The efficacy of tournament designs

Abstract

Tournaments are a widely used mechanism to rank alternatives in a noisy environment. This paper investigates a fundamental issue of economics in tournament design: what is the best usage of limited resources, that is, how should the alternatives be compared pairwise to best approximate their true but latent ranking. We consider various formats including knockout tournaments, multi-stage championships consisting of round-robin groups followed by single elimination, and the Swiss-system. They are evaluated via Monte-Carlo simulations under six different assumptions on winning probabilities. Comparing the same pair of alternatives multiple times turns out to be an inefficacious policy. While seeding can increase the efficacy of the knockout and group-based designs, its influence remains marginal unless one has an unrealistically good estimation on the true ranking of the players. The Swiss-system is found to be the most accurate among all these tournament formats, especially in its ability to rank all participants. A possible explanation is that it does not eliminate a player after a single loss, while it takes the history of the comparisons into account. The results can be especially interesting for emerging esports, where the tournament designs are not yet solidified.