Some recent qualifying tournaments, organised by the Union of European Football Associations (UEFA), establish restrictions in the draw of the group stage. In this case, the official mechanism used to assign the teams into groups is unevenly distributed, meaning that not all valid allocations are equally likely. Motivated by a simple illustrative example, the draw of the European Qualifiers to the 2022 FIFA World Cup is proved via simulations to exhibit a systematic bias: certain teams should play more matches on average only due to the design of the draw procedure. However, simple randomisation in the labelling of the groups can reduce that unfairness without any negative effects. Since UEFA has recently introduced an analogous reform, our recommendation has a good chance to be implemented soon.

翻译：最近由欧洲足球协会联合会(欧洲足联)组织的一些资格赛在组级赛中规定了限制,在这种情况下,分配组级赛团的官方机制分布不均,这意味着并非所有有效分配都有可能相同。 简单举例来说,模拟证明2022年国际足联世界杯欧洲资格赛的抽签显示出系统性的偏差:某些球队应平均进行更多的比赛,但只是因为设计了抽签程序。 然而,在组类标签中简单随机化可以减少这种不公平,而不会产生任何负面影响。 由于欧洲足联最近实行了类似的改革,我们的建议很有可能很快得到落实。