Measuring umpire Functionality
1 common method of assessing umpire performance is to have a binary outcome variable (was a shot pitch called a strike or a ball?) And compare it to a binary explanatory variable (was a taken pitch really a hit or a ball?) . While this and other types of accuracy measures are informative (as in this FanGraphs article), they also lose information. In dismissing the exact location of where each pitch crossed the strike zone, then a pitch straight down the center, for instance, is treated exactly the same as one an inch inside the corner of the plate.
Luckily, MLB supplies the exact location of each taken pitch as it crossed the plate. Given that the attack zone—at least how it’s called by umpires—more closely resembles an oval than a rectangle, generalized additive models (for more about GAMs, see examples here, here, and here) are a recommended tool. GAMs are attractive for attack identification in that an analyst does not need to, a priori, identify the exact association between pitch location and strike odds and instead can allow the data drive the most plausible relationship.
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