A paradox of tournament seeding

Abstract

A mathematical model of seeding is analysed for sports tournaments where the qualification is based on round-robin contests. The conditions of strategyproofness are found to be quite restrictive: if each team takes its own coefficient (a measure of its past performance), only one or all of them should qualify from every round-robin contest. Thus the standard draw system creates incentives for tanking in order to be assigned to a stronger pot as each team prefers to qualify with teams having a lower coefficient. Major soccer competitions are shown to suffer from this weakness. Strategyproofness can be guaranteed by giving to each team the highest coefficient of all teams that are ranked lower in its round-robin contest. The proposal is illustrated by the 2020/21 UEFA Champions League.Comment: 23 pages, 3 table