Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fairer group draw for sports tournaments with restrictions   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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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: math
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc