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Optimizing baseball defensive alignments through integer programming and simulation

Abstract Baseball is an incredibly complex game in which the manager makes numerous difficult decisions. This paper describes a stochastic integer program that determines the best defensive starting positions to minimize the expected batting average of a particular player. To test this optimal defense against other standard Major League Baseball® defenses, a simulation is created. A computational study demonstrates how the optimal defense can be used to decrease Derek Jeter’s batting average in a statistically significant manner.