solving the Model ....................................... 32
4.4 Moving Between Equilibria ................................ 34
4.5 Simulating the Model ..................................... 36
5 Unsustainable Runs with Revenue Sharing and Salary Caps ........ 43
5.1 Introduction ............................................ 43
5.2 Revenue Sharing Mechanics ............................... 44
5.3 Revenue Sharing and Unsustainable Runs in Theory ............ 45
5.4 Salary Cap Mechanics .................................... 47
5.5 Salary Caps and Unsustainable Runs in Theory ................ 50
v
vi Contents
6 Some Empirical Testing ...................................... 53
6.1 Introduction ............................................ 53
6.2 Tests for Speculative Bubbles .............................. 53
6.3 Estimating Structural Parameters in the Presence
of Multiple Equilibria ..................................... 55
6.4 Looking for Excess Unpredictability ......................... 55
6.5 Examining Payrolls ...................................... 60
6.6 Non-linear Effects in Revenues ............................. 63
6.7 Summing Up ........................................... 65
7 Concluding Remarks ........................................ 67
References .................................................... 71
Index ......................................................... 75
Chapter 1
Introducing Unsustainable Runs
1.1 Introduction
For many economists, the professional sports industry provides a rich source of
data to test various hypotheses suggested by microeconomic theory. The standard
classroom lessons that preach that labor is paid according to its contribution to
revenue for the employer (wage marginal revenue product), profit-maximizing
=
firms set their product prices in the elastic region of the demand curve or that
monopolists inflict welfare losses on consumers, lend themselves to empirical test-
ing in the professional sports industry due to the availability of data. Many “sports
economists” get their first exposure to the literature by finding interesting data
that would be difficult or even impossible to obtain for any other industry. In what
other industry are the outcomes as meticulously scrutinized and the inputs moni-
tored by constant public debate?
Although as diverse as any field in economics, the literature of the economics
of sport has several important questions that seem to dominate research output.
Are professional athletes paid according to the marginal revenue product rule? Do
monopsonistic leagues insure that players are underpaid? Do league policies, such
as revenue sharing, affect league parity and if so, how? Our purpose in this book is
to introduce a new question with the hope that it will spur further research interest
and carve out its own niche in this literature. Many of the important questions that
have dominated the sports economics literature can be grouped into labor market
issues, competition policy, and strategic behavior. The topic of this book bridges
all of these categories and yet does not fit well into any one of them.
Our purpose in this book is to construct a simple model of a professional
sports league that can display “unsustainable runs” resulting from the pres-
ence of multiple equilibria. An unsustainable run is a term we invent and define:
it is a rapid improvement in a clubs performance on the field, ice, or court that
requires implausibly large shifts in exogenous variables or parameters to fit tradi-
tional notions of profit-maximizing behavior. The club acquires expensive talent,
improves its performance, and perhaps even wins a championship, only to learn
D. W. Rockerbie and S. T. Easton, The Run to the Pennant, 1
Sports Economics, Management and Policy, DOI: 10.1007/978-1-4614-7885-0_1,
© Springer Science+Business Media New York 2014
2 1 Introducing Unsustainable Runs
that the higher stock of talent cannot be maintained given the lackluster perfor-
mance at the gate. The club then divests itself of its talent and returns to medioc-
rity. As we shall show in Chap. 3, an unsustainable run cannot occur in what is
known as the standard model of a professional sports league, yet these phenomena
are frequent as we shall demonstrate with some spectacular examples.
1.2 Unsustainable Runs in Sports Leagues: Some Examples
To develop a profit-maximizing model of a professional sports league that can
generate unsustainable runs is not hard, but it requires borrowing ideas from other
more traditional economic fields. The model we develop in this book relies on the
existence of more than one league equilibrium, an equilibrium defined as a set of
winning percentages that allow each club owner to maximize his or her profit. An
unsustainable run is characterized as a move from one equilibrium to another. As
we will show, this fits into the standard model of the professional sports league
with some modifications.
The rational expectations models used in macroeconomics and finance can gen-
erate so-called sunspot equilibria in macroeconomic aggregates and asset prices
that differ from their fundamental values for a period of time, only to return to
their fundamental values when the sunspot disappears. Azariadis (1981) and
Obstfeld (1984) provide good examples of these models. Rational expectations
models are difficult, but generally require that the current state of a variable be
partly determined by the conditional expectation of its future state. Agents can
then interpret any information as being relevant in determining the current state
even if the information is not (like a sunspot).
Models that generate multiple equilibria also have a long history in interna-
tional trade and development economics. “Marshall’s string tie” relating foreign
and domestic offer curves in the trade literature describes a stable equilibrium
flanked by unstable equilibria leading to one characterization of stability relating
to the sum of the two countries’ elasticities of import demand (Caves, Frankel and
Jones (2007)).
Early contributions in development economics include Rosenstein-Rodan (1943)
and Myrdal (1957). More recent contributions include Azaraidis (1996); Graham
and Temple (2006); Karayalcin and Mitra (1999); and Matsuyama (1991). All of
these papers develop models that rely on a “variable returns to scale” (VRS) pro-
duction technology at the industry- or economy-wide level. Firms produce output
with constant returns to scale, but total industry output is produced with increasing
returns to scale. This difference occurs due to “spillover effects” where an increase
in the amount of factors used by one rfi m increases output for the other rfi ms in
the industry; however, no single rfi m is able to capture this externality. If rfi ms (or
countries) could coordinate their actions, this externality could be internalized; how-
ever, since they cannot, these are often referred to as “coordination failure” models
(Cooper and John (1988)). The result is that factor demands at the industry level can
1.2 Unsustainable Runs in Sports Leagues 3
be upward sloping, resulting in the possibility of multiple equilibria. The emphasis
in the literature has been to determine the conditions under which VRS can occur,
the conditions under which multiple equilibria can occur given the presence of
VRS, and how industries and economies move from one equilibrium to another.
