A Markov Model for Baseball with Applications

Abstract

In this work we confirm a Markov chain model of baseball for 2013 Major League Baseball batting data. We describe the transition matrices for individual player data and their use in generating single and nine-inning run distributions for a given lineup. The run distribution is used to calculate the expected number of runs produced by a lineup over nine innings. We discuss batting order optimization heuristics to avoid computation of distributions for the 9! = 362, 880 distinct lineups for 9 players. Finally, we describe an implementation of the algorithms and review their performance against actual game data.