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.

中文翻译：

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抽签限制对淘汰赛的影响

本文分析了抽签限制如何影响淘汰赛的结果。该研究问题受到欧洲俱乐部足球比赛的启发，组织者通常在淘汰赛阶段的第一轮比赛中施加关联约束：来自同一国家的球队不能相互抽签。它的影响在理论和模拟模型中都得到了探索。发现第一轮中的关联约束在随后的每一轮中将相同国家对决的可能性增加到大致相同的程度。如果热门球队集中在一些协会，他们将有更高的概率在该政策下赢得比赛，但如果在更多轮次中使用，则增加不是线性的。