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Modifying Bradley-Terry and other ranking models to allow ties

Baker, Rose and Scarf, Philip 2021. Modifying Bradley-Terry and other ranking models to allow ties. IMA Journal of Management Mathematics 32 (4) , pp. 451-463. 10.1093/imaman/dpaa027

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Abstract

Models derived from distributions of order-statistics are useful for modelling ranked data. The well-known Bradley–Terry (BT) and Plackett–Luce (PL) models can be derived from the order statistics of the exponential distribution but cannot handle ties. However, ties often occur in sports, and the ability to accommodate them leads to more useful ranking models. In this paper, we use discrete distributions, principally the geometric distribution, to obtain modified BT and PL models and some others that allow tied ranks. Our methodology is introduced for some mathematically tractable and some less tractable distributions and is illustrated using test match cricket.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Business (Including Economics)
Publisher: Oxford University Press: IMA
ISSN: 1471-678X
Date of First Compliant Deposit: 18 December 2020
Date of Acceptance: 8 November 2020
Last Modified: 09 Dec 2021 16:30
URI: https://orca.cardiff.ac.uk/id/eprint/137067

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