Bradley–Terry modeling with multiple game outcomes with applications to College Hockey
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Date
2021
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Whelan, John T.
Klein, Jacob E.
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Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky
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Abstract
The Bradley–Terry model has previously been used in both Bayesian and frequentist interpretations to evaluate the strengths of sports teams based on win-loss game results. It has also been extended to handle additional possible results such as ties. We implement a generalization which includes multiple possible outcomes such as wins or losses in regulation, overtime, or shootouts. A natural application is to ice hockey competitions such as international matches, European professional leagues, and NCAA hockey, all of which use a zero-sum point system which values overtime and shootout wins as 2/3 of a win, and overtime and shootout losses as 1/3 of a win. We incorporate this into the probability model, and evaluate the posterior distributions for the associated strength parameters using techniques such as Gaussian expansion about maximum a posteriori estimates, and Hamiltonian Monte Carlo.
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Mathematics for Applications. 2021 vol. 10, č. 2, s. 157-177. ISSN 1805-3629
http://ma.fme.vutbr.cz/archiv/10_2/ma_10_2_whelan_klein_proof_final.pdf
http://ma.fme.vutbr.cz/archiv/10_2/ma_10_2_whelan_klein_proof_final.pdf
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Peer-reviewed
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en
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© Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky