Analytics，请保持谦逊：第四次进攻决策的统计学视角
Analytics, have some humility: a statistical view of fourth-down decision making
AI总结：
本文从统计学视角指出，基于机器学习的美式橄榄球第四次进攻决策存在巨大不确定性，通过 bootstrapping 方法量化不确定性，发现其实际不确定性远超体育媒体分析师所表达的程度。
摘要：
美式橄榄球第四次进攻决策的标准数学方法，是做出最大化估计获胜概率的决策。获胜概率估计源于由历史数据拟合的机器学习模型。这些模型试图捕捉嘈杂二元结果变量与充满交互和非线性的比赛状态变量之间的微妙关系，数据集仅包含几千场比赛。因此，必须将不确定性量化融入第四次进攻决策程序；我们使用 bootstrapping 实现了这一点。我们发现，估计的最优第四次进攻决策的不确定性，远大于当前体育分析师在大众体育媒体中所表达的不确定性。
英文摘要：
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 attempt to capture a nuanced relationship between a noisy binary outcome variable and game-state variables replete with interactions and non-linearities from a finite dataset of just a few thousand games. 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
