A Markov Approach to Modeling Baseball At-Bats and Evaluating Pitcher Decision-Making and Performance

Abstract

The author models baseball at-bats using absorbing Markov chains, formed based on pitch-by-pitch data for 90 pitchers from the 2015 season. These matrices are used to reverse-predict performance statistics that compare closely to actual values for these pitchers. The author finds that Markov chains are well-suited to model at-bats because they illuminate differences in pitching style and effectiveness and explain performance changes over time. After showing that Markov matrices provide a reasonable model, the author uses this model to examine the effectiveness of two traditional baseball strategies — a batter taking, or not swinging at, the first pitch of an at-bat, and a pitcher intentionally throwing a ball on an (0,2) count — and, more generally, to examine how pitchers could optimize their performance by making better decisions. The results show that taking the first pitch is significantly more effective against weaker pitchers, while the (0,2) waste pitch is generally more effective for strikeout pitchers than contact pitchers, but the difference is not significant. In addition, this thesis highlights the importance of “the count” in baseball and finds that pitcher performance is largely predictable based on the manner in which the count progresses in an average at-bat against him.