Leo Oh, Rice University
Baseball showcases a dynamic between pitchers and batters, where both players must act optimally to maximize their payoff. We frame this interaction as an independent sequence of static simultaneous games, specifically a zero-sum game where the expected run values are used as utilities. This paper aims to determine whether the players learn by updating their belief on the opponent’s probability of outcomes (PO) with two different models. The first model contains the nonconditional PO that does not use the first pitch as a prior, while the second model does the opposite and uses the conditional PO. We begin by calculating mixed strategy Nash equilibrium with linear programming but encounter pure strategies, which lead to zero-likelihood problems. Thus, we resort to quantal response equilibrium where human error is incorporated into the model, removing pure strategies. To interpret our results, we use the odds ratio from the two models’ likelihood calculated using their equilibrium to compare models empirically. For our chosen group of players, the odds ratios show that most play closer to the sophisticated model’s equilibrium, which holds on both aggregate and individual match-up levels. The following result implies that most players learn from the first count and adjust their actions in the second count, especially when experienced. However, limitations to the results include the assumption of homogeneity in players’ performance against corresponding strategies regardless of their opponent and the differences in magnitude of the odds ratio, which affects the interpretation of our results.
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