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

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Abstract
We provide a simple and intuitive stochastic process that accounts for the observed probability density functions governing career longevity in several professional sports leagues in various countries. Our mechanism characterizes the probability density functions governing career longevity with two parameters, \alpha and \tau . The exponent \alpha < 1 characterizes 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. In addition, 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, our process is a universal mechanism describing longevity in a competitive environment, with the exponent \alpha representing 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, our findings provide a robust method for establishing milestones surpassed only by statistically exceptional players.

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