The Human Element: Umpire Strike Zones

PITCHf/x data allows umpire performance to be examined. Umpire strike zones can be tracked, contrasted and compared, revealing new ways to look at baseball. Ian York has previously shown the effect catcher framing can have and here breaks down how the human element contributes.

Umpires are supposed to call a pitch a strike if it is in the official strike zone. Of course, they do not always call a strike a strike.

The strike zone is that area over home plate the upper limit of which is a horizontal line at the midpoint between the top of the shoulders and the top of the uniform pants, and the lower level is a line at the hollow beneath the kneecap. The Strike Zone shall be determined from the batter’s stance as the batter is prepared to swing at a pitched ball. ‒ Rule 2.00: The Strike Zone

The strike zone, as actually called, is wider than home plate and different for left-handed and  right-handed batters. The real-life zone has expanded over the past four years, and through pitch framing, some catchers can expand the strike zone even more.

Additionally, different umpires call different strike zones. Some umpires are known to be pitcher-friendly and call a relatively large strike zone; other umpires are batter-friendly and feature a tight window; and at least by reputation, some umpires are reputed to vary wildly, with no consistent zone.

Methodology

Since 2008, each umpire’s strike zone has become measurable because of the PITCHf/x system. PITCHf/x measures the actual location of each pitch, as well as what the umpire called. One side effect of this measurement seems to have been the overall expansion of the strike zone, as it has changed to more closely match the rulebook zone.

The following graphs and animations measure individual umpires’ strike zones, relative to the rest of baseball in each year. This is done year-by-year because the strike zone has changed shape and size several times since 2008. This article addresses the changes in the strike zone across MLB over the past seven seasons.  The zone was divided into small subsets: what the overall probability of a pitch in that area being called a strike was, what the individual umpire’s probability was, and how many pitches were actually delivered to that area.

For example, a pitch in the outside corner of a right-handed batter’s strike zone normally has a 10% chance of being called a strike, but an umpire ‒ “Enrico Palazzo” ‒ calls it a strike 90% of the time. If Palazzo saw 60 pitches in that area, he would have called 54 of them strikes. The average umpire would have only called six of them strikes, so the Palazzo would be awarded 48 extra strikes for that particular spot. The strike calls are totalled over all regions of the strike zone and then divided by the number of games he called, to generate extra strikes per game.

To maximize the number of samples per year yet make the sample size consistent, this is calculated with all umpires who called 30 or more games per year, each year between 2008 and 2014. This resulted in a total of 97 umpires across all years and about 69 umps in each year. Here is how “extra strikes per game” were distributed over the whole period:

Umpire Strike Zones IMG 1Most umpires are neutral – they call the average MLB strike zone, adding or taking away no more than 1.5 extra strikes per game. Of the outliers ‒ more than 2 or less than -2 extra strikes per game ‒ slightly more are pitcher-friendly, calling a larger strike zone than the average umpire. A few outliers give or take away 4 or more extra strikes per game.

Pitcher Friendly Strike Zone

This is what a strike zone looks like with an extremely pitcher-friendly umpire. In 2010, Bill Miller called 5.4 extra strikes per game compared to his colleagues. In this plot, areas that are less likely to have a strike called, compared to the overall probability in baseball, are colored blue; areas that are more likely to have a strike called are red. Intensity is proportional to the probability, as shown in the scale:

Umpire Strike Zones IMG 2

The gray oblongs are the de facto strike zones that umpires called in 2010; throughout MLB, a pitch outside the lines was less than 50% likely to be called a strike, inside the lines it was more than 50% likely to be a strike. Miller was more likely to call a strike (the red areas) at the top and the bottom of the strike zone for left- and right-handed batters, as well as both inside and outside to righties. A pitch down-and-in to a right–handed batter had around a 50% greater chance of being called a strike with Miller behind the plate.

Batter Friendly Strike Zone

Conversely, the smallest strike zone found in the study was called by Gerry Davis in 2010 with -4.8 extra strikes per game; 10 strikes per game fewer than Miller:

Umpire Strike Zones IMG 3

Davis squeezed the strike zone in on all sides, except for the top, where he called more or less the same location as average.

