Leveling the playing field or just lowering salaries? The effects of redistribution in baseball.

1. Introduction

The structure of Major League Baseball (MLB) is commonly seen as evolving into a league of haves and have-nots. On one end of the spectrum, we find a few large-market teams whose vast revenues allow them to accumulate the best talent and deepest benches. At the other end of the spectrum, we find a number of struggling teams whose ability to field a competitive team seemingly is hampered by the ability of their market to generate a sufficient level of revenue.

Critics charge that this imbalance in revenue potential is leading to a domination of the sport by the large-market teams. These concerns led Commissioner of Baseball Bud Selig to convene a panel during the 1990s to investigate the long-term state of competitive balance. (1) The Blue Ribbon Panel concluded that the disparity in revenues among clubs was growing, eroding the ability of small-market teams to effectively compete with large-market teams. (2) In spite of the league's repeated attempts to shift resources from rich teams to poor teams, the Blue Ribbon Panel ultimately charged that redistributive efforts to date had failed miserably in achieving the goals of moderating payroll disparities and improving competitive balance.

Currently, the league is involved in a number of different programs intended to promote competitive balance. Although national broadcasting revenues have long been shared equally among teams, disparities in local broadcast revenues have become one of the primary sources of inequities across market sizes. Prior to the 1995 Collective Bargaining Agreement (CBA), however, only a small part of local revenues were shared across teams. Revenue sharing was limited to gate revenues, with the American League following what was known as the "80/20 Plan" under which 20% of gate revenues were shared across teams, and the National League sharing only 5% of gate revenues. The 1995 agreement resulted in 17% of all local revenues being shared including, for the first time, local broadcasting revenues. The 2002 CBA increased the sharing of local revenues to 34%, and added a luxury tax for teams whose payrolls exceeded a specified threshold. Not surprisingly, the owners of the large-market teams are unhappy with these cross-subsidies and have tried to relocate, or even eliminate, some of the lower-revenue teams.

To successfully address the problem of imbalance in the league, redistribution must affect teams' marginal revenue functions. It is well known that the extent to which such redistribution equalizes competitive balance depends on whether the effect disproportionately lowers the marginal revenue of large market teams. Previous theoretical work has also shown that redistributing revenues from rich to poor teams will lower the marginal value of winning of all teams, thus reducing the payments to labor (Fort 2003). It is hardly surprising, then, that efforts to equalize league balance have been opposed by the players' union.

Different revenue sources are likely to respond differently to current and lagged winning percentages. While a team's share of the league's national television revenues is not sensitive to its performance, gate receipts and concessions are likely quite responsive to both current and lagged winning percentages. Local television and radio revenues can be expected to respond to lagged performance, and will respond to current performance if the number of games that are televised depends on performance or if payments are linked to ratings.

From a theoretical perspective, it remains an open question whether and which kind of redistribution improves competitive balance. While Quirk and El-Hodiri (1974), Fort and Quirk (1995), Vrooman (1995), Kesenne (2000), and Fort (2003) provide models in which gate revenue sharing has no effect on competitive balance (the so-called 'invariance principle'), Fort and Quirk (1995) showed that sharing local television revenues can improve competitive balance, while Kesenne (2000) showed that gate sharing can lead to more balance if owners are win-maximizers. Modeling a sports league as a non-cooperative game, Szymanski and Kesenne (2004) showed that league balance can suffer when gate revenue sharing is imposed. Hence, it remains an empirical question whether the net effects of such programs have had the intended results. Has league balance been enhanced or damaged by the complex mixture of existing programs? And if there is little impact on competitive balance, then the players' union would be right to see redistribution as just an attempt at lowering player salaries.

In this paper we provide an empirical assessment of whether redistributive efforts by MLB are likely to have succeeded in reallocating talent to less advantaged teams by estimating the effect of redistribution on the marginal revenue functions of small- and large-market teams. Data availability limits our analysis to the period between 1996 and 2001, when revenue sharing was expanded to include a portion of all local revenues, but before the luxury tax was instituted. Expanding the analysis to address the effects of the luxury tax will have to be left to future research, if and when post-2002 revenue data become available.

2. Theoretical Framework

Since the allocation of playing talent ultimately depends on the intensity of demand, we begin our analysis by looking at the demand for player talent. A team's demand for talent is its marginal revenue product, derived from its marginal revenue (MR) and the marginal product of players (MP). Most analysts believe that teams in big cities have an advantage over their small-city counterparts in that their marginal revenue, and hence demand for talent, is larger (Scully 1989; Burger and Walters 2003; Solow and Johnson 2004). As such, the dominance of the sport by the large-market teams is a free-market outcome ultimately explained by the greater value of a win in these cities.

While the market allocation of talent may be optimal from the perspective of any one team, it ignores the externality associated with the overall well-being of the league. First introduced by Rottenberg (1956), the uncertainty of outcome hypothesis maintains that fans prefer sports events in which the final outcome is exciting because of its uncertainty (see also Sloane 1971 and Cairns 1987). If large-market teams acquire the strongest rosters and deepest benches, then match-ups with small-market (and less talented) teams could have an adverse effect on the demand for the league as a whole.

To illustrate the effect of redistribution on the allocation of playing talent, assume the supply of talent is fixed, that teams are profit maximizers, and that the league consists of one large-market (L) and one small-market (S) team. This approach was pioneered by Fort and Quirk (1995) and has become one of the standard models used to study competitive balance. The distribution of winning percent (W) between the two teams is determined, with the large-market team's winning percent ([W.sub.L]) plotted on the horizontal axis (hence, [W.sub.s] is [1- [W.sub.L]]). Given this normalization assumption, each team's demand for talent is determined by its marginal revenue functions. As is common in this type of model, assume that the marginal revenue function of L is greater than that of S. (3) Under profit maximization, the market allocation of talent (without redistribution) occurs at the intersection of the two marginal revenue functions, where each is equal to the price of a unit of talent, [P.sub.T]. Given that [MR.sub.L] > [MR.sub.S], this allocation results in the large-market team winning more games than the small-market team (i.e., the equilibrium winning percent of the large-market team is greater than 50%).

If the league values competitive balance and we assume that the equilibrium distribution of wins is widely perceived as unacceptable, then this market mechanism must be overridden. But simply transferring revenues from large-market to small-market teams will not achieve this goal; the teams' marginal revenue functions must be changed to have an effect on the allocation of talent. It has been argued elsewhere that redistribution programs ultimately reduce the marginal value of a win because the amount taxed away from each team does not equal the amount returned to that team (Fort and Quirk 1995; Fort 2003). For example, consider how the current revenue-sharing program in MLB affects teams' marginal revenue functions. This agreement takes 17% of each team's local revenues, then returns an equal share (i.e., 1/30) back to each team. While winning an extra game adds to local revenues, some of this extra revenue is taxed away, meaning that the marginal value of a win net of redistribution payments will be smaller than that which ignores such payments.