The baseball statistic "Wins Above Replacement" (WAR) has emerged as one of the most popular evaluation metrics. But it is not readily observed and tabulated; WAR is an estimate of a parameter in a vaguely defined model with all its attendant assumptions. Industry-standard models of WAR for starting pitchers from FanGraphs and Baseball Reference all assume that season-long averages are sufficient statistics for a pitcher's performance. This provides an invalid mathematical foundation for many reasons, especially because WAR should not be linear with respect to any counting statistic. To repair this defect, as well as many others, we devise a new measure, Grid WAR, which accurately estimates a starting pitcher's WAR on a per-game basis. The convexity of Grid WAR diminishes the impact of "blow-up" games and upweights exceptional games, raising the valuation of pitchers like Sandy Koufax, Whitey Ford, and Catfish Hunter who exhibit fundamental game-by-game variance. Grid WAR is designed to accurately measure past performance, but also has predictive value insofar as a pitcher's Grid WAR is better than WAR at predicting future performance. Finally, at https://gridwar.xyz we host a Shiny app which displays the Grid WAR results of each MLB game since 1952, including career, season, and game level results, which updates automatically every morning.

翻译：棒球统计指标“胜利替代值”（WAR）已成为最受欢迎的评价指标之一。然而，它并非可直接观测和制表；WAR是一个定义模糊的模型中对某一参数的估计值，且伴随着各种假设。来自FanGraphs和Baseball Reference的行业标准先发投手WAR模型均假定赛季平均统计量足以代表投手表现。这从诸多方面提供了无效的数学基础，尤其因为WAR不应与任何计数统计量呈线性关系。为解决这一缺陷及其他诸多问题，我们设计了一个新指标——Grid WAR，它能基于每场比赛准确估算先发投手的WAR值。Grid WAR的凸性削弱了“崩盘”比赛的影响，并提升了突出比赛的权重，从而提高了诸如Sandy Koufax、Whitey Ford和Catfish Hunter等展现出显著逐场方差投手的估值。Grid WAR旨在精确衡量过去表现，同时也具有预测价值——投手的Grid WAR在预测未来表现方面优于传统WAR。最后，我们在https://gridwar.xyz托管了一个Shiny应用，展示自1952年以来每场MLB比赛的Grid WAR结果，包括职业生涯、赛季及单场数据，该应用每日清晨自动更新。