On career longevity distributions in professional sports and a stochastic mechanism underlying their empirical power-law behavior

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  • 23 October 2008
Abstract
Career length is a well-defined metric that distinguishes successful long tenures from unsuccessful short stints as a jobholder. We provide an exactly solvable stochastic process for the empirical probability density functions describing career longevity in several professional sports leagues in various countries. This mechanism characterizes the probability density functions describing career longevity with two parameters, \alpha and \tau. The exponent \alpha \leq 1 defines the scaling in the power-law regime, which is followed by an exponential cutoff after a critical value \tau, representing the mean lifetime in each sport. We also show that the probability density functions of career statistical metrics within each sport follow directly from the density functions of career longevity. Thus, this process is a universal mechanism describing longevity in a competitive environment, where the exponent \alpha quantifies the role of experience and reputation in career development. Because net career tallies of in-game success ultimately serve as a metric for classifying careers, these findings provide a robust method for establishing milestones surpassed only by statistically exceptional players.

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