  Many sports tournaments contain a group stage where the allocation of teams
is subject to some constraints. The standard draw procedure extracts the teams
from pots sequentially and places them in the first available group in
alphabetical order such that at least one assignment of the teams still to be
drawn remains acceptable. We show how this mechanism is connected to generating
permutations and provide a backtracking algorithm to find the solution for any
given sequence. The consequences of draw restrictions are investigated through
the case study of the European Qualifiers for the 2022 FIFA World Cup. We
quantify the departure of its draw procedure from even distribution and propose
two alternative approaches to increase the excitement of the draw.
