Applying the matching law to Major League Baseball (MLB)

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Christopher Watkins ^* and Vincent Berardi ^**

^(*) Computational and Data Sciences Program, Chapman University, Orange, California
^(**) Department of Psychology, Chapman University, Orange, California

Citation

Watkins, C., Berardi, V. (2025). Applying the matching law to Major League Baseball (MLB). International Journal of Sport Psychology, 56(3), 218-236. doi:10.7352/IJSP.2025.56.218

Abstract

The application of the generalized matching equation (GME) has been detailed in a variety of sports, including football, basketball, and others. However, only a limited number of studies have focused on Major League Baseball (MLB), and they typically have examined ≤ 5 players and/or focused on a single behavior. This paper increases the generalizability of such work by using newly available, state-of-the-art data from thousands of players to explore the GME in several scenarios within three aspects of a baseball game - defense, pitching and batting. We found that the GME accurately summarized response allocation in most scenarios, with r 2 ranging from 0.5 to 0.981, sensitivity ranging from 0.428 to 0.977, and bias ranging from -0.254 to 0.158. In addition, temporal trends in the applicability of the GME were examined within the context of changing philosophies in baseball strategy. These results indicate that the GME operated within several precisely defined dimensions of a baseball game and that analyses of this phenomenon can yield insight into prevailing trends in the sport. Furthermore, with the GME recognized as a ubiquitous phenomenon, teams can examine whether competitive advantages exist for GME adherence and adjust their strategies accordingly. From a psychological science perspective, this work helps establish the degree to which the GME generalizes to real-world contexts.

Keywords: Matching Law, MLB, Baseball

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