Using a Markov process model of an association football match to determine the optimal timing of substitution and tactical decisions

Authors: Hirotsu N.¹; Wright M.¹; Correspondence

Source: Journal of the Operational Research Society, Volume 53, Number 1, 1 January 2002 , pp. 88-96(9)

Publisher: Palgrave Macmillan

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Abstract:

A football match is modelled as a four-state Markov process. A log-linear model, fed by real data, is used to estimate transition probabilities by means of the maximum likelihood method. This makes it possible to estimate the probability distributions of goals scored and the expected number of league points gained, from any position in a match, for any given set of transition probabilities and hence in principle for any match. This approach is developed in order to estimate the optimal time to change tactics using dynamic programming, either by making a substitution or by some other conscious change of plan. A simple example of this approach is included as an illustration.

Journal of the Operational Research Society (2002) 53, 88–96. DOI: 10.1057/palgrave/jors/2601254

Keywords: football; Markov process; soccer; sports; decision; tactics

Document Type: Miscellaneous

Affiliations: 1: Lancaster University, Lancaster, UK

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