Three Prominent Tournament Formats : Predictive Power and Costs

We analyze tournaments of heterogeneous players from an organizer's perspective. Using a simple model of a noisy tournament, we demonstrate how the likelihood of selecting the best player, here termed the "predictive power" of a tournament, depends on the tournament format, the distribution of players' types, and the overall noise level. We formalize the organizer's decision problem for varying time and measurement costs and compare the predictive power of three widely used tournament formats - contests, binary elimination tournaments, and round-robin tournaments. We show which formats are preferred in the various scenarios and find that for certain parameter constellations, certain formats are not viable