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The standard mathematical approach to fourth-down decision making in Americanfootball is to make the decision that maximizes estimated win probability. Winprobability estimates arise from machine learning models fit from historicaldata. These models, however, are overfit high-variance estimators, exacerbatedby the highly correlated nature of football play-by-play data. Thus, it isimperative to knit uncertainty quantification into the fourth-down decisionprocedure; we do so using bootstrapping. We find that uncertainty in theestimated optimal fourth-down decision is far greater than that currentlyexpressed by sports analysts in popular sports media. Our contribution is amajor advance in fourth-down strategic decision making: far fewer fourth-downdecisions are as obvious as analysts claim.

Analytics, have some humility: a statistical view of fourth-down decision making