Efficiency Wages in Major League Baseball Starting Pitchers 1998-2001 Greg Madonia
Statement of Problem Free agency has existed in Major League Baseball (MLB) since 1974. This is a mechanism that allows a player to entertain contract offers from any franchise in MLB. This would allow a player to receive market value for his services. Before free agency existed all players were subject to what was called the reserve system. The reserve system allowed franchises to dictate what a player was worth; in essence a franchise owned a player until he retired. If a player did not agree with the contract offered, the player had very few options. In 1974, Catfish Hunter was awarded free agency after filing a grievance. Unfortunately, free agency brought new problems to MLB. The most prominent of these problems is the question of competitive balance. Theoretically, a team that has more money to spend than others is able to buy better players. These better players could then improve a team s chances of winning. In 2005, the New York Yankees spent 206 million dollars on their payroll, while the Kansas City Royals spent 37 million 1. That year the Yankees won 95 games and the Royals won 56. This disparity has led to some parties to call for MLB to institute a salary cap. This would limit the amount of money a franchise can spend on its players. There are two major components involved in baseball, offense and defense. The defensive component of baseball has two subdivisions: pitchers and fielders. This paper will test to see if one component, free agent starting pitchers in the years 1998 to 2001 with larger salaries, produced more wins than free agent starting pitchers with smaller salaries. In other words, does a larger salary have a positive effect on the amount 1 Payroll data can be found at ESPN s website at http://espn.go.com 2
of games won by a starting pitcher? This paper will look at the effect that salaries have on winning. Review of the Literature Analysis of the competitive balance in baseball has been going on for decades. Rottenburg (1956) believed that franchises were only financially successful if the other franchises in baseball were similar in quality level. Franchises would not want to have an overabundance of quality compared to their rivals. These franchises would not want to win pennants by large margins. If franchises consistently won pennants by large margins consistently over competitors, Rottenburg believed that fan demand for MLB would decrease. Franchises, according to Rottenburg, would inherently make sure that talent was equally distributed between franchises. Therefore, franchises would regulate the distribution of players to maximize profits. Unfortunately it seems that Rottenburg s theories may be not useful in discussions of competitive balance. One need only look at standings for recent years in MLB to consistently see the same teams at the top of the standings. The New York Yankees won 4 out of 5 World Series from 1996 to 2000. They also had the highest payrolls in those years. Rottenburg s theories may not apply for two reasons: a) the addition of free agency and b) the possibility that some franchises are uninterested in maximizing profits. If some franchises may be less interested in maximizing profits and competitive balance, but more interested in maximizing the number of wins during a season, then Rottenburg s theory of self-regulation becomes less applicable. 3
DeBrock, Hendricks and Koenker (2004) examined the impact that pay has on performance. In this paper, DeBrock, Hendricks and Koenker use efficiency wage theory to explain the production differences that similar players display during a season. Efficiency wage theory states that by paying a worker a higher wage than a worker with similar attributes and lower pay. Efficiency wage theory gives workers incentive for performing at their highest level. If the wage premium received is greater than the cost of performing at highest level, than workers should perform at their highest level. If a player is able to outperform another player with similar attributes because he is being paid more, this gives teams with higher payrolls a distinct advantage. Teams with higher payrolls should be able to consistently outperform teams with lower payrolls. Looking at recent trends in MLB, teams with higher payrolls are consistently performing better than teams with lower payrolls. Burger and Walters (2003) looked at the incentives that franchises have for producing wins. In their model, Burger and Walters found that team performance has a positive affect on marginal revenue. Large market teams gain as much as six times the marginal revenue than small market teams from an additional win. This disparity of marginal revenue gives large market teams the incentive to pay workers a higher wage to increase performance and therefore increase the probability of gaining a win. Krautmann, Gustafson and Hadley (2003) examined the salary equations of major league starting pitchers. Aggregation of the salaries of starters, long relievers and closers was the focus of their model. Krautmann, Gustafson and Hadley found that salaries of pitchers in MLB were not determined by preventing runs, but were determined by the 4
