A Probability Theory Framework for Baseball Strategy and Simulations

Abstract

In this paper, we look to answer specific questions about the game of baseball in the MLB. These questions pertain to in-game strategies such as base stealing, questions regarding optimal ways of modeling baseball simulations, and recommendations to teams regarding these results. The paper uses a probability theory framework focused on Markov chains to analyze play-by-play data from the 2014 Major League Baseball season. The data is analyzed in aggregate and also in specific cases of player performance. We hope these questions, results, and recommendations can influence further work done in not only baseball analytics, but analytics for the sports world as a whole. The results of this paper are focused on answering questions pertaining to advice to Major League managers and improving baseball board games. Regarding advice to managers, we provide recommendations pertaining to optimal base stealing strategies and lineup optimization techniques. We also provide recommendations for improvement in three aspects of baseball board games. The first recommendation suggests that pitchers pitch more effectively out of the windup position compared to the stretch position, and in order to create a more realistic simulation, board games should account for this difference. The second recommendation analyzes the cases of conditional walks in baseball. We determine that certain players are able to walk at different rates conditional on the plate appearance situation. Finally, we analyze the process of base stealing within a board game and provide a better metric for determining how certain baserunners are able to steal against certain pitchers. We hope these insights can o er improvements to in-game management and in designing better baseball simulations.