Minimax Play at Wimbledon: Comment

Abstract

In a recent contribution, Mark Walker and John Wooders (2001) analyzed serve choices in Grand Slam tennis matches to provide an empirical test of the mixed strategy equilibrium. They argued convincingly that unlike subjects in laboratories, professional players have sufficient experience to play games well, and that they are also highly motivated to win these games. Their results indicated that there were no statistical differences in win rates for male players across various strategies, which is consistent with the equilibrium prediction. They fairly noted, however, that even the top male players tended to switch from one strategy to another too often, resulting in serial dependence. This paper reexamines the results of Walker and Wooders (2001) by collecting and analyzing a broader dataset, including men’s, women’s, and juniors’ matches. We find that the support of the minimax hypothesis is stronger. The plays in our data pass all of the tests in Walker and Wooders (2001) and therefore are more consistent with the theory of equilibrium than those in Walker and Wooders (2001). In short, the two hypotheses implied by the equilibrium, i.e., the equal probability of winning serve directions and the serial independence of serves, are borne out in our data.