nature of their role. However, within each role, the salaries of pitchers were determined by skill level. Formulation of the model The purpose of this paper is to investigate and test the impact of salaries on starting pitchers and their output in MLB. The model that will be used for statistical analysis will measure team payroll, salary, team performance and previous pitching performance. The years and players observed are from 1998 to 2001. Additionally, only pitchers that started a minimum of 15 games and started 50% or more of the games they played in will be observed. The dependent variable that will be estimated by the model is Wins. Wins is a measure of the games won by a starting pitcher during one season. A win is as determined by the rules of MLB. The independent variables will be Salary (Salary), Games Started (Starts), Difference in team runs per game and runs allowed per game (Diff) and the pitcher s previous year number of wins (PWins). The variable that will be used to measure salary (Salary) is a measure of a freeagent starting pitcher from the years 1998 to 2001. This variable is measured in millions of dollars. This variable will be the main variable used to the effects of efficiency wage theory; if this variable is statistically significant at the 95% level, then there is evidence that efficiency wage theory holds up. The coefficient of this variable is expected to be positive; as a player s wage increases, according to efficiency wage theory, the number of games won in a year will also increase. 5
The variable that will be used to measure games started (Starts) is a measure of the number of games started by a free-agent starting pitcher from the years 1998 to 2001. This variable is to control the differences in the amount of games started from player to player. Since all players, due to injury or other causes, do not start the same amount of games in a year, this variable was necessary to account for differences in win opportunities. Since it is impossible to win a game without starting a game, the coefficient of this variable is expected to be positive. The variable Diff is a performance variable that is used to control the impact that the other members of a team has on the number of games won by a free-agent starting pitcher in a given year. Diff is measured as the difference between the number of runs scored per game by a team and the number of runs allowed per game by a team. All data is from the years 1998 to 2001. The expected sign of the coefficient is positive; if a team is scoring more runs than it is allowing, this lessens the chance that a pitcher will receive a loss or not receive a decision. If the difference between runs scored and runs allowed is large and positive it can also help a pitcher receive a win during a below-average performance. PWins is a variable that accounts for past performances for a given pitcher. This data is compiled for the 1998 to 2001 seasons. This variable is the number of wins a free agent starting pitcher has in the year prior to the year observed. The expected sign of the coefficient of this variable is positive; this variable is a measure of a starting pitchers past performances. Taking these factors into consideration the estimated models looks like: (1) Wins = β 0 + β 1 Salary + u 6
(2) Wins = β 0 + β 1 Salary + β 2 Diff + u (3) Wins = β 0 + β 1 Salary + β 2 Diff + β 3 PWins + u (4) Wins = β 0 + β 1 Salary + β 2 Diff + β 3 Pwins + β 4 Starts + u The variable that will be testing efficiency wage theory will be Salary. If this variable is significant at the 95% level, then there is evidence that efficiency wage theory is present. Data Sources and Description The data set used consists of all MLB free agent starting pitchers playing between the years 1998 to 2001. The sample size was 76 observations. Statistical summaries of each variable can be found in Table 1 in Appendix A. Model Estimation and Hypothesis Testing The first model tested (Model 1) wins as the dependent variable and salary as the only independent variable. The adjusted R-squared was.1074. The F-test yielded a value of 10.02. The F-test value signifies that salary has some effect on wins. Salary was found significant at the 95% level, with a t-value of 3.17. The sign of the coefficient was, as expected, positive. The second model tested (Model 2) wins as the dependent variable with salary and diff as the independent variables. The adjusted R-squared was.1258. The F-test yielded a value of 6.40. This F-test value states that the independent variables have some effect on wins. Salary was found significant at the 95% level, with a t-value of 2.82. 7
