The Talent versus luck Model as an Ensemble of One-dimensional Random Walks

Abstract

The role of luck on individual success is hard to be investigated empirically. Simplified mathematical models are often used to shed light on the subtle relations between success and luck. Recently, a simple model called “Talent versus Luck” showed that the most successful individual in a population can be just an average talented individual that is subjected to a very fortunate sequence of events. Here, we modify the framework of the TvL model such that in our model the individuals’ success is modelled as an ensemble of one-dimensional random walks. Our model reproduces the original TvL results and, due to the mathematical simplicity, it shows clearly that the original conclusions of the TvL model are the consequence of two factors: first, the normal distribution of talents with low standard deviation, which creates a large number of average talented individuals; second, the low number of steps considered, which allows the observation of large fluctuations. We also show that the results strongly depend on the relative frequency of good and bad luck events, which defines a critical value for the talent: in the long run, the individuals with high talent end up very successful and those with low talent end up ruined. Last, we considered two variations to illustrate applications of the ensemble of random walks model.