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 a non-trivial problem, 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. The results also uncover that the bias of the draw is non-negligible with respect to qualification, thus, there is a clear need for fairer draw procedures.

翻译：多项体育赛事包含小组循环赛阶段，其中球队需依据某些约束条件分配至各组。由于在满足既定标准的前提下完成球队分配并非易事，组织者通常采用计算机辅助随机抽签以避免死局——即剩余待抽球队无法填入空位的困境。然而，已知该流程存在不公平性：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，并评估其对各国晋级淘汰赛概率的影响。结果表明，在避免非预期偏差方面，官方采用的"第一档→第二档→第三档→第四档"抽签顺序显著优于其他23种可能的抽签顺序。研究同时揭示，抽签偏差对晋级概率的影响不可忽略，这明确表明亟需更公平的抽签流程。