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Several sports tournaments contain a round-robin group stage where the teamsare assigned to groups subject to some constraints. Since finding an allocationof the teams that satisfies the established criteria is a non-trivial problem,the organisers usually use a computer-assisted random draw to avoid any deadend, a situation when the teams still to be drawn cannot be assigned to theremaining empty slots. However, this procedure is known to be unfair: thefeasible allocations are not equally likely. Therefore, we quantify thedeparture of the 2018 FIFA World Cup draw procedure from an evenly distributedrandom choice among all valid allocations and evaluate its effect on theprobability of qualification for the knockout stage for each nation. Theofficial draw order of Pot 1, Pot 2, Pot 3, Pot 4 turns out to be asignificantly better option than the 23 other draw orders with respect to theunwanted distortions. The results also uncover that the bias of the draw isnon-negligible with respect to qualification, thus, there is a clear need forfairer draw procedures.

On the fairness of the restricted group draw in the 2018 FIFA World Cup