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

Singh, A; Scarf, P; Baker, RD

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.

Citation

Singh, A., Scarf, P., & Baker, R. (2022). A unified theory for bivariate scores in possessive ball-sports: the case of handball. European Journal of Operational Research, 304(3), 1099-1112. https://doi.org/10.1016/j.ejor.2022.05.010

• Journal Article Type: Article
• Acceptance Date: May 6, 2022
• Online Publication Date: May 13, 2022
• Publication Date: May 13, 2022
• Deposit Date: Jul 29, 2022
• Publicly Available Date: Jul 29, 2022
• Journal: European Journal of Operational Research
• Print ISSN: 0377-2217
• Publisher: Elsevier
• Volume: 304
• Issue: 3
• Pages: 1099-1112
• DOI: https://doi.org/10.1016/j.ejor.2022.05.010
• Publisher URL: https://doi.org/10.1016/j.ejor.2022.05.010