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

Krautmann, Anthony C.

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.

Given that each team's marginal revenue function is decreased as a result of the redistribution program, the remaining question is whether the net result on the allocation of talent is in the intended direction of greater competitive balance (i.e., towards small-market teams and away from large-market teams). For example, consider the case where both teams' marginal revenues fall by an identical amount. In this case, the allocation of talent is unaffected by the program and the only effect is the reduction of the equilibrium price of talent (i.e., [P'.sub.T] < [P.sub.T]). Such a case is illustrated in Figure 1. Of course, if redistribution has a greater impact on the marginal revenue of the large-market team, then the league will become more balanced. Conversely, if the program disproportionately affects the marginal revenue of the small-market team, then balance will suffer. (4) In all cases, however, the effect of redistribution on players' salaries is unambiguously negative.

[FIGURE 1 OMITTED]

3. Empirical Model

Whether or not the net effect of the complicated mixture of redistributive programs disproportionately lowers the marginal revenue functions of large-market teams is ultimately an empirical issue. To answer this question, we calculate teams' marginal revenue with and without the effects of redistribution. By separating teams on the basis of market size, we can then investigate whether these efforts are helpful or harmful to competitive balance. Our analysis is possible because the Blue Ribbon Panel provides measures of a team's revenues both with and without redistributive payments. In the Blue Ribbon Panel's terminology, a team's "total revenues" include the payments received from (or paid to) other teams, while its "local revenues" do not include these payments. (5) To avoid confusion with the total revenue/ marginal revenue distinction, as well as to emphasize that the difference involves redistribution and not merely where the revenues are earned, we will refer to these as net revenues (i.e., after redistribution) and gross revenues (i.e., before redistribution), respectively. Estimates of marginal revenue derived from each type of revenue provide a natural mechanism for investigating the impact of redistributive efforts on a team's demand for talent. The sample we use for this estimation involves a collection of team-specific data coming from the 1996 to 2001 seasons. Table 1 contains the descriptive statistics of this data.

To produce marginal revenue functions like those depicted in Figure 1, we need to estimate revenue functions that allow for marginal revenue to be a positive, yet decreasing function, of winning percentage (W). Because our data set gives us a considerable amount of cross-sectional variation across teams but little time-series variation for each team, we consider a model in which the effect of winning percentage on revenue is the same across teams. For simplicity, we assume a quadratic functional form that gives rise to linear marginal revenue functions. Since performance in the prior season often has a lasting effect on a team's revenues, we also include the lagged values of W in the model. Both metropolitan population (POP) and per capita income (INC) are interacted with winning percent so that variations in income and population can affect the team-specific intercepts of the marginal revenue functions. We use stadium age (STDAGE) to measure the effect of new stadiums on revenues, and allow for a diminishing effect by including age both linearly and quadratically. Finally, the model includes a trend variable (TREND), as well as a dummy variable (TWOTEAM) to control for the presence of two major league teams in the same city. (6)

An important factor that needs to be addressed is how a team's revenues are affected when the team reaches the post-season playoffs. There are two possible routes by which this effect could occur. Burger and Walters (2003) attribute the extra revenue of a playoff-contending team to so-called "bandwagon" fans who only attend games if their teams are likely to reach the post-season. But a team that reaches the playoffs also has increased revenues for the simple reason that it plays additional games. These additional playoff games must be accounted for since the revenues reported by the Blue Ribbon Panel include gate receipts from both regular season and postseason games. Sorting out these effects is potentially difficult; we suspect that the bandwagon effect that Burger and Walters modeled is confounded with the positive impact on revenues of playing extra games in the playoffs. To deal with this issue, we ignore the possibility of a bandwagon effect and simply divide revenues by the total number of games (G) played, both during the regular season and in the playoffs, making our dependent variable revenues per game.

Thus, the model we estimate is given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (13)

We expect the signs on the coefficients to be positive for [[beta].sub.1], [[beta].sub.2], [[beta].sub.3], c, [[beta].sub.5], [[delta.sub.2], and [[delta].sub.3] and negative for [[beta].sub.2], [[delta].sub.1] and [[delta].sub.4]. Because winning percentage is included with a lag, the present value of the marginal revenue per game from a change in winning percentage in year t is given by

[MR.sub.it] = [[beta].sub.1] + 2[[beta].sub.2] [W.sub.it] + [[beta].sub.3]/(1 + r) + [[beta].sub.4] [POP.sub.it] + [[beta].sub.5] [INC.sub.it], (2)

where r is the real interest rate used for discounting. (7) To measure the effect of a change in winning percentage on revenues over the entire season, one would need to multiply [MR.sub.it] by the number of games played.

