  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.