Professional sports leagues are natural candidates for spillover effects. Under
the Sports Broadcasting Act of 1961, the National Football League (NFL) was
allowed to negotiate television rights as a single entity, rather than have each
club negotiate its own rights. This monopoly bargaining power was subsequently
assumed by the other North American professional sports leagues. Individual clubs
are still able to negotiate their own local television broadcast rights. The current
annual national broadcast revenues are substantial: $2.9 billion for the NFL, $925
million for the National Basketball Association (NBA), $386 million for major
league baseball (MLB), and $200 million for the National Hockey League (NHL).
These revenues are split equally among the member clubs regardless of individual
needs or performance. When one club increases its stock of talent without affect-
ing any other club’s stock of talent, the league stock of talent will increase. If it is
the case that national revenues are at least partly determined by the league stock of
talent, all clubs will benefit and a spillover effect is present.
Unsustainable runs are a noticeable but not necessarily frequent occurrence in
professional sports leagues. We offer a sample of historical episodes below. None
of the examples come from the NFL and probably none ever will. The NFL and
some other leagues use a hard salary cap that can short-circuit unsustainable runs,
at least in theory. A zealous owner who wishes to improve his or her club cannot
acquire additional talent if the club payroll will exceed the salary cap. Of course
some salary caps are harder than others. The soft salary cap system used by the
NBA has many exemptions so that clubs may exceed the salary cap, making the
cap quite ineffective. Even in the hard-capped NFL, the highest payroll club in
2011 exceeded the lowest payroll club by approximately $30 million.1 Without
any salary cap system, MLB exhibits interesting episodes of unsustainable runs.
1.2.1 The 2008–2011 Tampa Bay Rays (MLB)
“When I came in here in 2005 and 2006, I saw the stars, and I was confident that we
could put a winning product on the field—and I was told by you guys and others that all
we needed was a winning team.” “Well, we won. We won. We won. And we won. And it
didn’t do it.”
Stuart Sternberg, owner of the Tampa Bay Rays, 2011
Major league baseball’s Tampa Bay Rays were the poster-boy example for a
speculative run. Stuart Sternberg purchased the club in 2004 for $200 million and
inherited a 2005 player payroll of only $37 million, the lowest in baseball. The club
1 http://www.osmguy.com/2011/12/2011-nfl-payrolls-by-team/.
4 1 Introducing Unsustainable Runs
Table 1.1 Financial data for the Tampa Bay Rays
Revenues Profit Franchise value MLB Average Rays
($ millions) ($ millions) ($millions) revenue revenue/MLB
($ millions) average revenue
2010 166 6.8 331 205 0.81
2009 156 15.7 316 197 0.79
2008 160 29.4 320 194 0.83
2007 138 29.7 290 183 0.75
2006 134 20.2 267 170 0.79
2005 116 20.3 209 158 0.74
Source Forbes magazine, business of baseball, various issues
won only 67, 61, and 66 games (out of 162 games) over the 2005–2007 seasons.
Despite this poor showing on the efi ld, revenues and protfis remained stable and
acceptable relative to the major league average. Table 1.1 above summarizes the
nfi ancial numbers for the 2005–2010 seasons. These are estimates as MLB clubs
are not required to report annual nfi ancial statements to the public; however, the reli-
ability of the estimated revenues is quite high based on tests in Rockerbie (2012).
Sternberg made signicfi ant investments in talent for the start of the 2007 season and
the payroll jumped to $57 million. The results began to show in the 2008 season when
the club won 97 games, clinching the Eastern Division pennant but losing the World
Series in 5 games. Unfortunately, the tremendous success did not translate into fan
interest and the club experienced only a modest improvement in revenue for 2008, but
did move up somewhat compared to the MLB average revenue. The Rays made the
play-offs again in the 2010 and 2011 seasons with the payroll reaching $80 million in
2010. But revenues did not keep up and protfis shrank to levels below the 2005 season
(it is quite likely that the Rays benetfied from baseball’s revenue sharing agreement
much more in 2005 than in 2010). By the end of the 2011 season, Sternberg gave in
and cut the Rays payroll to $40 million. As yet, it remains to be seen how the Rays
will perform in the 2013 season, but expectations are not high and the club is frus-
trated with the city of Tampa in negotiating a new stadium to be constructed for the
Rays. The Rays nfi ished a respectable third place (out of vfi e clubs) in the American
League East in 2012, missing the play-offs. The Rays payroll at the start of the 2013
season dropped again to $57.5 million (26th in MLB) with the loss of stars James
Shields and Wade Davis to the Kansas City Royals. The Toronto Blue Jays upped their
payroll from $75 million in the 2012 season (23rd in MLB) to $115 million for the
2013 season (11th in MLB) and could be a candidate for an unsustainable run.
1.2.2 The 1997 and 2003 Florida Marlins (MLB)
The major league baseball Florida Marlins made a run to the play-offs in 1997
and won the World Series. The Marlins had never enjoyed success on the field or
at the gate before 1997, yet the owner, H. Wayne Huizenga, thought it profitable