Issue
EPL
Volume 83, Number 5, September 2008
Article Number 50010
Number of page(s) 5
Section General
DOI http://dx.doi.org/10.1209/0295-5075/83/50010
Published online 03 September 2008
EPL, 83 (2008) 50010
DOI: 10.1209/0295-5075/83/50010

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

Alexander M. Petersen, Woo-Sung Jung and H. Eugene Stanley

Center for Polymer Studies and Department of Physics, Boston University - Boston, MA 02215, USA

ampl7@physics.bu.edu

received 15 April 2008; accepted in final form 18 July 2008; published September 2008
published online 3 September 2008

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 (2007), 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.

PACS
01.80.+b - Physics of games and sports.
89.75.Da - Systems obeying scaling laws.
02.50.Fz - Stochastic analysis.

© EPLA 2008