To evaluate the effect that redistribution efforts have on league balance, we use our estimates of Equation 1 to compare the predicted equilibrium after redistribution with the predicted equilibrium in the absence of redistribution. Given the specification above, each team's marginal revenue function can be written as [MR.sub.i]t = [a.sub.it] - b[w.sub.it], where from Equation 2, [a.sub.it] = [[beta].sub.1] + [[beta].sub.3]/(1 + r) + [[beta].sub.4] [POP.sub.i]t + [[beta].sub.5] [INC.sub.it] and b = -2 [beta].sub.2]. Equilibrium in year t requires that [MR.sub.it] = [k.sub.t] for all i, so in equilibrium,

[W.sup.*.sub.it] = ([a.sub.it] - [k.sub.t])/b. (3)

Summing across all N teams yields [N.summation over (i=1]) [W.sup.*.sub.it] = 1/b [N.summation over (i=1)] [a.sub.it] - [Nk.sub.t]/b.

However, the sum of the winning percentages of an N team league is always equal to N/2, so combining and solving for k gives

[k.sub.t] = [[bar.a].sub.t] - b/2, (4)

where [[bar.a].sub.t] is the average of the [[alpha].sub.it]. It follows from Equations 3 and 4 that the equilibrium winning percentage for team i in year t is

[W.sup.*.sub.it] = 1/2 + [a.sub.it] - [[bar.a].sub.t]/b.

Equation 5 expresses the intuitive result that a team's equilibrium winning percentage will exceed 0.500 by an amount that depends on how much the intercept of their marginal revenue function exceeds the average marginal revenue intercept for the league as a whole.

Taking the estimates from Equation 1 using gross revenues then gives us the equilibrium winning percentage of each team under the counterfactual without redistribution. A similar calculation using net revenues gives us the equilibrium winning percentage when the redistribution programs of the late 1990s are imposed. If redistribution has the intended effect, then we would expect the winning percentages of large-market teams to fall and those of small-market teams to rise.

4. Empirical Results

Table 2 contains the Ordinary Least Squares (OLS) estimates of Equation 1 for both gross and net revenues per game. All of the coefficients are significant and have the expected signs. For example, our estimates are consistent with diminishing returns in terms of both winning percent as well as the age of the stadium. (8) The positive coefficients on both (W) x (POP) and (W) x (INC) imply that MR rises with either measure of market size. Finally, the negative coefficient on TWOTEAMS suggests that when there are two MLB teams in a city, there are fewer fans available to support each team.

Of immediate interest here is the change in MR across market sizes. In Table 3 we present estimates of teams' MRs at different winning percentages and market sizes, where we have focused attention on four market sizes corresponding to the smallest, largest, smallest 25th percentile, and largest 25th percentile. Figure 2 illustrates this information graphically. As expected, we find that the MR with redistribution is less than the MR without redistribution for all market sizes. This is, to our knowledge, the first empirical verification that the redistribution efforts instituted by MLB adversely affects teams' MR functions.

[FIGURE 2 OMITTED]

Table 4 presents the predicted equilibrium winning percentages from Equation 5, based on the regression estimates from gross revenues in column 1 and net revenues in column 2; column 4 presents each team's actual winning percentages. (9) Comparing the two values of [W.sup.*] in columns 1 and 2, it is clear that the redistribution program in place in MLB during this period had no discernable effect on league balance (see column 3). Since winning one extra game adds approximately six points (0.006) to winning percentage, the only teams whose records were affected by even one-half of a game were the two teams in New York and in San Francisco.

Our model does a reasonably good job of predicting the actual performance of MLB teams during the 1996 to 2001 period (see column 5). Of the 26 teams in our sample, we predict the average performance of 12 teams within five games, and only a handful are under-predicted (5) or over-predicted (3) by 10 games or more. However, some of the under-predictions (Atlanta, Cleveland) and over-predictions (Los Angeles Angels, New York Mets) are quite large.

Since the equilibrium price of a unit of talent should equal its marginal revenue product, a reduction in the equilibrium value of marginal revenue caused by redistribution will lead to an equal proportional reduction in salaries. Using Equation 4, we can also estimate the effect that redistribution had on equilibrium salaries during the 1996--2001 period. Using average values of income and population over the time period to calculate an [[alpha].sub.i] for each team both before and after redistribution and then averaging across teams, we estimate that salaries were approximately 22% lower than they otherwise would have been as a result of that redistribution.

