The effects of draw restrictions on knockout tournaments

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research 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.

查看原文本刊更多论文

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。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.