Lopez (2020) demonstrates clearly how the lack of precise, high-quality data can lead to imprecise results or analyses. In particular, this paper shows that once you know the precise distance to the first down line (“yards to go”) rather than just the integer-valued distances provided in the NFL’s play-by-play data, the decisions made by coaches are more closely in line with what we would expect from rational, data-driven decision-makers in their situation. However, from anNFL team’s perspective, it is unclear if player-tracking data was necessary to help individual coaches in this particular case. Could NFL teams and coaches make approximately the same decisions from a model trained on only play-by-play data, but evaluated in real-time with more precise inputs for yards to go? Fourth-down decisions are typically analyzed with expected points models and/or win probability models (Romer 2006). When making fourth-down decisions, analysts contend that NFL teams should input their current game situation into one of these models (including information such as the down, distance, yard line, score differential, time remaining, etc), and analyze the output. If the model’s computed win probability for a given situation is maximized by “going for it,” the coach should leave the offense on the field; if win probability is maximized by punting, the coach should elect to punt; and if it is maximized by attempting a field goal, the coach should put his field goal unit on the field. Yurko, Horowitz andVentura (2019) provide a detailed explanation of how to build expected points and win probability models, but briefly, the expected points model is a linear model (specifically, a multinomial logistic regression model), and the win probability model is a generalized additive model. Importantly, although only integer-valueddistances (“yards to go”) areprovided in the

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接下来我们将学到什么？洛佩兹（2020）的含义

洛佩兹（Lopez，2020年）清楚地证明了缺乏精确，高质量的数据如何导致不精确的结果或分析。特别是，本文显示，一旦您知道到第一条下降线的精确距离（“走的码数”），而不仅仅是NFL逐场比赛数据中提供的整数值距离，教练的决定就是更符合我们对理性，以数据为导向的决策者所处境地的期望。但是，从NFL团队的角度来看，尚不清楚在这种特殊情况下是否需要球员跟踪数据来帮助单个教练。NFL球队和教练能否根据仅根据逐项比赛数据训练的模型做出大致相同的决定，但是要进行实时评估，并提供更精确的输入码以供选择？通常采用期望点模型和/或获胜概率模型来分析第四向下决策（Romer 2006）。在做出第四击倒的决定时，分析师认为NFL球队应将其当前比赛情况输入这些模型之一（包括诸如击倒，距离，码线，得分差，剩余时间等信息），并分析输出结果。如果通过“坚持下去”使模型在给定情况下的获胜概率最大化，则教练应将进攻留在现场；如果通过打底球使获胜的可能性最大化，教练应选择打底球；如果尝试射门得分使射门得分最大化，教练应将其射门得分单位放在射门上。尤尔科 Horowitz和Ventura（2019）提供了有关如何建立期望点和获胜概率模型的详细说明，但简单来说，期望点模型是线性模型（具体来说是多项式Lo​​gistic回归模型），获胜概率模型是广义加性模型。重要的是，尽管只有整数值的距离（“要走的码”）在