Skill or chance? A Bayesian analysis of dependence and heterogeneity in penalty shootouts in football

Document Type

Article

Publication Title

Journal of Sports Analytics

Abstract

Penalty shootouts in association football are sometimes criticized by fans and pundits as an imperfect tie-breaking procedure. In this study, we analyze through a Bayesian model if shootouts are governed more by skill or by chance. Using a representative dataset from twelve recent European seasons, we fit a hierarchical logistic model with appropriate random effects and a within–shootout latent autoregressive state to capture evolving pressure. The model is implemented through Hamiltonian Monte Carlo approach. Our proposed framework allows us to quantify the amount of skill involved in shootouts by the proportion of logit-scale variance attributable to persistent heterogeneity versus idiosyncratic and state noise. We also compare the full specification to nested alternatives via PSIS-LOO, stacking, and decision-oriented scores computed from leave-one-shootout-out predictive distributions. Empirically, persistent individual effects are found to be small: the posterior SkillShare is near zero in the full model, suggesting that shootouts are primarily chance dominated. As a byproduct of our approach, we show how the proposed model can also be utilized to rank the shooters as well as to optimize penalty-taking orders. We also discuss a few alternative tie-breaking procedures as future recommendations which can be evaluated in a similar modeling framework.

Publication Date

24-4-2026

Publisher

Sage Publishing

Volume

Vol.12

Link to Full Text
Request Access

Share

COinS