Luck Of Outcome In The Talent Versus Luck Model

This paper analyzes the Talent versus Luck model, which examines the impact of talent and luck on an individual’s career success. The original simulation-based model demonstrated that the distribution of capital has a heavy tail, and the most successful individuals are not necessarily the most talented. While the implications of the original model are intriguing, those findings were based solely on numerical calculations, and it was unclear how generally valid they are. Challet et al. generalize the original model using an analytical approach and successfully clarify the relationship between talent, lucky events, and capital when talent is constant and follows a uniform distribution. We reformulate a simplified model and derive more general propositions about the relationship between luck and talent in individual success by introducing the new concept of luck of outcome in addition to the luck of opportunity in previous models. We show that the capital distribution generated from a simplified talent versus luck model follows a lognormal distribution even when the talent is subject to a normal distribution. Moreover, we specify the relationship between the inequality of the distribution, which is indicated by the Gini coefficient, and the parameters of talent distribution.