Just for comparison, here is a neutral umpire. In 2013, Jim Joyce had precisely 0.0 extra strikes per game:

Umpire Strike Zones IMG 4

Neutral Strike Zone

A neutral umpire will not necessarily call strikes with exactly MLB-average probability everywhere. In principle, an umpire could call far more strikes at the top and could still be neutral by calling fewer at the bottom. That is not really the case here: Joyce is slightly less likely to call strikes at the top of the RHB zone and slightly more likely to call them on the inside and outside. Since most of the colors are faint, the difference in probability is slight.

Are umpires consistent in their zones over time? Alternatively, is this approach actually measuring anything except statistical noise? In general, umpires are pretty consistent year to year: An umpire who called a big zone in 2008 is very likely to call a big zone in 2014. (The correlation coefficients over time are about 0.60 to 0.70.) We can show this by walking through Miller’s various zones since 2008:

Umpire Strike Zones IMG 5

The absolute amount and position of areas with increased strike probability do change slightly, but year after year Miller is much more likely to call strikes where other umpires do not.

Here are the extra strike per game numbers for some of the more interesting umpires:

Umpire 2008 2009 2010 2011 2012 2013 2014
Doug Eddings 5.1 3.7 3.5 3.2 3.7 2.7 4.2
Ron Kulpa 1.1 0.7 3.1 1.2 2.9 3.3
Tim Welke 1.7 1.6 2.6 0.9 1.5 1.2 3.1
Bill Miller 2.7 3.6 5.4 3.6 4.3 3.8 3.1
Angel Hernandez 0.3 0.3 -0.2 -0.6 2.4 1.4 3.1
Brian O’Nora 2.1 1.9 1.7 0.5 1.4 3.0 2.8
Jim Joyce 1.2 -2.0 -0.2 -0.4 0.0
Mark Wegner -1.2 -0.1 -1.8 -0.5 0.0 -1.2
Mark Carlson 0.7 -0.6 1.3 -0.9 0.8 -1.2
Gerry Davis -3.3 -3.0 -4.8 -3.3 -1.2 -0.5 -1.9
Paul Schrieber -4.4 -3.1 -3.4 -2.6 -3.8

Kulpa and Welke went from moderately large zones in 2008 to quite large zones in 2014. (Kulpa didn’t call enough games to qualify for the 30-game cutoff in 2009, hence the blank spot.) Eddings and Miller have always called a big zone. In 2014, only Schrieber had an exceptionally small strike zone, as he has since at least 2008. Davis had a smaller than average zone at -1.9 extra strikes per game, but only 10 of the 79 qualifying umpires called fewer than -1.5 extra strikes per game than the average. In contrast, five umpires called 3 or more extra strikes per game.

It appears that umpires as a whole are more likely to call a slightly larger strike zone than to call a smaller than average zone. However, the majority of umpires, as noted above, call a more or less neutral game.

In 2014, Wegner and Carlson were nearly neutral umpires with identical -1.2 extra strikes per game. But look at how they reached neutrality:

Umpire Strike Zones IMG 6

Umpire Strike Zones IMG 7

Wegner is moderately batter-friendly to left-handed batters, with -1.5 extra strikes per game to left-handed batters. But he is neutral to slightly pitcher-friendly to right-handed batters at 0.4 extra strikes per game. Carlson is the opposite, taking strikes away from RHB (-1.9 extra strikes per game) but slightly pitcher-friendly to LHB (0.8). Even with his nearly neutral LHB strike zone, he is not neutral all around. He takes away strikes from the inside of the plate and compensates for it by adding strikes back outside and at the bottom of the zone. The shape and size of an umpire’s strike zone depends on the umpire.

Two final notes:  First, the impact of the difference in strike zones is even-handed. Even though several of these umpires expand the strike zone as much as an elite pitch-framing catcher can, the umpire has – we hope – the same strike zone for both teams. Since the umpires rotate through the home plate position during a series, it is hard for any one team to take any kind of long-term advantage. Additionally, MLB players can rapidly adapt to the differing strike zones, so long as the zone is consistent from at-bat to at-bat. This kind of consistency (which isn’t being measured in the approach used here) is probably much more important in an umpire than is the raw size of their strike zone. Still, consistent or not, even-handed or not, the size and shape of the strike zone is an important factor for pitchers and batters.


Follow Ian on Twitter @iayork.

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