arXiv Open Access 2022

Football Group Draw Probabilities and Corrections

Gareth O. Roberts Jeffrey S. Rosenthal

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Abstrak

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.

Topik & Kata Kunci

stat.AP

Penulis (2)

Gareth O. Roberts

Jeffrey S. Rosenthal

Format Sitasi

APA MLA BibTeX

Roberts, G.O., Rosenthal, J.S. (2022). Football Group Draw Probabilities and Corrections. https://arxiv.org/abs/2205.06578

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Informasi Jurnal

Tahun Terbit: 2022
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