  Several sports tournaments contain a round-robin group stage where the teams
are assigned to groups subject to some constraints. Hence, 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. This procedure is known to be unfair: the feasible allocations are not
equally likely. We quantify the unfairness of the 2018 FIFA World Cup draw and
evaluate its effect on the probability of qualification for the knockout stage
for each national team. 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. Nonetheless, the non-uniform draw
distorts the probability of qualification by more than one percentage point for
two countries. Our results call attention to the non-negligible role of draw
order and make it possible for policymakers to decide whether the use of fairer
draw mechanisms is justified.
