Effort Shadows and Spillovers in Elimination Tournaments

Jennifer Brown, Northwestern University

Abstract
Personnel tournaments, innovation competitions and runoff elections all examples of elimination contests where the pool of competitors is winnowed in successive rounds of play. In this paper, we consider how the strategies of players in multi-round elimination tournaments are shaped by past, current, and future competitors. We present a two-round model: two pairs of players face off in the first round and the winner of each pairing advances to the final round. The model yields three main results. First, we identify an underdog advantage in the final round—the probability of winning is greater for the weaker player in the final round, relative to earlier rounds. Second, we identify a shadow effect of future competition—the weaker the future competitor, the greater the effort of both players in current round. Third, we find an effort spillover effect—more effort in earlier rounds leads to a lower probability of winning in later rounds. We test our theoretical predictions using data from professional tennis matches. We find strong evidence of effort spillover and the shadow effect in early rounds of tennis tournaments. Moreover, we find some evidence suggesting that worse-ranked players are more likely to upset a better-ranked opponent in final round rather than mid-tournament rounds.

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