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Football group draw probabilities and corrections
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Roberts, Gareth O. and Rosenthal, Jeffrey S. (Jeffrey Seth) (2022) Football group draw probabilities and corrections. Journal of the Royal Statistical Society: Series A (Statistics in Society) . (Submitted)
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Abstract
This paper considers the challenge of designing football group draw mechanisms which have the uniform distribution over all valid draw assignments, but are also entertaining, practical, and transparent. We explain how to simulate the FIFA Sequential Draw method, to compute the non-uniformity of its draws by comparison to a uniform Rejection Sampler. We then propose two practical methods of achieving the uniform distribution while still using balls and bowls in a way which is suitable for a televised draw. The solutions can also be tried interactively.
Item Type: | Submitted Journal Article | ||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||||||
Library of Congress Subject Headings (LCSH): | Soccer -- Statistical methods , Soccer matches, Probabilities, Stochastic processes | ||||||||||||
Journal or Publication Title: | Journal of the Royal Statistical Society: Series A (Statistics in Society) | ||||||||||||
Publisher: | Royal Statistical Society ; Wiley | ||||||||||||
ISSN: | 0964-1998 | ||||||||||||
Official Date: | 2022 | ||||||||||||
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Status: | Not Peer Reviewed | ||||||||||||
Publication Status: | Submitted | ||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
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