Layered Dirichlet Modeling to Assess the Changing Contributions of MLB Players as they Age

TL;DR

This paper introduces Layered Dirichlet Modeling to analyze how MLB players' contributions change with age, focusing on measurable performance outcomes and identifying where older players add value beyond athletic peaks.

Contribution

The paper develops a novel Layered Dirichlet Modeling framework for analyzing compositional data to assess age-related changes in player contributions in baseball.

Findings

LDM identifies significant differences in performance components across age groups.

The framework pinpoints specific areas where older players contribute most.

Results suggest older players provide value through experience and mentorship.

Abstract

The productive career of a professional athlete is limited compared to the normal human lifespan. Most professional athletes have retired by age 40. The early retirement age is due to a combination of age-related performance and life considerations. While younger players typically are stronger and faster than their older teammates, older teammates add value to a team due to their experience and perspective. Indeed, the highest--paid major league baseball players are those over the age of 35. These players contribute intangibly to a team through mentorship of younger players; however, their peak athletic performance has likely passed. Given this, it is of interest to learn how more mature players contribute to a team in measurable ways. We examine the distribution of plate appearance outcomes from three different age groups as compositional data, using Layered Dirichlet Modeling (LDM). We develop a hypothesis testing framework to compare the average proportions of outcomes for each component among 3 of more groups. LDM can not only determine evidence for differences among populations, but also pinpoint within which component the largest changes are likely to occur. This framework can determine where players can be of most use as they age.