Superstars: Talented or merely lucky? The effect of competition on rank-based talent attribution
44 Pages Posted: 1 Oct 2019 Last revised: 26 Jul 2021
Date Written: July 22, 2021
Abstract
We characterize the relationship between talent, luck, and successful performance in highly competitive environments. We show that in many plausible settings, world beating performance is a rather weak signal of underlying ability. For many standard statistical distributions, competition cannot identify talent, i.e., as the number of competitors increases without bound, the probability that the best performer is talented is bounded away from one. When performance equals ability plus Normally distributed noise, competition can identify talent. However, the probability that the best performer is talented increases so slowly with increased competition that, for plausible signal/noise ratios drawn, for example, from the empirical literature on mutual fund performance, confident attribution of talent to the best performer is impossible under any practically conceivable scale of competition. Increased competition need not even favor talent, i.e., increase the probability that the best performer is talented. We provide sufficient conditions both for competition favoring talent and for competition favoring luck. Using these conditions, we show that, in a fairly natural setting---a single-shot forecasting contest where a forecaster's performance is measured by her accuracy and a forecaster's ability is measured by the precision of her Normally distributed information signal, competition favors luck. In other words, increasing the number of competing forecasters always reduces the probability that the most accurate forecaster is talented. In forecasting contests, besting one rival in a two-shot contest provides a stronger signal of ability than topping an arbitrarily large number of rivals in a single-shot contest.
Keywords: contest, selection, talent attribution, mutual fund tournament, forecasting competition
JEL Classification: D81, D82, J24, M50
Suggested Citation: Suggested Citation