Stochastic modelling of football matches using dynamic regressors

Luiz Fernando G.N. Maia, Teemu Pennanen, Moacyr A.H.B. da Silva and Rodrigo S. Targino

International Journal of Forecasting, 2026, vol. 42, issue 2, 691-707

Abstract: This paper develops a general framework for stochastic modelling of goals and other events in football (soccer) matches. The events are modelled as Cox processes (doubly stochastic Poisson processes) where the event intensities may depend on all the modelled events as well as external factors. The model has a strictly concave log-likelihood function, which facilitates its fitting to observed data. Besides event times, the model describes the random lengths of stoppage times, which can have a strong influence on the final score of a match. The model is illustrated on eight years of data from Campeonato Brasileiro de Futebol Série A. We find that dynamic regressors significantly improve the in-game predictive power of the model. In particular, (a) when a team receives a red card, its goal intensity decreases more than 30%; (b) the goal scoring rate of a team increases by 10% if it is losing by one goal and by 20% if its losing by two goals; and (c) when the goal difference at the end of the second half is less than or equal to one, the stoppage time is on average more than one minute longer than in matches with a difference of two or more goals.

Keywords: Stochastic football modelling; In-game forecasts; Cox process; Convex optimization; Dynamic regressors (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:intfor:v:42:y:2026:i:2:p:691-707

DOI: 10.1016/j.ijforecast.2025.10.006

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