The effects of draw restrictions on knockout tournaments

IF 1.1 Q3 SOCIAL SCIENCES, MATHEMATICAL METHODS

Journal of Quantitative Analysis in Sports Pub Date : 2021-10-26 DOI:10.1515/jqas-2022-0061

L'aszl'o Csat'o

引用次数: 6

Abstract

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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抽签限制对淘汰赛的影响

摘要:本文分析了平局限制对淘汰赛结果的影响。研究问题的灵感来自欧洲俱乐部足球比赛，在淘汰赛阶段的第一轮，组织者通常会施加协会限制:来自同一国家的球队不能相互抽签。在理论和仿真模型中探讨了其影响。研究发现，第一轮的关联约束在随后的每一轮中增加了相同国家配对的可能性，其程度大致相同。如果最受欢迎的球队集中在一些协会，在这种政策下，他们赢得比赛的可能性会更高，但如果在更多轮中使用这种政策，这种增长就不是线性的。我们的研究结果可以解释最近在16支球队的淘汰赛附加赛和欧联杯和欧联杯16强赛中引入的协会约束。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Quantitative Analysis in Sports SOCIAL SCIENCES, MATHEMATICAL METHODS-

CiteScore

2.00

自引率

12.50%

发文量

期刊介绍： The Journal of Quantitative Analysis in Sports (JQAS), an official journal of the American Statistical Association, publishes timely, high-quality peer-reviewed research on the quantitative aspects of professional and amateur sports, including collegiate and Olympic competition. The scope of application reflects the increasing demand for novel methods to analyze and understand data in the growing field of sports analytics. Articles come from a wide variety of sports and diverse perspectives, and address topics such as game outcome models, measurement and evaluation of player performance, tournament structure, analysis of rules and adjudication, within-game strategy, analysis of sporting technologies, and player and team ranking methods. JQAS seeks to publish manuscripts that demonstrate original ways of approaching problems, develop cutting edge methods, and apply innovative thinking to solve difficult challenges in sports contexts. JQAS brings together researchers from various disciplines, including statistics, operations research, machine learning, scientific computing, econometrics, and sports management.