The effects of draw restrictions on knockout tournaments

Abstract

The paper analyses how draw constraints influence the outcome of a knockout tournament. The research question is inspired by European club football competitions, where the organiser generally imposes an association constraint in the first round of the knockout phase: teams from the same country cannot be drawn against each other. Its effects are explored in both theoretical and simulation models. An association constraint in the first round(s) is found to increase the likelihood of same nation matchups to approximately the same extent in each subsequent round. If the favourite teams are concentrated in some associations, they will have a higher probability to win the tournament under this policy but the increase is less than linear if it is used in more rounds. Our results might explain the recent introduction of the association constraint for both the knockout round play-offs with 16 teams and the Round of 16 in the UEFA Europa League and UEFA Europa Conference League.

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“…First, the reason for the difference between the standard and the reversed UEFA mechanisms has not been fully explored, although the complexity of the problem has been highlighted. Second, we have considered the effects of draw constraints only on the fairness of the draw, but they might influence the later stages of the tournament, too (Csató, 2022a). These issues are especially important because analogous draw conditions can be used to achieve strategic goals such as minimising the threat of unfair behaviour by the teams (Csató, 2022c).…”

“…The same algorithm is used in other UEFA club tournaments such as the UEFA Europa League and the UEFA Europa Conference League for the draw of the knockout round play-offs and the Round of 16 (Csató, 2022a). Furthermore, it is applied to allocate teams into groups with more than two teams in several competitions for national teams (Csató, 2023): the FIBA Basketball World Cup, the UEFA Euro qualifying, the UEFA Nations League, and the European Qualifiers to the FIFA World Cup.…”