Selecting the Best? Spillover and Shadows in Elimination Tournaments

We consider how past, current, and future competition within an elimination tournament a§ect the probability that the stronger player wins. We present a two-stage model that yields the following main results: (1) a shadow e§ectóthe stronger the expected future competitor, the lower the probability that the stronger player wins in the current stage and (2) an e§ort spillover e§ectóprevious e§ort reduces the probability that the stronger player wins in the current stage. We test our theory predictions using data from high-stakes tournaments. Empirical results suggest that shadow and spillover e§ects ináuence match outcomes and have been already been priced into betting markets.