Fairer group draw for sports tournaments with restrictions
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Some recent sports tournaments establish restrictions in the draw of the group stage. In this case, the mechanism used by the Union of European Football Associations (UEFA) to assign the teams into groups is unevenly distributed since not all valid allocations are equally likely. It is shown by illustrative examples how a careful choice of the pot labels and randomisation in the size of the groups can reduce that unfairness. According to our Monte Carlo simulations, the draw of the European Qualifiers to the 2022 FIFA World Cup could have been closer to uniform distribution without any negative effects. Our recommendation has a good chance to be implemented in practice.
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