Reconsideration of the best batting order in baseball: Is the order to maximize the expected number of runs really the best? - Hirotsu, N. (Journal of Quantitative Analysis in Sports, 2011)
In previous studies for analyzing the batting order of baseball games, the order is evaluated by its expected number of runs scored in a game, under the Markov chain model on the D`Esopo and Lefkowitz runner advancement model. However, the order to maximize the expected number of runs may not be the best order in the sense that it may not get more than 0.5 in probability of winning the game against other possible batting orders. In this sense, the best batting order is reconsidered, and it is tried to find better orders than the order which maximizes the expected number of runs. In this paper, the existence of such orders and the difference between the best orders and the order to maximize the expected number of runs are concretely shown by taking into account of not only the expected number of runs but also the standard deviation of runs, based on the data of Major League teams.