5. Concluding Remarks

Struggling to contend with the growing divergence in local revenues generated by teams from differing market sizes, MLB has engaged in a number of programs to redistribute the wealth. While the intent is to enhance the balance of talent across the league, it is also well known that such programs ultimately depress players' salaries. If the net effect of revenue sharing were to "equalize talent" (in any case, more so than would occur in the absence of such programs), then perhaps we might feel that this reduction in salaries paid to players is justified because of its beneficial effects on competitive balance. The question of interest in this paper is whether the net effect of redistribution has helped or harmed the balance of talent in the league. Since redistribution in theory depresses the MR curves of all teams, the ultimate comparison is whether the MR of large-market teams falls by more, or less, than that of the small-market teams in equilibrium.

Based on our estimates, we find that the MR curves of teams were indeed reduced by the redistribution efforts undertaken by Major League Baseball from 19962001. We find, however, that the overall effect of those efforts on league balance was neutral, leaving teams' winning percentages essentially where they would have been had revenue not been redistributed. Our results are thus consistent with the invariance principle, and suggest that the assumptions behind those models that conclude that redistribution will affect league balance either positively or negatively do not hold. At the same time, our results indicate that redistribution led to an economically significant reduction in players' salaries. Of course, the subsequent increase in local revenue sharing and the implementation of the luxury tax in 2002 may have had further effects that we are unable to determine from our data. Empirical evaluation of those changes will have to wait until more recent data become available. At this point, though, our results support the Blue Ribbon Commission's conclusion in 2000 that redistributive efforts had failed miserably in achieving the goals of moderating payroll disparities and improving competitive balance.

We would like to thank the many participants who commented on our paper at the 2005 Western Economics Association meetings in San Francisco, especially Rod Fort, John Burger, and John Fizel, as well as two referees. All the usual caveats apply.

Received December 2005; accepted June 2006.

References

Blue Ribbon Panel. 2000. The report of the independent members of the Commissioner's Blue Ribbon Panel on baseball economics. Richard C. Levin, George J. Mitchell, Paul A. Volker, and George F. Will, chairs. New York: Major League Baseball.

Burger, John, and Stephen Walters. 2003. Market size, pay, and performance: A general model and application to Major League Baseball. Journal of Sports Economics 4:108-25.

Cairns, John. 1987. Evaluating changes in league structure: The organisation of the Scottish Football League. Applied Economics 19:259-75.

Fort, Rodney. 2003. Sports market outcomes. In Sports' economics. New Jersey: Prentice Hall.

Fort, Rodney, and James Quirk. 1995. Cross subsidization, incentives, and outcomes in professional team sports leagues. Journal of Economic Literature 33:1265-99.

Kesenne, Stefan. 2000. Revenue sharing and competitive balance in professional team sports. Journal of Sports Economics 1:56-65.

Krautmann, Anthony. 2007. Market size and the demand for talent in Major League Baseball. Applied Economics, In press.

Quirk, James, and Mohamed El-Hodiri. 1974. The economic theory of a professional sports league. In Government and the sports business, edited by Roger Noll. Washington, DC: Brookings Institution.

Rottenberg, Simon. 1956. The baseball players' labor market. Journal of Political Economy 64:242-58.

Schmidt, Martin, and David Berri. 2001. Competitive balance and attendance: The case of Major League Baseball. Journal of Sports Economics 2:145-67.

Scully, Gerald. 1989. The business of Major League Baseball. Chicago, IL: University of Chicago Press.

Sloane, Peter. 1971. The economics of professional football: The football club as a utility maximiser. Scottish Journal of Political Economy 17:121-46.

Solow, John, and Quinn Johnson. 2004. Does size really matter? The effect of market size on marginal revenue in Major League Baseball. University of Iowa Working Paper.

Szymanski, Stefan, and Stefan Kesenne. 2004. Competitive balance and gate revenue sharing in team sports. Journal of Industrial Economics 42:513-25.

Vrooman, John. 1995. A general theory of professional sports leagues. Southern Economic Journal 61:971-90.

Zimbalist, Andrew. 1992. Salaries and performance: Beyond the Scully model. In Diamonds are forever: The business of baseball, edited by Paul M. Sommers. Washington, DC: Brookings Institution.

(1) This Blue Ribbon Panel consisted of: Richard C. Levin (professor of Economics and president of Yale University); former United States Senator George J. Mitchell; Paul Volcker (former chairman of the Federal Reserve System); George F. Will (political columnist); and representatives from 12 MLB clubs.

(2) For an opposing view, which holds that league balance has not been declining, see Schmidt and Berri (2001).

