The efficacy of tournament designs

Abstract

Tournaments are a widely used mechanism to rank alternatives in a noisy environment. We investigate 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 pairs of alternatives multiple times turns out to be an inefficacious policy. The Swiss-system is found to be the most accurate among all these designs, especially in its ability to rank all participants. A possible explanation is that it does not eliminate an alternative after a single loss, while it takes the history of the comparisons into account. Hence, this particular format may deserve more attention from the decision-makers such as the governing bodies of major sports.

Merging Knockout and Round-Robin Tournaments: A Flexible Linear Elimination Tournament Design

“…After all, if we have a really good estimate for the power rankings, we may not even need a tournament in the first place. Interestingly, real data suggests that the performance in tournaments can be very different from any existing past performance; which makes seeding a somewhat marginal component in improving the efficiency of the tournaments [1]. This claim is supported by the study in the UEFA Europa League and the UEFA Champions League [89], which shows that the seeding by itself is insufficient in its contribution to the success of better teams.…”

“…We study the design of tournaments, which is scheduling the pairwise comparisons between participating competitors (players) [1]. There are varying formulations for such designs.…”

“…There are varying formulations for such designs. While, in the literatures of sports, economics and management sciences, the formulation includes the distribution of some effort (intensity) for the sake of achieving some goal [2]- [9]; we consider the effort to be constant across the competition [1]. This formulation assumes that the competitors perform at their peak in all matches, which manifests itself in a lot of situations such as high stakes competitions, e.g., elections [10], musical competitions [11], contests for crowdsourcing [12], sports tournaments [13], innovation contests [14]- [16].…”

“…However, this becomes increasingly more difficult as the number of players and the number of matches increase. If the tournament also has a convoluted structure, this method becomes intractable [1]. For this reason, the standard approach is using Monte Carlo simulations.…”

“…The works in [77], [78] have studied tournament designs with 8 or 16 players. The works in [1], [83] studies the tournaments with 32 competitors. Although they study various tournament structures, the limitations on the number of participants is problematic.…”