论文标题
比赛播种的悖论
A paradox of tournament seeding
论文作者
论文摘要
我们分析了一个通过旋转式资格赛的运动比赛的数学播种模型。基于测量团队历史表现的系数的标准播种系统被证明是不公平的，因为它可能会在下一阶段平均面对更强大的对手来惩罚团队的更好结果。大型足球比赛被发现遭受了这种弱点的困扰。可以通过为每个合格的团队提供最高系数的所有球队中的最高系数，这些球队以播种目的的排位赛排名较低。 2020/21欧洲冠军联赛说明了我们的建议。
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.