(3) Numerous empirical studies confirm the validity of this assumption (see Burger and Waiters 2003; Solow and Johnson 2004; Krautmann 2007).

(4) It is important to note that this correspondence between the change in MRs and its effect on competitive balance is a direct consequence of the assumed fixed supply of talent.

(5) According to Appendix III in the July 2000 report, local revenues consist of "gate receipts, television, radio and cable fees, ballpark concessions and other baseball revenues" (BRP, 2000, p. 59). Total revenues, on the other hand, "reflects revenue from all sources--local revenue and Central Fund revenue" (BRP, p. 21-22). The Central Fund revenues include those revenues returned to the team from such sources as the national broadcast contract, as well as redistributed local revenues.

(6) An alternative method for controlling for two-team cities is to divide the population in half for those cities with more than one team (see Scully 1989; Zimbalist 1992; and Burger and Walters 2003).

(7) While certainly arbitrary, we assume the relevant discount rate to coincide with the historical long-term real interest rate of 3%.

(8) The statistical significance of diminishing returns in terms of both winning percentage and stadium age is a testimony to their economic significance, given that both factors are so highly correlated with their squared values (i.e., cor(W, [W.sup.2]) - 0.996 and cor(STDAGE, [STDAGE.sup.2]) = 0.952).

(9) The figures in columns 1 and 2 are based on average incomes and populations over the 1996 to 2001 period; the actual winning percentages reported in column 4 are also averaged over that period.

John L. Solow * and Anthony C. Krautmann ([dagger])

* Department of Economics, University of Iowa, Iowa City, IA 52242, USA; E-mail john-solow@uiowa.edu.

([dagger]) Department of Economics, DePaul University, Chicago, IL 60604, USA; E-mail akrautma@depaul.edu; corresponding author.

Table 1. Summary Statistics

 Standard
 Mean Error

[W.sub.it] (a) 0.5034 0.070
[STDAGE.sub.it] 29.1 25.4
[STDAGE.sub.it.sup.2] 1491.8 2290
[TREND.sub.t] 2.5 1.7
POPULATION (1000s) 6653 5571
INCOME (1996$) 30,097 3717
[W.sub.it] x [POP.sub.it] 3439 3121
[W.sub.it] x [INC.sub.it] 15,221 3213
[TWOTEAM.sub.it] 0.308 0.46
[GROSSREV.sub.it] 69,410,000 36,780,000
[GROSSREV.sub.it]/
 [GAME.sub.it] 419,897 215,185
[NETREV.sub.it] 86,870,000 30,860,000
[NETREV.sub.it]/
 [GAME.sub.it] 526,899 178,999

 Minimum Maximum

[W.sub.it] (a) 0.327 0.716
[STDAGE.sub.it] 0 89
[STDAGE.sub.it.sup.2] 0 7921
[TREND.sub.t] 0 5
POPULATION (1000s) 1657 21,363
INCOME (1996$) 24,200 42,909
[W.sub.it] x [POP.sub.it] 699 14,695
[W.sub.it] x [INC.sub.it] 8269 25,703
[TWOTEAM.sub.it] 0 1
[GROSSREV.sub.it] 16,850,000 195,500,000
[GROSSREV.sub.it]/
 [GAME.sub.it] 104,689 1,105,000
[NETREV.sub.it] 40,670,000 190,700,000
[NETREV.sub.it]/
 [GAME.sub.it] 251,056 1,077,000

[W.sub.it] = Winning percent of [i.sup.-th] team in
season t. [STDAGE.sub.it] = age of the stadium in
season t.

[TREND.sub.t] = trend variable, starting with 1996 = 0.
[POP.sub.it] = metropolitan population in season t, in
thousands. [INC.sub.it] = metropolitan income per household
at time t, in 1996$. [TWOTEAM.sub.it] = 1 if there are two
teams in the home city; = 0 otherwise. [GROSSREV.sub.it] =
team is gross revenues in season t (excludes redistribution),
in 1996$. [NETREV.sub.it] team i's net revenues in season t
(includes redistribution), in 1996$. [GAME.sub.it] = total
number of games played by [i.sup.-th] team during season
t (includes playoff games).

(a) Mean winning percent does not equal 0.500 because the
sample omits the expansion teams.

