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 machine learning models fit from historical data. These models, however, are overfit high-variance estimators, exacerbated by the highly correlated nature of football play-by-play data. Thus, it is imperative to knit uncertainty quantification into the fourth-down decision procedure; we do so using bootstrapping. We find that uncertainty in the estimated optimal fourth-down decision is far greater than that currently expressed by sports analysts in popular sports media. Our contribution is a major advance in fourth-down strategic decision making: far fewer fourth-down decisions are as obvious as analysts claim.

翻译：美式橄榄球中第四次进攻决策的标准数学方法，是选择能够最大化预期获胜概率的方案。预期获胜概率的估算依赖于基于历史数据训练的机器学习模型。然而，这些模型是过拟合的高方差估计器，而橄榄球逐回合数据的强相关性进一步加剧了这一问题。因此，将不确定性量化纳入第四次进攻决策流程至关重要——我们通过自助法实现这一点。研究发现，估算的最优第四次进攻决策中的不确定性，远大于当前流行体育媒体中分析师所表达的程度。我们的贡献是第四次进攻战略决策的重大突破：远非分析师声称的那样，绝大多数第四次进攻决策并非如此明确。