Modelling a baseball game to optimise pitcher substitution strategies incorporating handedness of players

This paper proposes a method for identifying the optimal strategy for substituting players in a baseball game, taking into consideration the handedness of players, which is one of the main factors in terms of managerial decision-making for substitution. Using a Markov chain model, we incorporate the effect of the handedness of players by introducing the concept of the defensive earned run average as a measure of the defensive ability of pitchers and calibrating the batting probabilities of players depending on their handedness. We then develop a dynamic programming formulation including the effect of the handedness of players. This method is illustrated using a match based on the real line-ups of the Colorado Rockies and the San Francisco Giants in the National League of Major League Baseball, especially focusing on the introduction of a relief pitcher in consideration with his handedness.