Expected goals under a Bayesian viewpoint: uncertainty quantification and online learning

While the use of expected goals (xG) as a metric for assessing soccer performance is increasingly prevalent, the uncertainty associated with their estimates is often overlooked. This work bridges this gap by providing easy-to-implement methods for uncertainty quantification in xG estimates derived from Bayesian models. Based on a convenient posterior approximation, we devise an online prior-to-posterior update scheme, aligning with the typical in-season model training in soccer. Additionally, we present a novel framework to assess and compare the performance dynamics of two teams during a match, while accounting for evolving match scores. Our approach is well-suited for graphical representation and improves interpretability. We validate the accuracy of our methods through simulations, and provide a real-world illustration using data from the Italian Serie A league.