Tom Tango Takes on Umpire Stats
As most people who read The Pastime regularly have noticed, I’ve been hung up on umpire stats a lot lately. I’ve used graphs, tables and charts to try and get an idea of how varied MLB umpires really are.
I tried to shine my candle into the depths and shadows of the under-explored topic. I believe that I illuminated enough to come away with a pretty good idea of the umpires’ individual traits.
Tom Tango, aka tangotiger, the man behind The Book, and someone I’d consider to be one of the most influential sabermetricians of our era, chose to turn his analytical floodlight onto our hypothetical dark corner of umpire stats.
Here’s what he has to say on the topic:
I added the “strikes + balls” of each umpire. (Balls in Play were excluded. And, it seems that the data is somewhat off, as I expected strikes+balls+battedBall to equal pitches. It doesn’t.)
I took the 64 umpires with the most strikes+balls (which I’ll now call pitches, which I hope is not confusing.) The strike percentage, or strikes per pitch, was .534. I figured for each umpire what one standard deviation would be, if all calls followed a binomial around this population mean. And then, figured how many standard deviations they were above the population mean, which is their z-score. I then took the standard deviation of the z-score.
(A similar process was followed here in more detail: http://www.tangotiger.net/dipsbands.html )
If we get a z-score of 1.00, then we know it was all random, and umpires call it by the book. The z-score was a high 1.65.
Congratulations if you made it through the dense statistical forest in that snippet.
What he’s getting at is essentially an affirmation of the conclusions I reached last week; namely, that umpires have quite varied strikezones.
In the comments section, there is also some corroboration of my premise that QuesTec has changed the way some umpires call balls and strikes, but not all.
All in all, there’s some very interesting thoughts being flung about over on Tango’s site. I’d encourage you to read them, even if comments such as the following put you off:
But var(pit) can’t be zero unless all the umpires see *exactly* the same pitchers. In real life, it might be small, but not zero. What I’m wondering is: how small?
The theoretical SD should have been .0056. But after the effects of random pitcher distribution, what would it be? .00561? .0057? .0060? .0062?
It wouldn’t affect the conclusion that umpires have different strike zones, because obviously the SD won’t rise all the way to the observed .0092.
If you can’t stomach all of that, though, here’s a gentle reminder: I have pretty pictures here.