用贝叶斯框架量化球员射门能力，支持'如果换人会怎样'的模拟分析。
What If They Took the Shot? A Hierarchical Bayesian Framework for Counterfactual Expected Goals
- 构建分层贝叶斯模型，融合专家评分与真实数据，稳定少数射门球员的估计。
- 模型预测与基准相关性达R²=0.75，识别出阿圭罗、萨拉赫等球员的专项能力。
- 可进行球员间射门机会重分配模拟，揭示替换策略对进球预期的显著影响。
本研究提出一种分层贝叶斯框架，整合专家领域知识以量化球员个体差异在预期进球（xG）估算中的作用，弥补传统模型将所有球员视为同质射手的缺陷。基于StatsBomb 2015-16赛季9,970次射门数据及Football Manager 2017评分，结合贝叶斯逻辑回归与有信息先验，稳定低样本球员的估计结果。分层模型相比弱先验显著降低后验不确定性，外部有效性强：分层与基线预测相关系数R²=0.75，XGBoost基准与StatsBomb xG对比达R²=0.833。模型揭示可解释的专长特征，包括一对一射门（阿圭罗、苏亚雷斯、贝洛蒂、伊姆比佩、马蒂厄）、远射（博格巴）、第一触球完成（因西涅、萨拉赫、加梅罗）。同时发现表现不佳球员如伊姆比佩和贝洛蒂的潜在能力。该框架支持条件一致下的反事实“如果他们射门”分析。案例显示，桑松若接替贝拉迪的射门机会，可带来+2.2 xG提升，主要源于高压情境；而瓦尔迪与吉鲁互换则呈现显著不对称：瓦尔迪换吉鲁导致约-7 xG下降，反向替换仅约-1 xG影响。本工作为球员评估、引援与战术规划提供带不确定性的工具，并为技能与情境共同影响表现的领域提供通用方法。
原文摘要 · Abstract (English)
This study develops a hierarchical Bayesian framework that integrates expert domain knowledge to quantify player-specific effects in expected goals (xG) estimation, addressing a limitation of standard models that treat all players as identical finishers. Using 9,970 shots from StatsBomb's 2015-16 data and Football Manager 2017 ratings, we combine Bayesian logistic regression with informed priors to stabilise player-level estimates, especially for players with few shots. The hierarchical model reduces posterior uncertainty relative to weak priors and achieves strong external validity: hierarchical and baseline predictions correlate at R2 = 0.75, while an XGBoost benchmark validated against StatsBomb xG reaches R2 = 0.833. The model uncovers interpretable specialisation profiles, including one-on-one finishing (Aguero, Suarez, Belotti, Immobile, Martial), long-range shooting (Pogba), and first-touch execution (Insigne, Salah, Gameiro). It also identifies latent ability in underperforming players such as Immobile and Belotti. The framework supports counterfactual "what-if" analysis by reallocating shots between players under identical contexts. Case studies show that Sansone would generate +2.2 xG from Berardi's chances, driven largely by high-pressure situations, while Vardy-Giroud substitutions reveal strong asymmetry: replacing Vardy with Giroud results in a large decline (about -7 xG), whereas the reverse substitution has only a small effect (about -1 xG). This work provides an uncertainty-aware tool for player evaluation, recruitment, and tactical planning, and offers a general approach for domains where individual skill and contextual factors jointly shape performance.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。