We consider the task of determining a football player’s ability for a given event type, for example, scoring a goal. We propose an interpretable Bayesian model which is fit using variational inference methods. We implement a Poisson model to capture occurrences of event types, from which we infer player abilities. Our approach also allows the visualisation of differences between players, for a specific ability, through the marginal posterior variational densities. We then use these inferred player abilities to extend the Bayesian hierarchical model of Baio and Blangiardo (2010, Journal of Applied Statistics, 37(2), 253–264) which captures a team’s scoring rate (the rate at which they score goals). We apply the resulting scheme to the English Premier League, capturing player abilities over the 2013/2014 season, before using output from the hierarchical model to predict whether over or under 2.5 goals will be scored in a given game in the 2014/2015 season. This validates our model as a way of providing insights into team formation and the individual success of sports teams.

中文翻译：

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确定足球运动员能力的贝叶斯方法

我们考虑确定给定事件类型（例如进球）的足球运动员能力的任务。我们提出了一个可解释的贝叶斯模型，该模型适合使用变分推理方法。我们实现了一种泊松模型来捕获事件类型的发生，从而从中推断玩家的能力。我们的方法还可以通过边际后方变化密度来可视化特定能力下玩家之间的差异。然后，我们使用这些推断的玩家能力来扩展Baio和Blangiardo的贝叶斯层次模型（2010年，《应用统计》，37（2），253–264），该数据可反映出球队的得分率（他们进球的得分率）。我们将所得方案应用于英超联赛，在2013/2014赛季中捕获球员的能力，然后使用分层模型的输出来预测在2014/2015赛季中给定游戏中进球数是否超过2.5个。这验证了我们的模型是提供洞察团队形成和运动队个人成功的一种方式。