Abstract In many sports, such as soccer, a coach has to decide whether to adopt an “offensive” or a “defensive” approach to a match. This strategic decision depends on the strengths and weaknesses of his team with respect to the opponent, but also on the strategy chosen by the opponent’s coach. The fact that a draw also results in a point, which may be important for the ranking, further complicates this decision, as the coach must assess whether it is better to adopt a defensive team formation in order to obtain a draw, or to aim for victory despite the increased risk of defeat. We study this topic by means of a game-theoretical approach, and we develop an algorithm which allows to compute the optimal strategy. The algorithm tests the stability of the outcome with respect to uncertainty in the estimated win probabilities. Furthermore, our approach can handle in-game events, which may provoke changes in optimal strategy. Finally, our model also allows us to assess the effect of various point systems on the willingness of teams to opt for attacking play. Our method is applied to a case study, based on the match Italy – Costa Rica (World Cup 2014).

中文翻译：

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足球中的进攻性或防守性游戏：一种基于游戏理论的方法

摘要在许多运动中，例如足球，教练必须决定对比赛采用“进攻”还是“防守”的方法。这个战略决定取决于他的球队相对于对手的优势和劣势，还取决于对手教练选择的战略。平局也会导致得分的事实，这可能对排名很重要，这使决定变得更加复杂，因为教练必须评估采用防守型球队以取得平局还是瞄准更好胜利，尽管失败的风险增加。我们通过博弈论的方法来研究这个主题，并且我们开发了一种算法，可以计算出最佳策略。该算法根据估计获胜概率中的不确定性来测试结果的稳定性。此外，我们的方法可以处理游戏中的事件，这可能会引发最佳策略的变化。最后，我们的模型还允许我们评估各种积分系统对球队选择进攻性比赛的意愿的影响。我们基于意大利-哥斯达黎加（2014年世界杯）比赛将其方法应用于案例研究。