Statistical laws for career longevity

Career length distinguishes successful long tenures from unsuccessful short stints, and partially reflects the contributions of an employee to the goals of the employer. In some professions, there are well-defined metrics that quantify career longevity, prowess, and productivity, which together contribute to the overall success rating for an individual employee. In this talk, I motivate a stochastic model for career development that relies on two key ingredients, random progress within the career and random stopping times terminating the career. This model is exactly solvable, predicting the probability density function (pdf) of career longevity, characterized by two parameters, $\alpha$ and $x_{c}$. The parameter $\alpha$ quantifies the power-law scaling of the pdf, which is terminated by an exponential cutoff after a crossover value $x_{c}$, representing the mean career lifetime. We test the model with the large quantity of empirical data available for several professional sports leagues, American baseball, Korean baseball, American basketball, and English soccer, finding excellent agreement with the model's predictions. In all, the generality of the model suggests that there may be common stochastic forces that underly progress, success, and longevity in various professions.