In this paper we present a novel approach to optimise tactical and strategic decision making in football (soccer). We model the game of football as a multi-stage game which is made up from a Bayesian game to model the pre-match decisions and a stochastic game to model the in-match state transitions and decisions. Using this formulation, we propose a method to predict the probability of game outcomes and the payoffs of team actions. Building upon this, we develop algorithms to optimise team formation and in-game tactics with different objectives. Empirical evaluation of our approach on real-world datasets from 760 matches shows that by using optimised tactics from our Bayesian and stochastic games, we can increase a team chances of winning by up to 16.1\% and 3.4\% respectively.

中文翻译：

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优化足球比赛策略

在本文中，我们提出了一种优化足球（足球）战术和战略决策的新方法。我们将足球比赛建模为多阶段游戏，该游戏由贝叶斯游戏组成，用于对赛前决策进行建模，而随机游戏则用于对赛中状态转换和决策进行建模。使用这个公式，我们提出了一种方法来预测游戏结果的概率和团队行动的回报。在此基础上，我们开发算法以优化具有不同目标的团队形成和游戏中的战术。对来自 760 场比赛的真实世界数据集的方法的实证评估表明，通过使用来自贝叶斯和随机游戏的优化策略，我们可以分别将团队获胜的机会提高 16.1% 和 3.4%。