Modifying Bradley–Terry and other ranking models to allow ties

Baker, RD; Scarf, PA

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.

Citation

Baker, R., & Scarf, P. (2021). Modifying Bradley–Terry and other ranking models to allow ties. IMA Journal of Management Mathematics, 32(4), 451-463. https://doi.org/10.1093/imaman/dpaa027

• Journal Article Type: Article
• Acceptance Date: Nov 8, 2020
• Online Publication Date: Dec 9, 2020
• Publication Date: Oct 1, 2021
• Deposit Date: Sep 15, 2021
• Journal: IMA Journal of Management Mathematics
• Print ISSN: 1471-678X
• Electronic ISSN: 1471-6798
• Publisher: Oxford University Press
• Volume: 32
• Issue: 4
• Pages: 451-463
• DOI: https://doi.org/10.1093/imaman/dpaa027
• Publisher URL: https://doi.org/10.1093/imaman/dpaa027
• Related Public URLs: http://imaman.oxfordjournals.org/
• Additional Information: Additional Information : ** Article version: VoR ** From Crossref journal articles via Jisc Publications Router **Journal IDs: pissn 1471-678X; eissn 1471-6798 **History: published 06-09-2021; issued 09-12-2020; published_online 09-12-2020 **License for this article: starting on 09-12-2020, , https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model