by Evan Zepfel

Since the advent of free agency in 1975, certain Major League Baseball teams have benefited from the ability to acquire talented players through free agency. This system, however, rewards the teams with the largest payrolls by allowing them to sign the best players, and consequently, win more games. Since 1985, salary and winning percentage are positively correlated, and a simple linear regression suggests that an increase in aggregate player salary predicts an increase in winning percentage (significant at the 0.05 level, although the R^2 value is relatively low). [1] Baseball officials recognized the inherent inequality in this system, and in 1994 attempted to implement changes to improve the competitive balance in the game.

While baseball doesn’t have a salary cap, the revenue sharing structure and competitive balance tax (commonly known as the luxury tax) seek to ensure that team revenues are relatively equal. This structure is designed to financially punish teams that spend excessively in the market for players. In the current structure, all teams pay a certain proportion of their “net local income” (all baseball related income apart from revenue sharing income), and certain clubs pay an extra portion based on their performance, in order to ensure that the most profitable clubs pay more and the least profitable clubs receive more. This plan should allow clubs with lower gross revenues to compete in the market for players with those who have higher gross revenues, thus providing a more level playing field.

This study seeks to determine whether the implementation of revenue sharing and competitive balance taxes have increased parity across all MLB teams. I use the standard deviation of team winning percentages in a given season as a proxy for parity, as a lower standard deviation means that teams are more centered on the median winning percentage and that more teams are able to compete for the limited number of postseason spots. Additionally, I use yearly Gini Coefficients of team salary on a year-by-year basis to approximate the payroll equality in Major League Baseball. [2]

One would expect that as revenue sharing and competitive balance taxes came into effect, the Gini coefficient of payroll should increase (more even distribution of payroll). Additionally, as payroll equality increases, parity should increase, reflected by a decreased standard deviation of winning percentage. In fact, the opposite has been the case. As is clear in the figure above, the payroll inequality in MLB has substantially increased since 1985. The Lorenz curves for both 1985 and 1994 are substantially closer to the equal salary distribution line than is the curve for 2013. The increase in year-by-year Gini coefficients is also evident in figure 2 below. There appears to be a relationship between the Gini coefficient and the two standard deviation measures, which will be explored below.

It is interesting to note that the standard deviation of Pythagorean win percentage is systematically lower than the standard deviation of realized win percentage. This is likely a result of the fact that the Pythagorean win percentage removes much of the day-to-day noise related with win percentage, and rather focuses on season-long run scoring and run allowing statistics that better approximate a team’s true talent.

I also expect that an increase in salary Gini coefficient should increase the standard deviation of winning percentages, as salaries that are more unequal should cause more dispersion in team performance. Both winning percentage and Pythagorean winning percentage are positively correlated with increases in salary Gini coefficient, although the result is only significant at the 0.05 level for Pythagorean winning percentage. [3] As noted above, the Pythagorean winning percentage attempts to control for day-to-day statistical noise and is thus a more appropriate measure to determine true parity levels over a longer time horizon. The linear relationship between salary Gini coefficient and Pythagorean winning percentage is evident in Figure 3 below. The R-squared value is also greater for Pythagorean winning percentage (14% vs. 10% for actual winning percentage).

A simple linear regression analysis predicts the following equation for standard deviation of winning percentage based on changes in the Gini coefficient of salary:

*SD=*0.091*g* + 4.56%

Where * **g*= Gini coefficient of salary

This equation predicts that an increase of 0.05 in the Gini coefficient should add 2.28% to the standard deviation of Pythagorean winning percentage. Additionally, the R-squared measure for this particular linear regression indicates that the differences in Gini coefficient explain 14% of the variation in standard deviation of winning percentage.

Given the increasing inequality in payroll spending by Major League teams (and the consequences that increasing inequality has on actual parity), MLB would benefit from examining the causes of this payroll inequality. Just as adding two additional playoff spots has increased the importance of a number of late-season games, increased parity would ensure that a greater number of teams is able to remain competitive later in the season, likely increasing attendance and TV viewership.

The most significant shortcoming of the competitive balance system is MLB’s reluctance to collect an appropriate share from certain local television contracts; while those deals fall under the “Net Local Revenue” which is taxed at 34%, some teams have specific provisions that allow them to contribute less than this amount. [4] These specific provisions can allow teams that generate strong television earnings to retain a greater portion of their earnings than they would normally be allowed under the revenue sharing agreement. Additionally, it is likely that the disparity among contracts signed by large market and small market teams is greater than the revenue sharing agreement is currently equipped to address. Similarly, the even distribution of the MLB central fund (which brings in revenue from national TV contracts and licensing deals, among other things) does nothing to further address the revenue and salary disparity.

[1] All data is courtesy of the Lahman database. The years 1985-2013 were selected because those are the years for which player-by-player salary data is available.

[2] Gini coefficients range from 0 to 1, where 0 would represent a situation where all team payrolls are equal and 1 would represent a situation where one team controls all of the payroll dollars. The Gini coefficient is derived from the ratio of the area between the line of equality and the Lorenz curve to the total area under the line of equality.

[4] The Dodgers TV deal is only valued at $84 million (despite being worth over $240 million), meaning that all cash received from the deal over $84 million is not subject to revenue sharing. Arrangements that give the team an equity stake in the broadcaster might similarly protect the team from additional revenue sharing payments.

What are possible solutions to help the inequality between MLB teams? How will these solutions affect the economy of baseball?