Computing an Optimal Pitching Strategy in a Baseball At-Bat

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The field of quantitative analytics has transformed the worldof sports over the last decade. To date, these analytic ap-proaches are statistical at their core, characterizing what isand what was, while using this information to drive decisionsabout what to do in the future. However, as we often viewteam sports, such as soccer, hockey, and baseball, as pairwisewin-lose encounters, it seems natural to model these as zero-sum games. We propose such a model for a baseball at-bat,which is a matchup between a pitcher and a batter. Specifi-cally, we propose a novel model of this encounter as a zero-sum stochastic game, in which the goal of the batter is to geton base, an outcome the pitcher aims to prevent. The valueof this game is the on-base percentage (i.e., the probabilitythat the batter gets on base). In principle, this stochastic gamecan be solved using classical approaches. The main techni-cal challenges lie in predicting the distribution of pitch loca-tions as a function of pitcher intention, predicting the distri-bution of outcomes if the batter decides to swing at a pitch,and characterizing the level of patience of a particular batter.We address these challenges by proposing novel pitcher andbatter representations as well as a novel deep neural networkarchitecture for outcome prediction. Our experiments usingKaggle data from the 2015 to 2018 Major League Baseballseasons demonstrate the efficacy of the proposed approach.