Prediction and evaluation in College Hockey using the Bradley–Terry–Zermelo model

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dc.contributor.authorWhelan, John T.
dc.contributor.authorWodon, Adam
dc.coverage.issue2cs
dc.coverage.volume8cs
dc.date.accessioned2020-05-05T06:21:04Z
dc.date.available2020-05-05T06:21:04Z
dc.date.issued2019cs
dc.description.abstractWe describe the application of the Bradley–Terry model to NCAA Divi-sion I Men’s Ice Hockey. A Bayesian construction gives a joint posterior probabilitydistribution for the log-strength parameters, given a set of game results and a choiceof prior distribution. For several suitable choices of prior, it is straightforward to findthe maximum a posteriori point (MAP) and a Hessian matrix, allowing a Gaussianapproximation to be constructed. Posterior predictive probabilities can be esti-mated by 1) setting the log-strengths to their MAP values, 2) using the Gaussianapproximation for analytical or Monte Carlo integration, or 3) applying importancesampling to re-weight the results of a Monte Carlo simulation. We define a methodto evaluate any models which generate predicted probabilities for future outcomes,using the Bayes factor given the actual outcomes, and apply it to NCAA tournamentresults. Finally, we describe an on-line tool which currently estimates probabilitiesof future results using MAP evaluation and describe how it can be refined using theGaussian approximation or importance sampling.en
dc.formattextcs
dc.format.extent131-149cs
dc.format.mimetypeapplication/pdfen
dc.identifier.citationMathematics for Applications. 2019 vol. 8, č. 2, s. 131-149. ISSN 1805-3629cs
dc.identifier.doi10.13164/ma.2019.09en
dc.identifier.issn1805-3629
dc.identifier.urihttp://hdl.handle.net/11012/186969
dc.language.isoencs
dc.publisherVysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematikycs
dc.relation.ispartofMathematics for Applicationsen
dc.relation.urihttp://ma.fme.vutbr.cz/archiv/8_2/ma_8_2_3_whelan_wodon_final.pdfcs
dc.rights© Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematikycs
dc.rights.accessopenAccessen
dc.titlePrediction and evaluation in College Hockey using the Bradley–Terry–Zermelo modelen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
eprints.affiliatedInstitution.departmentÚstav matematikycs
eprints.affiliatedInstitution.facultyFakulta strojního inženýrstvícs
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