The strike zone advantage for the home team

Last week I saw a tweet that referenced findings from the 2011 book Scorecasting which found an overwhelming strike zone advantage for the home team. This is something that fans have long suspected to be true, and as a consequence there have been a number of studies investigating the phenomenon.

In fact, just prior to the release of the book, THT’s own John Walsh did some work for the 2011 Hardball Times Annual that dealt with this exact topic. John’s article touched on a number of situations where the size and shape of the strike zone are likely to fluctuate (for more on this topic read Jon Roegele’s recent piece at BP). This included evidence of a clear, but limited advantage for home team pitchers. John found that “the strike zone is about 2.5 percent smaller for the visiting team,” and ultimately accounted for “a little more than a third of the home-field advantage.”

Jesse-Douglas Mathewson also looked into Scorecasting’s results during his time at Beyond the Box Score, and found that “the home team undoubtedly has an advantage when it comes to the strike zone, but this advantage just isn’t very big.” Jesse also estimated about a 2.4 percent advantage for home field pitchers.

So, we’ve been shown in many ways our assumptions are correct—Umpires do show a bias towards home team pitchers. But at just two and a half percent, this effect seems much smaller than some of us might have guessed.

Now, I haven’t read Scorecasting, so I apologize to its authors if I’m mischaracterizing their findings (I have since ordered a copy, however). But I did read that their conclusions were drawn from the discovery that the advantage was most prominent when the game was experiencing its most critical moments. In other words, Umpires were more biased towards the home team when the game was on the line.

To this point, I found a quote from the book referenced at Phil Birnbaum’s Sabermetric Research blog:

“If the umpire is going to show favoritism to the home team, he or she will do it when it is most valuable — when the outcome of the game is affected the most.”

So I decided to attempt to illustrate this alleged leverage-influenced advantage by breaking down the strike zone across various game states, mostly just to quench my own curiosity on the matter.

Retrosheet

I started by using Retrosheet data from 2002-2012 (only because it was immediately accesible) and looked at called strikes per all pitches ‘taken’ (or non-swings) for both home and away pitchers. Overall, home team pitchers saw a marginally better rate of called strikes per take at 32.3 to the visitor’s 31.7 percent– significant, thought perhaps not exactly unearthing evidence of a grand umpire conspiracy.

But sure enough as I filtered the data adding more and more critical game states, I found that advantage did increase noticeably the more crucial the situation:

Split PA Home Str/Take% Away Str/Take% Difference
All 2053949 32.3% 31.7% 0.57
<=1-run game, 9th inn 52904 31.3% 30.3% 0.92
Tie game, 9th inn 21405 30.3% 29.3% 1.09
Tie game, 9th inn, RISP 6166 27.3% 25.2% 2.11
Tie game, 9th inn, Bases loaded 798 29.7% 27.2% 2.48

What is generally an advantage of just half a percentage point on average, baloons slowly but surely as we focus our attention on more critical late and close scenarios. Then, as we require more base runners in a tie game in the ninth inning, we see that advantage grows even further.

Naturally, there are a number of things that can create some noise here. Obviously, this isn’t controlling for the count (which certainly affects the size of the zone), umpire, pitcher, or batter-handedness. But mostly this technique is less than ideal because we aren’t looking at an actual change in where strikes and balls are called, but rather just an estimate. To find bias in the actual size of the strike zone, we would need to look at PITCHf/x data.

PITCHf/x

So, using pitch location data back until 2007, I broke down home and away pitches into two categories: the percentage of pitches outside the zone that were called strikes (OZCS%), and the percentage of pitches inside the zone that were called balls (IZBall%). (The ‘zone’ defined here is the so-called Mike Fast zone.) I also limited most of this query to 0-0 counts, to eliminate any potential bias with regard to counts, and excluded intentional balls.

As you might expect, the splits did mirror the Retrosheet findings:

Split avg LI Count Takes Home advantage in IZBall% Home advantage in OZCS%
All 1.0 ALL 2624133 -0.72 0.44
All 1.0 0 0 929495 -0.68 0.68
1-run game, 9th inn 2.7 0 0 23378 -2.63 1.10
Tie game, 9th inn 2.7 0 0 9434 -4.44 1.17
Tie game, 9th inn, RISP 4.3 0 0 2133 -3.31 2.13
Tie game, 9th inn, Bases loaded 6.4 0 0 304 -6.53 3.62

Naturally with just under five seasons of data, by the time we get to tie game, ninth inning, bases loaded situations, the sample size has thinned dramatically, with just over 300 taken pitches to observe. Nevertheless, the trends here do suggest support for the theory that umpires substantially ramp up their bias with the game on the line. As we trek upwards along the LI spectrum, we see the home team gets more called strikes outside the zone and fewer balls called inside the zone.

