Searching for home field advantage with PITCHf/x

Derek Jeter steps into the batter’s box in the bottom of the eight inning at Yankee Stadium. The count is full with two outs.

Jon Lester delivers a cut fastball that just crosses over the outside corner of the plate for strike three. However, the umpire rules ball four and Jeter takes his base. Lester is halfway to the dugout when he realizes that the umpire did not call the pitch a strike, and he cannot believe it.

Would the pitch have been called a strike at Fenway Park? Was the umpire biased when making the call because Jeter was playing in his home stadium?

This scenario is hypothetical, but I’m sure that as baseball fans we’ve come across situations like it countless times. Maybe the umpire simply missed the call, but fans of Boston would almost assuredly argue that the umpire was biased.

Luckily, with the availability of PITCHf/x data we can measure possible umpire home field bias more accurately.

Are umpires biased toward the home team on balls just off the plate?

My goal is to test whether umpires will actually rule in favor of the home team more often than the away team when calling balls and strikes on pitches that are close. The first step was to define a “close” pitch.

Based on PITCHf/x, the strike zone is typically defined as thus:

For right-handed batters: -1.03 < px (horizontal location) < 1.00 and (0.92 + batter_height*0.136) < pz (vertical location) < (2.60 + batter_height*0.136)‬

For left-handed batters: -1.20 < px < 0.81 and (0.35 + batter_height*0.229) < pz < (2.00 + batter_height*0.229)‬

I defined “close” pitches as those either three inches outside of the zone off either corner while within the strike zone vertically, or three inches above or below the zone vertically while within the strike zone horizontally.

All these pitches should be called balls, but umpires are obviously not perfect and thus will call these pitches strikes fairly often.

Next came the study. First, I looked at every pitch in the 2012 regular season that was either a called strike or ball located within the parameters that I defined as close, and found the number of these pitches that were called a strike.

To test for any sign of home field advantage, I found the percentage of strikes called on these types of pitches at each home field and separated them by the strike percentage when the home pitcher was on the mound and the strike percentage when the away pitcher was throwing. Below are the results:

The Incompleat Starting Pitcher
The end of the nine-inning start and how we got here.

Team HomePerc Away Perc Gap at Home
Yankees 31.1% 23.2% 7.9%
Rays 23.0% 16.1% 6.9%
Padres 27.8% 21.3% 6.5%
Braves 27.2% 20.7% 6.5%
Brewers 26.1% 21.3% 4.7%
Giants 25.0% 21.1% 3.8%
Nationals 24.0% 20.2% 3.8%
Cardinals 21.7% 18.4% 3.3%
Astros 24.8% 21.9% 2.8%
Orioles 18.2% 16.7% 1.6%
White Sox 23.3% 22.1% 1.2%
Angels 22.3% 21.5% 0.9%
Diamondbacks 22.0% 21.4% 0.6%
Rockies 19.8% 19.2% 0.6%
Phillies 22.3% 21.8% 0.5%
Twins 16.0% 15.7% 0.4%
Indians 18.1% 18.0% 0.1%
Mets 22.3% 22.2% 0.0%
Red Sox 25.5% 26.1% -0.6%
Rangers 18.1% 18.9% -0.7%
Blue Jays 20.1% 20.8% -0.8%
Athletics 18.1% 18.9% -0.8%
Tigers 19.5% 20.4% -0.8%
Dodgers 21.6% 22.5% -0.9%
Reds 24.8% 25.8% -1.0%
Pirates 18.4% 19.7% -1.4%
Marlins 22.0% 23.5% -1.5%
Cubs 20.8% 22.9% -2.1%
Royals 14.9% 20.0% -5.0%
Mariners 15.4% 24.9% -9.6%

When these results are taken at face value it seems that the New York Yankees got the benefit of almost 8 percent more strikes called on close pitches than their opposing team when playing at Yankee Stadium. Teams such as the Atlanta Braves and Tampa Bay Rays also seemed to have benefitted from some type of home field advantage.

The only issue with interpreting the results in this way is the fact that these results can in no way be taken at face value.

According to research done by Max Marchi at Baseball Prospectus, Brian McCann (Braves), Jose Molina (Rays), Russell Martin (Yankees) and David Ross (Braves) ranked as four of the top six catchers in terms of catch framing over the 2008-11 seasons.

Would one be crazy to assume that much of what these results were picking up on was, in fact, each catcher’s ability to frame pitches that were close rather than umpires actually favoring the home team?

If people were not convinced, they would need to look no further than the bottom of this table and see that the Seattle Mariners had almost 10 percent fewer strikes called with their pitchers on the mound at home than their opponents. Last year, the Mariners’ catching corps was Jesus Montero, Miguel Olivo and John Jaso, none of whom are known for their ability as catchers.

Also, it is possible that certain teams have pitchers who consistently throw pitches that are in general “closer” to the plate, within this close definition, than other pitchers.

