I haven't seen it for a number of years but there was a website that kept track of hitters' batting averages for each home plate umpires for the season. The home plate umpires will average around 40 games a year behind the plate.

 

Does anyone keep track of this anymore? The one year I remember there was a large gap between the highest and lowest batting average.

Baseball Reference keeps track of umpire records for pitchers, but not for hitters.

I couldn't find it baseball-reference. . There are other umpire stats websites but I haven't found one that list batting averages when behind the plate. They used to have it on some gambling site.

This isn't totally what you're looking for, but interesting none the less

 

http://www.thespread.com/mlb-baseball-umpire-stats#.UtK_Tp5dXNl