Real-time Forecasting Within Soccer Matches Through a Bayesian Lens

Journal: Journal of Royal Statistical Society Series A

Synopsis: The concept of within-game forecasting is turning out to be a very important aspect in soccer, arguably the most watched sport in the world. There are numerous techniques to forecast the outcome of a soccer match based on aggregated data at the beginning of a match, but they lack the flexibility to update the predictions based on the sequence of events during the match. The current study aims to fill the void in existing literature in this domain by constructing a predictive Bayesian model tailored for in-game soccer forecasting. The proposed methodology employs ordinal response modeling, incorporating relevant game covariates and events into a latent variable structure.

The authors model the outcome of a game from the perspective of the team playing at home. With the focus on predicting the outcome in real-time, that is, after every minute of the match. At the end of every minute t, they record a set of covariates from minutes 1 through t. Then, they define a latent variable, modelled as a combination of the effects of time-invariant covariates, time-varying effects of different events and random error. It is important to observe that they use 90 different models for different time points in a complete Bayesian framework to estimate the model parameters and provide a probabilistic forecast for the response variable through the procedure of Gibbs sampling. Due to the Bayesian setup, they can also obtain credible intervals for the predictions at every time-point. For completeness of the study, they compare their model with a few other potential statistical as well as machine learning approaches. They use F1-score and Brier score, to evaluate the predictive accuracy of the models.

In order to show the efficacy of their approach, they use data from English Premier League (EPL) matches from the 2008-09 season to the 2015-16 season. They observe that the proposed model comfortably outperforms the competing models and offers insights about the effects of different events on the outcome. Particularly, they find that not only the goals, but also the events like crosses and corners have defining effect on the potential outcome of the match, especially towards the end of the match. 

Their robustness checks, based on team strength heterogeneity and home advantage, ascertain that the proposed method works across different scenarios. For further illustration, they present the real-time forecasts of two case studies, one of which is shown below (Fig 1). 

They strongly believe that the proposed methodology can be an extremely useful tool to maintain audience engagement in broadcasting soccer matches, or for the betting markets in real-time. It can also be modified and adapted to other applications in future.

Figure 1: Minute-by-minute forecast of win probability for both teams during Chelsea vs Portsmouth