Thus, I adjusted these results by attempting to control for catcher framing, looking at the strike percentage on close pitches for each team when it was playing on the road. I list the results below:

Team Road Strike Perc
Braves 26.8%
Brewers 26.1%
Mets 25.0%
Yankees 24.9%
Cardinals 24.3%
Giants 24.3%
Rays 24.1%
Reds 24.1%
Astros 23.1%
Blue Jays 22.5%
White Sox 22.5%
Red Sox 22.1%
Nationals 21.7%
Padres 20.9%
Phillies 20.7%
Angels 19.7%
Orioles 19.2%
Diamondbacks 19.2%
Marlins 18.9%
Cubs 18.4%
Rangers 17.8%
Dodgers 17.7%
Royals 17.2%
Rockies 17.0%
Athletics 17.0%
Pirates 16.7%
Tigers 15.9%
Twins 15.5%
Mariners 15.5%
Indians 14.0%

Not surprisingly, these numbers jibe pretty well with past studies on which catchers are adept at framing pitches.

I found the average strike percentage on close pitches for each team on the road (20.4 percent). This average was then subtracted from each team’s road strike percentage to create a quasi-expected home field strike percentage gap.

Expected home field strike gap = road strike percentage – Lg. Avg. road strike percentage

In theory, this expected home field strike gap should be close to the gap found in the first piece of this study (the gap between a team’s strike percentage on close pitches at home and that of its opponents.)

Below, I compared each team’s actual gap in strike percentage at home and its expected home field gap:

Team Actual Home Field Gap Expected Home Field Gap Adjusted Home Field Gap
Indians 0.1% -6.5% 6.6%
Padres 6.5% 0.4% 6.0%
Twins 0.4% -4.9% 5.3%
Rockies 0.6% -3.4% 4.0%
Tigers -0.8% -4.5% 3.7%
Yankees 7.9% 4.5% 3.4%
Rays 6.9% 3.7% 3.1%
Orioles 1.6% -1.2% 2.8%
Athletics -0.8% -3.5% 2.7%
Nationals 3.8% 1.3% 2.5%
Pirates -1.4% -3.7% 2.3%
Rangers -0.7% -2.7% 2.0%
Diamondbacks 0.6% -1.2% 1.9%
Dodgers -0.9% -2.8% 1.9%
Angels 0.9% -0.7% 1.6%
Phillies 0.5% 0.3% 0.2%
Astros 2.8% 2.7% 0.2%
Braves 6.5% 6.3% 0.1%
Marlins -1.5% -1.5% 0.0%
Cubs -2.1% -2.1% 0.0%
Giants 3.8% 3.9% 0.0%
Cardinals 3.3% 3.9% -0.6%
Brewers 4.7% 5.6% -0.9%
White Sox 1.2% 2.1% -0.9%
Royals -5.0% -3.2% -1.8%
Red Sox -0.6% 1.7% -2.3%
Blue Jays -0.8% 2.1% -2.9%
Mets 0.0% 4.6% -4.5%
Mariners -9.6% -4.9% -4.6%
Reds -1.0% 3.7% -4.7%

The final column (Adjusted Home Field Gap) is my best attempt at controlling for a home field advantage on balls and strikes for last season. The average strike percentage for home teams on close pitches was 0.9 percent higher than expected for 2012.

This possible home field advantage effect sounds small, but is it?

The average number of close pitches thrown by a home team in 2012 was 1,237. Thus, the ~one percent home field advantage resulted in only 11 more strikes per team. According to a rough estimate that comes from Tom Tango, the run value of a called strike over a ball is 0.16 runs.

Thus, based on this study the average home field advantage for 2012 on close pitches was less than 2 runs per team. The effect of home field advantage seems to be very small, even at the extreme.

According to this study, the Cleveland Indians were the worst team in terms of strike percentage on close pitches on the road. Yet at home, they received about the same amount of strike calls as their opponent.

These facts resulted in 82 more strikes being called on close pitches than expected for the Indians at home; which is roughly equivalent to 13 runs. This number is larger in comparison to what was found at the league level, but 13 runs is worth just over one win over the course of the entire season and of course, Cleveland’s case is at the extreme.

My conclusion, based on this study, is that there seems to be some effect of home field bias on umpires calling balls and strikes, but the effect is not large enough to cause any real significant difference over what is expected during one season of play.

A few brief shortcomings

Although this study came back to show that teams did not seem to be receiving any really significant home field advantage on balls and strikes, that doesn’t mean home field advantage does not exist in baseball or that umpires are not subconsciously biased towards the home team.

I say this because this study was in no way perfect.

For one thing, the sample may have not been the best. I tested only one season in this sample and I also looked at only pitches that were outside the strike zone. There could be some home field bias on pitches in the strike zone that are called balls. Also, I did not control for pitch type or for umpire, as each umpire’s strike zone is different.

Two critical assumptions when calculating the expected home field gap also may have been flawed.

First it likely was unsafe to assume that pitchers’ and catchers’ playing times for each team were evenly distributed between home and road games. Also, teams do not have an even proportion of road games across all of the stadiums in baseball. This is an issue because it has been shown that PITCHf/x cameras have biases that vary by stadium. The flaws in both of these assumptions could have resulted in some bias within this study.

References & Resources
All PITCHf/x data comes courtesy of Baseball Heat Maps.

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Jon Roegele
Jon Roegele

Fantastic, thorough study, Glenn.

As I was reading it, I kept thinking “oh, maybe it could be partly because of this too”….and then you’d cover off that issue or mention it as a potential issue.

I’m surprised that the effect wasn’t a little more significant for teams like the Yankees, to be honest.

Glenn DuPaul
Glenn DuPaul

Jon, thank you and I’m glad you enjoyed it.  I was also surprised that the effect was so small, but I think part of the issue may have been the fact that I ignored the pitches in the zone which could have decreased the found effect of home field advantage.