A unified theory for bivariate scores in possessive ball-sports: the case of handball

Singh, A ORCID: https://orcid.org/0000-0002-1588-1862, Scarf, P ORCID: https://orcid.org/0000-0001-5623-906X and Baker, RD ORCID: https://orcid.org/0000-0003-3555-3425 2022, 'A unified theory for bivariate scores in possessive ball-sports: the case of handball' , European Journal of Operational Research .

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Abstract

We present a unified theory that posits three fundamental models as necessary and sufficient for modelling the bivariate scores in possessive ball-sports. These models provide the basis for perhaps more complicated models that can be used for prediction, experimentation, and explanation. First is the Poisson-match, for when goals are rare, or when goals are frequent but the restart after a goal is contested. Second is the binomial-match, for when goals are frequent and the restart uses the alternating rule. Third is the Markov-match, for when the restart uses the catch-up rule. We describe in detail the new model among these, the Markov-match, which is complementary to rather than competing with the binomial-match. The Markov-match is a bivariate generalisation of the Markov-binomial distribution. Its structure (catch-up restart) induces a larger correlation between the scores of competitors than does the binomial-match (alternating restart) but slightly more tied outcomes. The Markov-match is illustrated using handball, a high-scoring sport. In our analysis the time-varying strengths of 45 international handball teams are estimated. This poses some mathematical and computational problems, and in particular we describe how to shrink the strength-estimates of teams that play fewer games in tournaments because they are weaker. For the handball results, the Markov-match gives a better fit to data than the Poisson-match.

Item Type: Article
Schools: Schools > Salford Business School
Journal or Publication Title: European Journal of Operational Research
Publisher: Elsevier
ISSN: 0377-2217
SWORD Depositor: Publications Router
Depositing User: Publications Router
Date Deposited: 29 Jul 2022 11:13
Last Modified: 29 Jul 2022 11:13
URI: http://usir.salford.ac.uk/id/eprint/63938

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