Table 2. OLS Estimates of Revenues per Game

 Gross Net
 Revenue Revenue
 per Game per Game

Constant -926,721 ** -537,900 **
[W.sub.it] 2,508,600 * 1,911,800 *
[w.sub.it - 1] 930,800 ** 691,400 **
[w.sub.it.sup.2] -2,294,900 * -1,827,200 *
[STDAGE.sub.it] -10,686 ** -8217
[STDAGE.sub.it.sup.2] 119.7 ** 91.4 **
[TREND.sub.t] 38,733 ** 47,573 **
[W.sub.it] x [POP.sub.it] 38.82 ** 31.65 **
[W.sub.it] x [INC.sub.it] 9.33 * 8.47 **
[TWOTEAM.sub.it] -103,874 ** -89,457 **
[R.sup.2] 0.76 0.81
Observations (N) 156 156

** Significant at the 5% level.

* Significant at the 10% level.

Table 3. Marginal Revenues by Market Size (Effect of
Winning an Additional Game on Season Revenues)

 Marginal Revenue from Gross Revenue
Win
Percentage Smallest 25th 75th Largest

0.300 2,325,460 2,397,794 2,625,582 3,265,002
0.400 1,866,480 1,938,814 2,166,602 2,806,022
0.500 1,407,500 1,479,834 1,707,622 2,347,042
0.600 948,520
0.700 489,540 561,874 789,662 1,429,082

 Marginal Revenue from Net Revenue
Win
Percentage Smallest 25th 75th Largest

0.300 1,744,160 1,805,898 1,995,876 2,526,320
0.400 1,378,720 1,440,458 1,630,436 2,160,880
0.500 1,013,280 1,075,018 1,264,996 1,795,440
0.600 647,840 709,578 899,556 1,430,000
0.700 282,400 344,138 534,116 1,064,560

Smallest: Using the smallest values of POP (i.e., 1657)
and INC (i.e., $24,200) in the sample. 25th percentile:
Using the 25th percentile values of POP (2751) and INC
($27,401) from sample. 75th percentile: Using the 75th
percentile values of POP (7432) and INC ($32,339) from
sample. Largest: Using the largest values of POP (21,363)
and INC ($42,909) in the sample.

Table 4. Predicted Equilibrium and Actual Winning Percentages

 (1) (2) (3)

 [W.sup.*] [W.sup.*]
 Before After Effect of
Team Redistribution Redistribution Redistribution

Los Angeles 0.571 0.572 0.001
 Angels
Atlanta 0.475 0.475 0.000
Baltimore 0.512 0.513 0.001
Boston 0.498 0.499 0.001
Chicago Cubs 0.521 0.522 0.001
Chicago White 0.521 0.522 0.001
 Sox
Cincinnati 0.454 0.452 -0.002
Cleveland 0.463 0.461 -0.002
Texas 0.484 0.483 -0.001
Colorado 0.468 0.467 -0.001
Detroit 0.487 0.486 -0.001
Houston 0.480 0.479 -0.001
Kansas City 0.454 0.452 -0.002
Los Angeles 0.571 0.572 0.001
 Dodgers
Florida 0.465 0.463 -0.002
Milwaukee 0.455 0.454 -0.001
Minnesota 0.473 0.472 -0.001
New York Mets 0.631 0.635 0.004
New York 0.631 0.635 0.004
 Yankees
Oakland 0.517 0.520 0.003
Philadelphia 0.495 0.495 0.000
Pittsburgh 0.458 0.456 -0.002
San Diego 0.462 0.460 -0.002
Seattle 0.475 0.475 0.000
San Francisco 0.517 0.520 0.003
St. Louis 0.461 0.460 -0.001

 (4) (5)

 Prediction
 Actual Error
 Winning (in Games
Team Percentage Won) (a)

Los Angeles 0.480 15
 Angels
Atlanta 0.606 -21
Baltimore 0.494 3
Boston 0.531 -5
Chicago Cubs 0.467 9
Chicago White 0.513 1
 Sox
Cincinnati 0.494 -7
Cleveland 0.569 -17
Texas 0.508 -4
Colorado 0.483 -3
Detroit 0.423 10
Houston 0.545 -11
Kansas City 0.434 3
Los Angeles 0.525 8
 Dodgers
Florida 0.458 1
Milwaukee 0.461 -1
Minnesota 0.446 4
New York Mets 0.534 16
New York 0.601 6
 Yankees
Oakland 0.512 1
Philadelphia 0.451 7
Pittsburgh 0.443 2
San Diego 0.508 -8
Seattle 0.554 -13
San Francisco 0.535 -2
St. Louis 0.522 -10

(a) Prediction Error compares [W.sup.*] After Redistribution
to Actual Winning Percent, converted into the implied number
of games. Negative values in column 5 imply that the prediction
underestimated the actual values, while a positive value implies
an overprediction