Traditional methods of computing WAR (wins above replacement) for pitchers are based on an invalid mathematical foundation. Consequently, these metrics, which produce reasonable values for many pitchers, can be substantially inaccurate for some. Specifically, FanGraphs and Baseball Reference compute a pitcher's WAR as a function of his performance averaged over the entire season. This is wrong because WAR must be a convex function of the number of runs allowed by the pitcher in a game. Hence we propose a new way to compute WAR for starting pitchers: Grid WAR (GWAR). The idea is to compute a starter's GWAR for each of his individual games, and define a starter's seasonal GWAR as the sum of the GWAR of each of his games. We show that GWAR is indeed a convex function in the number of runs allowed during a game. As such, GWAR accounts for a fundamental baseball principle that not all runs allowed have the same impact in determining the outcome of a game: for instance, the difference in GWAR between allowing 1 run in a game instead of 0 is much greater than the difference in GWAR between allowing 6 runs in a game instead of 5. Moreover, Jensen's inequality implies that, by ignoring the convexity of WAR, current implementations of WAR undervalue certain pitchers, particularly those who allow few runs (specifically, 0 or 1 run) in many games. It also unfairly penalizes pitchers who are credited with a large number of runs in a short outing. These flaws are corrected by GWAR.
翻译:计算投手的传统的 WAR (胜于替换) 方法基于一个无效的数学基础。 因此, 这些为许多投手创造合理值的衡量标准对一些人来说可能在很大程度上不准确。 具体地说, FanGraphs 和 Basball Reference 将投手的战争计算成其整个赛季平均性能的函数。 这是错误的, 因为 WAR 必须是投手在游戏中允许的赛跑次数的组合函数。 因此, 我们提出一种新的方法来计算开球投手的比赛的计算方法: Gred War (GWAR) 。 其想法是计算一个启动者为许多投手的游戏的合理值, 对于每个投手的投手者来说,这些衡量标准可能大大不准确。 GWAR 的季节性 GWAR 的季节性 GWAR, 定义一个季节性 GWA 的游戏的总和数。 在游戏中, GWA 的赢率比赢家的赢家的赢家要大得多。