Several sports tournaments contain a round-robin group stage where the teams are assigned to groups subject to some constraints. Since finding an allocation of the teams that satisfies the established criteria is non-trivial, the organisers usually use a computer-assisted random draw to avoid any dead end, a situation when the teams still to be drawn cannot be assigned to the remaining empty slots. However, this procedure is known to be unfair: the feasible allocations are not equally likely. Therefore, we quantify the departure of the 2018 FIFA World Cup draw procedure from an evenly distributed random choice among all valid allocations and evaluate its effect on the probability of qualification for the knockout stage for each nation. The official draw order of Pot 1, Pot 2, Pot 3, Pot 4 turns out to be a significantly better option than the 23 other draw orders with respect to the unwanted distortions. Governing bodies in football are encouraged to make similar calculations immediately before the draw of major sporting events in order to avoid using a highly unfair draw order that can be easily improved by a simple relabelling of the pots.

翻译：体育赛事常设循环赛制小组赛阶段，分组需满足特定约束条件。由于满足既定标准的球队分配方案具有非平凡性，主办方通常借助计算机辅助随机抽签避免出现"死局"（即待抽球队无法填入剩余空位的状况）。然而，该流程存在公认的不公平性：可行分配方案的出现概率并不均等。因此，我们量化了2018年国际足联世界杯抽签流程偏离所有有效分配方案均匀随机选择的程度，并评估了该偏差对各国家队晋级淘汰赛概率的影响。在非期望畸变方面，官方采用的第一档至第四档球队按序抽签方案，显著优于其他23种抽签顺序。建议足球管理机构在重大赛事抽签前立即进行类似计算，以避免采用可通过简单重排档位顺序即可改善的高度不公平抽签顺序。