Bayes-xG: player and position correction on expected goals (xG) using Bayesian hierarchical approach

Area of Science:

• Sports Analytics
• Statistical Modeling
• Football Analytics

Background:

• The expected goals (xG) metric is crucial for evaluating shot quality in football.
• Understanding factors influencing xG, such as player position and individual skill, is vital for performance analysis.

Purpose of the Study:

• To investigate the impact of player position and individual player effects on predicting expected goals (xG) using Bayesian methodologies.
• To determine if player or positional factors significantly influence the probability of a shot resulting in a goal.

Main Methods:

• Bayesian hierarchical logistic regressions were applied to football shot data.
• Analysis utilized publicly available StatsBomb data from the English Premier League, Spain's La Liga, and Germany's Bundesliga.
• Models incorporated predictors such as distance to goal, shot angle, and player-specific adjustments.

Main Results:

• Positional effects on xG were observed in basic models, with forwards and attacking midfielders showing higher scoring likelihood.
• These positional effects diminished with the inclusion of more informative predictors.
• Significant player-level effects persisted, indicating that individual players have distinct impacts on their xG, independent of other factors.

Conclusions:

• Player-specific adjustments are a persistent and significant factor in expected goals (xG) prediction.
• Bayesian models provide sound results for analyzing football shot data, though prior distribution choices can be refined for efficiency.
• The findings offer valuable insights for player evaluation and tactical analysis in football.