The anatomy of hitting: assessing age-related changes in MLB performance via layered Dirichlet modeling

The productive career of a professional athlete is short relative to the human lifespan, with most Major League Baseball (MLB) players retiring by age 40. Although younger players often possess superior physical tools, older players may differ in the composition of plate appearance outcomes, such as walk rates or extra-base hit production. Understanding how these outcomes vary across age groups requires a framework that accounts for their compositional structure. We develop a likelihood ratio test (LRT) for comparing mean compositions across more than two groups under a nested Dirichlet distribution (NDD). This extends existing methodology by enabling multi-group inference for compositional data with complex dependence structures. In addition to detecting overall differences, the proposed test identifies which components drive these differences. We apply this framework to MLB plate appearance data from 2000 to 2010, comparing outcomes (e.g. single, double, out) across three age groups. Treating each player-season as an independent observation, we find strong evidence of compositional differences in every season. The components driving these differences shift over time, from plate discipline and on-base outcomes to power-related outcomes. These results highlight the value of compositional modeling for understanding differences in performance across age groups.