Equilibrium Outcome Path and Predictability in Baseball Games

comprised of multiple ‘pitcher-batter’ interactions under complete information about types of opponents and payoff structures. In discussing the equilibrium outcome, the factor of randomness matters. A batter or the pitcher can choose the best possible response to his opponent’s play, but his strategy can result in an unintended outcome; for instance, although a batter hits well, the hit can end up in an out. Overall, baseball outcomes are random. By taking into account this randomness, an equilibrium outcome can be anticipated. Formally, both batter and pitcher play a min-max game for the number of bases. Given the probability distribution, a batter strategically acts to maximize his expected base while the pitcher aims to minimize it. A Nash Equilibrium can be characterized for a ‘pitcher-batter’ constituent game. A baseball game can be represented as a finite repetition of ‘pitcher-batter’ constituent games, allowing one to generalize the equilibrium outcome path. With the result, this research can contribute to predicting a game result.