Selecting the best? Spillover and shadows in elimination tournaments

We consider how past, current, and future competition within an elimination tournament affect the probability that the stronger player wins. We present a two-stage model that yields the following main results: (1) a shadow effect wherein the stronger the expected future competitor, the lower the probability that the stronger player wins in the current stage; and (2) an effort spillover effect wherein previous effort 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 effects influence match outcomes and have already been priced into betting markets.