Whether they know it or not, seems they might be:

We explore how umpires’ racial/ethnic preferences are expressed in their evaluation of Major League Baseball pitchers. Controlling for umpire, pitcher, batter and catcher fixed effects and many other factors, strikes are more likely to be called if the umpire and pitcher match race/ethnicity. This effect only exists where there is little scrutiny of umpires’ behavior – in ballparks without computerized systems monitoring umpires’ calls, at poorly attended games, and when the called pitch cannot determine the outcome of the at-bat. If a pitcher shares the home-plate umpire’s race/ethnicity, he gives up fewer hits, strikes out more batters, and improves his team’s chance of winning. The general implication is that standard measures of salary discrimination that adjust for measured productivity may be flawed. We derive the magnitude of the bias generally and apply it to several examples.

Source: "Strike Three: Umpires’ Demand for Discrimination" from IZA DP No. 3899, 12/08

This is one of my favorite baseball books because it reads like a detective novel.

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