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Keeping the Hitter Off Balance: Mixed Strategies in Baseball
Jesse Weinstein-Gould
Journal of Quantitative Analysis in Sports, April 2009
Abstract:
Mixed strategies are a key component of game theory. Investigations into whether or not people use optimal mixed strategies have largely been limited to laboratory settings and have produced mixed results. Recently, the empirical framework has been extended into professional sports. This study uses pitch-level data from Major League Baseball games to see if pitchers mix their pitches optimally. The scope of this study is limited to the first pitch of a plate appearance and finds that pitchers are mixing optimally to have success on the first pitch of the plate appearance, but the null hypothesis of optimal play for the plate appearance outcome is rejected.
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Optimizing Football Game Play Calling
Jeremy Jordan, Sharif Melouk & Marcus Perry
Journal of Quantitative Analysis in Sports, April 2009
Abstract:
Play calling strategies during football games are extremely important to the success of a team. In the past, coaches and players have subjectively determined the plays to call based on past experiences, personal biases, and various observable factors. This research quantifies these decisions using game theoretic techniques; updating optimal decision policies as new information becomes available during a game. A decision maker changes his perceived optimal strategy based on the information known about the opponent's strategy at the time of the decision. Additionally, utility theory is used to capture the different risk preferences of the decision makers. Furthermore, we use design of experiments and response surface methodology to optimize the risk strategies of each decision maker. By exploring the interaction of two football teams' risk preferences, optimal risk strategies can be suggested in the form of a varying mixed strategy. The techniques presented can be utilized in a precursory analysis to forecast different decisions a coach or player may encounter throughout the game, during a game to optimize each play called, or as a posterior analysis technique to dissect the decisions made and determine the effectiveness of the plays called. The procedures are easily transitioned to rapidly assist football teams or other sports teams in making better decisions through quantitative modeling and statistical analysis. A numerical example is presented to demonstrate the usefulness of the solution approach.
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