Bayes-xG: Player and Position Correction on Expected Goals (xG) using
  Bayesian Hierarchical Approach
Alexander Scholtes Oktay Karakuş
This study employs Bayesian methodologies to explore the influence of player
or positional factors in predicting the probability of a shot resulting in a
goal, measured by the expected goals (xG) metric. Utilising publicly available
data from StatsBomb, Bayesian hierarchical logistic regressions are
constructed, analysing approximately 10,000 shots from the English Premier
League to ascertain whether positional or player-level effects impact xG. The
findings reveal positional effects in a basic model that includes only distance
to goal and shot angle as predictors, highlighting that strikers and attacking
midfielders exhibit a higher likelihood of scoring. However, these effects
diminish when more informative predictors are introduced. Nevertheless, even
with additional predictors, player-level effects persist, indicating that
certain players possess notable positive or negative xG adjustments,
influencing their likelihood of scoring a given chance. The study extends its
analysis to data from Spain's La Liga and Germany's Bundesliga, yielding
comparable results. Additionally, the paper assesses the impact of prior
distribution choices on outcomes, concluding that the priors employed in the
models provide sound results but could be refined to enhance sampling
efficiency for constructing more complex and extensive models feasibly.