The standard mathematical approach to fourth-down decision making in American football is to make the decision that maximizes estimated win probability. Win probability estimates arise from a statistical model fit from historical data. These machine learning models, however, are overfit high-variance estimators, exacerbated by the highly correlated nature of football play-by-play data. We develop a machine learning framework that accounts for this auto-correlation and knits uncertainty quantification into our decision making. In particular, we recommend a fourth-down decision when we are confident it has higher win probability than all other decisions. Our final product is a major advance in fourth-down strategic decision making: far fewer fourth-down decisions are as obvious as analysts claim.

翻译：美式橄榄球中第四档决策的标准数学方法是选择最大化预期获胜概率的方案。获胜概率的估计源自基于历史数据拟合的统计模型。然而，这些机器学习模型是过拟合的高方差估计器，而橄榄球比赛实时数据的强相关性进一步加剧了这一问题。我们开发了一个机器学习框架，该框架考虑了这种自相关性，并将不确定性量化融入决策过程。具体而言，我们仅在确信某一第四档决策的获胜概率高于其他所有选项时，才推荐其执行。我们的最终成果是第四档战略决策领域的重大突破：与分析师所宣称的情况不同，实际上远没有那么多第四档决策是显而易见的。