Analysing the restricted assignment problem of the group draw in sports tournaments
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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.
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