Beyond Expected Goals: A Probabilistic Framework for Shot Occurrences in Soccer

TL;DR

This paper introduces xG+, a probabilistic framework that models shot occurrence and quality in soccer at the possession level, improving prediction accuracy and player skill assessment over traditional expected goals models.

Contribution

xG+ jointly models shot occurrence and quality at the possession level, addressing limitations of standard xG models by providing more accurate predictions and player insights.

Findings

Improves team-level shot prediction accuracy

Produces more persistent player skill signals

Remedies conditioning-on-shots limitation of standard xG

Abstract

Expected goals (xG) models estimate the probability that a shot results in a goal from its context (e.g., location, pressure), but they operate only on observed shots. We propose xG+, a possession-level framework that first estimates the probability that a shot occurs within the next second and its corresponding xG if it were to occur. We also introduce ways to aggregate this joint probability estimate over the course of a possession. By jointly modeling shot-taking behavior and shot quality, xG+ remedies the conditioning-on-shots limitation of standard xG. We show that this improves predictive accuracy at the team level and produces a more persistent player skill signal than standard xG models.