Introducing Grid WAR: Rethinking WAR for Starting Pitchers

In recent years, the baseball statistic "Wins Above Replacement" (WAR) has emerged as one of the most popular evaluation metrics. It is different from fundamental counting statistics such as batting average, strikeouts, or home runs insofar as it is not readily observed and tabulated; WAR is an estimate of a parameter in a vaguely defined model and 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 is not linear with respect to any counting statistic; in particular, WAR must be a convex function of the number of runs allowed in a game. To repair this defect (among many others), we devise a new measure, Grid WAR (GWAR), which estimates a starting pitcher's WAR on a per-game basis. We then define a starting pitcher's seasonal GWAR as the sum of the GWAR of each of his games. Formulated this way, GWAR is indeed a convex function of runs allowed. We find that averaging pitcher performance over the course of an entire season tends to, in general, undervalue worse pitchers and overvalue better pitchers. This is because the convexity of GWAR diminishes the seasonal impact of any game in which a pitcher allows many runs. Moreover, we show that Grid WAR has predictive as well as historical value insofar as a pitcher's historical 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.