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Statistical analysis is a major aspect of baseball, from player averages tohistorical benchmarks and records. Much of baseball fanfare is based aroundplayers exceeding the norm, some in a single game and others over a longcareer. Career statistics serve as a metric for classifying players andestablishing their historical legacy. However, the concept of records andbenchmarks assumes that the level of competition in baseball is stationary intime. Here we show that power-law probability density functions, a hallmark ofmany complex systems that are driven by competition, govern career longevity inbaseball. We also find similar power laws in the density functions of all majorperformance metrics for pitchers and batters. The use of performance-enhancingdrugs has a dark history, emerging as a problem for both amateur andprofessional sports. We find statistical evidence consistent withperformance-enhancing drugs in the analysis of home runs hit by players in thelast 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 leaguebaseball, which recently revealed that over 5 percent of major league baseballplayers tested positive for performance-enhancing drugs in an anonymous 2003survey.

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