Again the sign of the coefficient was positive. The diff variable coefficient was also positive; however it was statistically insignificant at the 95% level. Its t-value was 1.60. The third model tested (Model 3) wins as the dependent variable with salary, diff and pwins as independent variables. The adjusted R-squared was.1224. The F-test yielded a value of 4.49. This F-test value states that the independent variables have some effect on wins. Salary was found to be significant at the 95% level, with a t-value of 2.65. Its coefficient was positive. Diff was again statistically not significant at the 95% level; however the sign of the coefficient was positive. The pwins coefficient was negative; not as expected. However, it also was statistically not significant at the 95% level. The third model tested (Model 4) wins as the dependent variable with salary, diff, pwins and starts as independent variables. The adjusted R-squared was.6851. The F-test yielded a value of 41.79. This F-test value states that the independent variables have some effect on the dependent variable: wins. Salary, diff and starts all had positive coefficients as expected. As in Model 3, pwins again had a negative coefficient. Results, with coefficient values, can be found in Table 2 in Appendix B. Interpretations of the Results Analysis of the results does suggest that efficiency wage theory is correct. These results are in agreement with the hypothesis that as salaries increase, output (wins) also increases. Salary is 95% significant in all four models. Previous studies have shown that players are offered higher contracts based on past performance. These results suggest players will perform better as salaries increase. 8
In the models 1 3, the beta values of salary were between.40995 and.52283. In model 4, this beta value of salary decreased to.27182. This occurred when the number of starts was added to the model. This suggests that salary was picking omitted variable bias in models 1 3. Due to time constraints the standard errors in this project are not heteroskedastically robust. Although this would not effect parameter estimates, it would have an influence of standard errors and therefore over t-statistics. Conclusions and Limitations of the Study This paper has examined the effects of efficiency wage theory as applied to MLB. This analysis of the MLB labor market has isolated the effects of salary levels on free agent starting pitchers. The results of this paper do suggest that efficiency wage theory is correct in its hypothesis that: output will increase when workers are paid higher salaries. These results can then be used to analyze competitive balance issues within MLB. If franchises can increase the productivity of players by increasing the players wages, then how can smaller revenue teams remain competitive with larger revenue teams? The main limitation of this paper is a conceptual one; these findings may not be applicable outside of MLB. Simply put, because efficiency wage theory may exist within MLB, it does not prove that it exists outside MLB. Certain assumptions were made during this study that may make its results less conclusive. The first and most important limitation put on this paper is the assumption that all contracts lasted only one year. This paper only took into account the first year of 9
any given contract. Some contracts in MLB can be either front-weighted or backweighted. This means that players, instead of earning the average amount of their contract every year, may earn less than the average one year while making more in another. This is done by franchises to adjust payrolls in certain years. Another limitation of this study is the size of the sample. There were only 76 observations for this study. If time constraints were not an issue, more years would have been studied, and therefore more observations. 10
References: Burger, J., Stephen K. Walters; (2003); Market Size, Pay, and Performance; Journal of Sports Economics; Vol. 4 No. 2; pp. 108-125 DeBrock, L., W. Hendricks, R Koeckner; (2004); Pay and Performance; Journal of Sports Economics; Vol. 5 No. 3; pp. 243-261 Krautmann, A., Elizabeth Gustafson, Lawrence Hadley; (2003); A Note on the Structural Stability of Salary Equations; Journal of Sports Economics; Vol. 4 No. 1; pp 56-63 Rottenburg, S.; (1956); The Baseball Players Labor Market; Journal of Political Economy; Vol. 64; pp. 243-256 11
Appendix A Table 1 Variable Name Desciption Source Wins Number of wins by a free agent starting pitcher in observed year 1 Salary Salary, in millions of dollars, for starting pitcher in observed year 2 Diff Difference between runs scored per game for a team and runs 1 allowed per game for a team in observed year Pwins Number of wins by a free agent starting pitcher in year prior to 1 observed year Starts Number of games started by a free agent starting pitcher in 1 observed year 1. Retrosheet: http://www.retrosheet.org/boxsetc/index.html#players 2. Business of Baseball: 1998: http://roadsidephotos.sabr.org/baseball/1998.htm 1999: http://roadsidephotos.sabr.org/baseball/1999.htm 2000: http://roadsidephotos.sabr.org/baseball/2000.htm 2001: http://roadsidephotos.sabr.org/baseball/2001.htm 12
Appendix B Table 2: Results of Regressions of Salary on Wins and Team Characteristic Control Variables Regressor Model 1 Model 2 Model 3 Model 4 Salary 0.45635** 0.40995** 0.52883**.27182** (3.17) (2.82) (2.65) (2.26) Diff 1.10018 1.23012* 1.52134** (1.60) (1.74) (3.59) Pwins -0.1074-0.22544** (-0.85) (-2.94) Starts.48783** (11.39) Intercept 7.44842** 7.54631** 8.11359** -2.62342** (11.39) (11.61) (8.69) (-2.39) Summary Statistics MSE 14.829 14.523 14.579 5.231 Adj R-Sq 0.1074 0.1258 0.1224 0.6851 n 76 76 76 76 These regressions were estimated using free agent starting pitchers during the years 1998 2001, as described in the the paper. The t-value is in parenthesis under the coefficient value. * indicates significance at the 90% level ** indicates significance at the 95% level 13