从机器学习转向统计学：以美式橄榄球中的预期得分为例
Moving from Machine Learning to Statistics: the case of Expected Points in American football
AI总结：
针对机器学习估计美式橄榄球预期得分时的选择偏差、过拟合、不确定性缺失和数据依赖问题，本文构建统计预期得分模型，并提出用催化先验平滑机器学习模型的通用方法。
摘要：
预期得分是一种价值函数，在整个体育分析（尤其是美式橄榄球）中对球员评估和比赛中的战略决策都至关重要。为了估计预期得分，橄榄球分析师使用机器学习工具，但这些工具无法应对某些挑战。它们存在选择偏差，表现出反直觉的过拟合伪影，不能量化点估计中的不确定性，也没有考虑观测橄榄球数据中强烈的依赖结构。这些问题并非美式橄榄球乃至体育分析所独有；它们是分析师在各种统计应用中都会遇到的普遍问题，尤其是在用机器学习替代传统统计模型时。我们详细探讨了这些问题，并设计了能够将其纳入考量的预期得分模型。我们还提出了一种适用范围广泛的新型方法论来缓解过拟合，即使用催化先验来平滑我们的机器学习模型。
英文摘要：
Expected points is a value function fundamental to player evaluation and strategic in-game decision-making across sports analytics, particularly in American football. To estimate expected points, football analysts use machine learning tools, which are not equipped to handle certain challenges. They suffer from selection bias, display counter-intuitive artifacts of overfitting, do not quantify uncertainty in point estimates, and do not account for the strong dependence structure of observational football data. These issues are not unique to American football or even sports analytics; they are general problems analysts encounter across various statistical applications, particularly when using machine learning in lieu of traditional statistical models. We explore these issues in detail and devise expected points models that account for them. We also introduce a widely applicable novel methodological approach to mitigate overfitting, using a catalytic prior to smooth our machine learning models.
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。
