Minimax after money-max: why major league baseball players do not follow optimal strategies

ABSTRACT

Using real-life sports data of Major League Baseball, this paper investigates whether professional players follow the minimax theorem in their strategies. Our empirical results using the 2010 regular-season data show that baseball players do not optimize their strategies: there is a significant difference in their payoffs across strategies, and the sequence of their strategy choices is predictable from their previous actions. Further analysis using individual salaries and key contract variables indicates that a higher salary has a positive impact on following minimax strategies in the regular season. By contrast, a longer contract decreases a player’s incentive to pursue optimal strategies in the postseason. These results have important implications for compensation practices in various fields.

KEYWORDS:

• Minimax
• baseball
• optimal strategy
• salary
• contract length

JEL CLASSIFICATION:

• C70
• D00
• D80

Acknowledgments

We would like to thank Larry Blume, Nancy Chau, and Francesca Molinari for helpful comments. All remaining errors are the responsibility of the authors. The views expressed in this paper are the responsibility of the authors only and should not be representing those of United States Department of Agriculture.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Other studies have been conducted to answer the question on whether minimax behaviour is observable in real life. In a laboratory setting with a controlled environment, most findings have refuted the minimax theory. The studies of Lieberman (1960), Messick (1967), Fox (1972) and Brown and Rosenthal (1990) are examples.

² Here, a tennis game is defined by Walker and Wooders (2001) as a ‘point’ game, in which the outcome of the game is one point.

³ Alternative approaches to model the action space are conceivable, such as a pitch-type approach, but this has its own set of difficulties. First, it is difficult to set a cut-off point for velocity for categorizing. Second, similar to the movement criteria, some pitchers’ slower pitches may be faster than other pitchers’ fastballs.

⁴ A batter can neither be a starting batter nor a pinch hitter if he was a substitute during a defence inning.

⁵ In Section 6, we exclude the first innings to test the robustness of our results.

⁶ In Section 6, we run several robustness tests to ensure that our results are not sensitive to the different number of at-bat games played by batters.

⁷ Fixed effects estimation and LSDV estimation yield identical results (Wooldridge 2010). Hence, we use LSDV estimation to report the results.

⁸ We tried many different combinations of control variables and find that the results are almost identical.