Sportsman Leagues
| Date | 01 February 2015 |
| Published date | 01 February 2015 |
| Author | John Vrooman |
| DOI | http://doi.org/10.1111/sjpe.12066 |
SPORTSMAN LEAGUES
John Vrooman*
ABSTRACT
This paper compares duopsony profit-maximization and sportsman leagues and
analyzes the effects of revenue sharing in both leagues. This involves formulation
of a duopsony model that compares game-theoretic approaches and price-taking
models. This duopsony game is played in open and closed talent markets with a
supply function that approaches perfect inelasticity in the limit. The analysis
explores welfare optimality of competitive balance, fan preference and revenue
sharing. Revenue sharing minimizes payrolls and reduces overall talent in profit-
max leagues. This leads to the conclusion that a sportsman league with optimal
revenue sharing is welfare superior.
The goal is to win. It’s not about making money.
—Roman Abramovich, owner Chelsea FC
II
NTRODUCTION
According to received theory, the perfect game is a symbiotic contest between
equally matched opponents. The practical economic problem is that profes-
sional sports leagues form imperfectly competitive natural cartels where games
are played between teams with asymmetric market power. The natural duality
of sports leagues implies that dominant teams may only be as strong as their
weakest opponents and that competitive balance is welfare superior. The suc-
cess of unbalanced leagues throughout Europe that are perennially dominated
by a few powerful clubs raises the empirical question that optimal competitive
balance may obtain at less than absolute equality of teams.
The economics of sports has been preoccupied with two empirical proposi-
tions that have been deemed to be true a priori (Rottenberg, 1956). The first
truth is the invariance proposition that free agency for baseball players would
yield the same talent distribution as the reserve (transfer) system that bound a
player to one team for life. The revenue-sharing paradox holds that revenue
sharing among asymmetric clubs has no effect on talent distribution among
teams and that it serves only to deepen player exploitation.
1
*Vanderbilt University
1
“A market in which freedom is limited by a reserve rule such as that which now governs
the baseball players labor market distributes players among about as a free market would”
(Rottenberg, 1956, p. 255).
Scottish Journal of Political Economy, DOI: 10.1111/sjpe.12066, Vol. 62, No. 1, February 2015
©2015 Scottish Economic Society.
90
In theory, the most efficient way to defeat a large-market club is to increase
product market competition by addingteams to monopoly markets. Anotherway
is for the large-market clubs to internalize diseconomies of their dominance.
According to the Yankeeparadox fans prefer winning closecontests and therefore
large-market dominance could be self-defeating.
2
The Yankee paradox rests on
the second assumed truth that fans prefer balanced competition, when they may
in fact prefer perennially dominant clubs. In reality there a several ways to defeat
large-market clubs, including the possibility that club owners could be sportsmen
whose ultimate goalis to win, rather than maximizing profit.
3
The revenue-sharing paradox was formalized in two adaptations of sports lea-
gue theory to the changing American sport-scape (Fort and Quirk, 1995; Vroo-
man, 1995) (QFV). European theorists (Szymanski, 2004; Szymanski and
Kesenne, 2004) (SK) used a contest success function (CSF) to show that the
invariance proposition does not hold in the open markets of European football,
and that revenue sharing leads to less competitive balance. The distinction
between open and closed markets may not make any difference, because both
models assume that club owners maximize profits. It is possible that owners are
utility maximizing sportsmen who sacrifice profit in order to win.
In his 1971 article celebrated in this Journal, Sloane observed that, “Rotten-
berg’s argument rests on his assumption that teams are profit maximisers.
However, if the clubs are utility maximizers, this (Coasian) result may not fol-
low and star players will not be equally distributed between teams (Sloane,
1971, p. 138). Following a classic argument by Scitovszky (1943), Vrooman
(1997, 2000) formalizes the sportsman proposition:
The optimization problem facing the sportsman owner concerns
the joint maximization of franchise value and the satisfaction
derived from winning. The sportsman owner sacrifices franchise
value for winning and expands the talent of his club beyond its
value maximum. The resulting undervaluation of the franchise
is the sportsman effect (1997a, p. 596).
In the limit, sportsman owners become win-maximizers, who are only con-
strained by zero profit. Win-max leagues are less balanced than profit-max
leagues and revenue sharing increases competitive balance (K
esenne, 1996;
Vrooman, 2007, 2009).
Following QFV the basic sports-league model generally assumes a two-team
league where owners are seen as monopolists in product markets, but then
2
Also called uncertainty of outcome hypothesis: “No team can be successful unless its com-
petitors also survive and prosper. Two teams opposing each other in play are like two firms
producing a single product” (Rottenberg, 1956, p. 254).Glasgow rivals Celtic and Rangers
are collectively called the “Old Firm”.
3
Rottenberg anticipated the sportsman effect. “Let franchises be distributed so that the
size of the product market is equal for all teams (6 teams in New York, 3 in Chicago). If
attendance is a unique function of the size of the market then such a distribution of teams
may equalize revenues among teams. But attendance is a function of several variables. If the
psychic income is not zero for all team owners or if it is not zero for all owners differences in
revenues will still occur” (Rottenberg, 1956, p. 257–258, italics added).
SPORTSMAN LEAGUES 91
Scottish Journal of Political Economy
©2015 Scottish Economic Society
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