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A copula-based multivariate hidden Markov model for modelling momentum in football

Author

Listed:
  • Marius Ötting

    (Bielefeld University)

  • Roland Langrock

    (Bielefeld University)

  • Antonello Maruotti

    (Libera Universita Maria Ss. Assunta
    University of Bergen)

Abstract

We investigate the potential occurrence of change points—commonly referred to as “momentum shifts”—in the dynamics of football matches. For that purpose, we model minute-by-minute in-game statistics of Bundesliga matches using hidden Markov models (HMMs). To allow for within-state dependence of the variables, we formulate multivariate state-dependent distributions using copulas. For the Bundesliga data considered, we find that the fitted HMMs comprise states which can be interpreted as a team showing different levels of control over a match. Our modelling framework enables inference related to causes of momentum shifts and team tactics, which is of much interest to managers, bookmakers, and sports fans.

Suggested Citation

  • Marius Ötting & Roland Langrock & Antonello Maruotti, 2023. "A copula-based multivariate hidden Markov model for modelling momentum in football," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(1), pages 9-27, March.
    • Handle: RePEc:spr:alstar:v:107:y:2023:i:1:d:10.1007_s10182-021-00395-8
    DOI: 10.1007/s10182-021-00395-8
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    References listed on IDEAS

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    1. David W. Lehman & Jungpil Hahn, 2013. "Momentum and Organizational Risk Taking: Evidence from the National Football League," Management Science, INFORMS, vol. 59(4), pages 852-868, April.
    2. Marius Ötting & Roland Langrock & Christian Deutscher & Vianey Leos‐Barajas, 2020. "The hot hand in professional darts," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(2), pages 565-580, February.
    3. Härdle, Wolfgang Karl & Okhrin, Ostap & Wang, Weining, 2015. "Hidden Markov Structures For Dynamic Copulae," Econometric Theory, Cambridge University Press, vol. 31(5), pages 981-1015, October.
    4. Bruno Gonçalves & Diogo Coutinho & Sara Santos & Carlos Lago-Penas & Sergio Jiménez & Jaime Sampaio, 2017. "Exploring Team Passing Networks and Player Movement Dynamics in Youth Association Football," PLOS ONE, Public Library of Science, vol. 12(1), pages 1-13, January.
    5. Chris Sherlock & Tatiana Xifara & Sandra Telfer & Mike Begon, 2013. "A coupled hidden Markov model for disease interactions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(4), pages 609-627, August.
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    Cited by:

    1. Marius Ötting & Dimitris Karlis, 2023. "Football tracking data: a copula-based hidden Markov model for classification of tactics in football," Annals of Operations Research, Springer, vol. 325(1), pages 167-183, June.

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