Do younger umpires call a more accurate strike zone?
In a post on the economic incentives facing would-be umpires, J.C. Bradbury has an interesting study on how older umpires are more likely to have a larger or smaller strike zone.
Bradbury ran a regression, to predict an umpire's season strikeout-to-walk ratio based on his age and who he is. He found that the older the ump, the more different his strike zone size. He writes,
"It turns out that every year an umpire ages he increases his deviation from the league average by about 0.8% [.16 change in K/BB ratio]. That doesn’t seem like a lot—and it really isn’t a huge effect—but over a period of 12 years that pushes the umpire a full standard deviation (9.5%) [.19] above/below the average deviation. Thus, by the end of an umpire’s career, his calls are about two standard deviations from the typical deviation. This is evidence of a tenure effect or a loss of competency." [square brackets mine.]
How big is that effect? Well, 0.19 might be the difference between a K/BB ratio of 2 and a ratio of 2.19. Assuming the same number of total K+BB, that means that instead of (say) 20 strikeouts for every 10 walks, there would be 20.6 strikeouts for every 9.4 walks. That turns 0.6 walks into strikeouts per 30 K+BB events, which is about 0.35 runs.
In 2009, there were 10.33 such events per game (per team), not 30. That means a standard deviation is worth a bit over a third of .35, or .12 runs per game. So a pitcher's ERA might go up or down by .11. For two standard deviations, it would be .24 runs or .22 earned runs. Assuming both teams are equal, there would obviously be no effect on who wins the game (although it seems likely that pitchers may be affected differently).
What's that in terms of pitches? A study I did (.pdf, page 4) finds that the difference between a ball and a strike is about 0.14 runs. So, at 2 standard deviations, an umpire calls about 1.7 pitches differently per game, per team. That means that more than 95% of umpires are less than 1.7 pitches per game different from the mean.
But since the pitchers and batters are presumably aware of the differences between umpires, they would adjust accordingly. So the effect might be more than .12 runs per SD -- it could be .12 for the actual strikeouts and walks observed, but it might cost the batter another .12 (or some other number) in having to swing at bad pitchers (which would be called balls by another umpire).
And, of course, even umpires who call normal numbers of strikeouts and walks might have their own particular strike zone -- it might be the same size, but have a different shape or location.
Bradbury concludes that, as umpires gain experience, they get more confident and less reverent, and feel less of a need to stick to the league's interpretation of where the strike zone should be. That sounds reasonable, especially considering that Bradbury's regression controlled for calendar year.
It's worth reading Bradbury's entire post, which includes a list of umpires and their individual K/BB ratios.
(Note: post was updated in response to an e-mail from Guy, who pointed out I had misinterpreted Bradbury's percentages and got the effect being half of what it should be. I think it's correct now.)