On the distribution of career longevity and the evolution of home run prowess in professional baseball

TL;DR

This paper analyzes career longevity and performance metrics in professional baseball, revealing power-law distributions and evidence of performance-enhancing drug use over the past 25 years.

Contribution

It demonstrates that career durations and performance metrics follow power-law distributions and provides statistical evidence of performance-enhancing drug use in recent baseball history.

Findings

Career longevity follows a power-law distribution.

Performance metrics for players also follow power-law distributions.

Evidence suggests increased performance-enhancing drug use in the last 25 years.

Abstract

Statistical analysis is a major aspect of baseball, from player averages to historical benchmarks and records. Much of baseball fanfare is based around players exceeding the norm, some in a single game and others over a long career. Career statistics serve as a metric for classifying players and establishing their historical legacy. However, the concept of records and benchmarks assumes that the level of competition in baseball is stationary in time. Here we show that power-law probability density functions, a hallmark of many complex systems that are driven by competition, govern career longevity in baseball. We also find similar power laws in the density functions of all major performance metrics for pitchers and batters. The use of performance-enhancing drugs has a dark history, emerging as a problem for both amateur and professional sports. We find statistical evidence consistent with performance-enhancing drugs in the analysis of home runs hit by players in the last 25 years. This is corroborated by the findings of the Mitchell Report [1], a two-year investigation into the use of illegal steroids in major league baseball, which recently revealed that over 5 percent of major league baseball players tested positive for performance-enhancing drugs in an anonymous 2003 survey.