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

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Abstract
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.

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