Using Pitch F/X to Determine an Umpire's Strike Zone

With Pitch F/X there has been quite a bit of work on looking at different pitchers. I decided to extend the work I did on umpire scoring and link that information to pitch F/X. I used the standard strike zone of -1, 1 for the width of home plate and then adjusted the batter's height to the vertical standard of 1.5 to 3.5. Here is a spreadsheet with the percentage of pitches that each umpire called strikes and ball and and how they compare to the standard strike zone (-1,1 to 1.5,3.5). I drew the cutoff line to include umpires with more than 1456 called balls and strikes (The bottom 11 umpires called 918 or less strikes).

Then, I ask for some help in determine what percent of pitches in a zone should constitute the area that balls and strikes are normally called by the umpire. I decided to take their advice and use the value of 90%. I increased or decreased the standard strike zone in equal increments until 90% of the pitches were strikes or balls. Here is the dimensions of the strike zone (along with the percentages of correct calls with the normal zone). I added these two differences together to get the amount these areas overlap (inconsistency of the umpire).

Average value for:	Value
% of strikes called strikes	78.8%
% of balls called balls	85.4%
% correct	83.2%
Adjustment for Strikes (90% zone)	0.15
Adjustment of Called Balls (90% zone)	0.09
Combined Adjustment Distance	0.24

Here is an image of the normal strike zone (black) along with the actual zone where strikes are called strikes (inside the red square) and the zone when balls are called balls(area outside the yellow box) 90% of the time.

After that, I went ahead and determined the zone for each individual umpire (on previously link spreadsheet).

Finally for a few of umpires, I have looked to find find how their strike zone compared to a centered zone. Basically, do they call the a little lower or outside. I having a tough time find a good to determine this zone, but am making progress, I will update these values as I figure them out and will let everyone know when the values are complete.

I went ahead and linked the previous data I had on umpire effects to the Pitch F/X, but I am wanting to do the R/G, K/G, etc for the same seasons I did the pitch F/X analysis. I want to include park factors and finally get an umpire factor for each umpire that can be applied to each pitcher to see how much the home plate umpire effected their season. As always thanks for your time and and I am open to comments and suggestions.