锦标赛种子排位的一个悖论
A paradox of tournament seeding
AI总结：
研究揭示循环赛资格制下基于历史系数的标准种子排位会惩罚成绩更好的球队，并提出以资格赛排名靠后球队的最高系数确保激励相容。
摘要：
我们分析了一种采用循环赛资格赛的体育赛事种子排位数学模型。基于衡量球队历史表现的系数的标准种子排位制度被证明是不公平的，因为它可能因球队取得更好成绩而对其形成惩罚，使其在下一阶段平均不得不面对更强的对手。研究揭示，主要足球赛事都存在这一缺陷。通过在种子排位时让每支晋级球队获得其资格赛中排名低于该队的所有球队中的最高系数，可以保证激励相容性。我们的提议以2020/21赛季UEFA Champions League为例进行了说明。
英文摘要：
We analyse a mathematical model of seeding for sports contests with round-robin qualifying tournaments. The standard seeding system based on coefficients measuring the historical performance of the teams is shown to be unfair as it might potentially punish a team for its better results by having to face stronger opponents on average in the next stage. Major football competitions are revealed to suffer from this weakness. Incentive compatibility can be guaranteed by providing each qualified team with the highest coefficient of all teams that are ranked lower in its qualifying tournament for seeding purposes. Our proposal is illustrated by the 2020/21 UEFA Champions League.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