At our peak leverage state—with an average LI of 6.4—the home team sees 8.5 of their pitches outside the zone called for strikes, while the visiting team’s pitchers got the benefit of the call just under five percent of the time. Add to that a six and a half point difference in balls called inside the zone, and we have ourselves evidence of a major game-changing bias.

Ideally, we’d like to use more than just 300 pitches to determine whether umpires need to curb their affection for the home crowd, but that will have to wait until more data from future seasons comes in. But this should hopefully serve as a fair starting point for such an endeavor.

Curiously, when I expanded this uber-critical tie game, ninth-inning, bases loaded game state to include extra-innings as well, the advantage for OZCS% increased yet again to a 4.5 point gap, while the advantage in IZBall% retreated back to 3.3 point difference (with a sample size of 758 takes). These numbers could certainly be jumping around because of noise within the limited sample, but it is a hunch of mine that extra-innings feel less dire than the ninth to both fans and umpires, despite the similar LI scores. (Am I alone in having this impression?)

Umpire psychology

We can only speculate as to why this home field advantage becomes so exacerbated in heightened conditions. Presumably, as the crowd gets louder, they become more persuasive and old ‘Blue’ becomes less apt to disappoint them. I’ll choose not to attempt to impress you with reckless insight from the hazy remains of just one or two psych 101 courses, but I would like to open up that conversation: What is motivating the umpire to please the home crowd?

Is it the fear of enraging thousands of people? Is it the allure of igniting an entire stadium with roars of delight after one pump of your own fist?

I’ll admit this inquiry leads to a lot more questions than answers, and some of those questions I’d like to pursue in the future. Such as, are certain umpires more vulnerable to this impulse and can we identify the greatest abusers?

I’d also like to investigate whether Umpire bias increases when the outcome of the game will have a larger effect on the season. If umpires are more likely to please the home crowd when the in-game situation is dire, will they therefore grant the home team even more of an advantage if there are post-season implications at stake? Or what about the post-season itself? Is there an even larger bias in favor of home teams in these hyper-critical games—including the World Series?

References & Resources
Thanks to Retrosheet and Fangraphs.

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Comments

  1. Detroit Michael said...

    “Presumably, as the crowd gets louder, they become more persuasive…”

    Seems like one could check this by looking at home field advantage in the 10% of games at a ballpark with the biggest crowds compared to the 10% of games with the smallest crowds.  Admittedly, that’s inexact because attendance is measured by paid, not actual, attendance, but it still may be worth checking.

  2. Brian Mills said...

    Good stuff, James.  To your point about crowd noise, there is research on this in the Soccer literature.

    However, in my study on the strike zone currently in Managerial and Decision Economics, I find no interactive effect of the Home advantage in the zone and the size of the crowd.  I was disappointed as this would have been a neat result.  Of course, there may be other ways to check this.

    I think you are right that when this bias happens is just as important (or perhaps more) as the bias itself.  If it just happens at the same rate across all games, then it won’t matter much due to the balanced schedule.  But if one finds it to happen more in critical times, then this could be very important (I believe Scorecasting found this to be the case).

  3. Brian Mills said...

    Another note: I do find that as the game progresses, on average, umpires tend to expand their zone.

    This may be happening in these critical situations, but could also be explained by the framing and pitcher quality effect.  Pitchers that come into high leverage spots are probably more likely to hit the catcher’s glove without it moving as much as a middle reliever or worn out starter.  Mike Fast tells us this should result in higher strike rates—though this doesn’t explain the bias across home and away through this time necessarily.

  4. bucdaddy said...

    Just a thought inspired by Brian Mills’ mention of “pitcher quality effect,” but IIRC many (if not most) managers as the visiting team won’t use the closer in the ninth inning, saving him to get the home team out in extra innings if his team takes a lead. But some managers as the home team WILL use the closer in the top of the ninth of a tie game to keep the visitor at bay and give his team a chance to win it with a run in the bottom.

    Closer bias?

    But then, probably shooting down my own theory, you’d be very likely to have closers involved in a one-run game in the ninth, and the slimmest of biases shows up there.

    So maybe I’m right back where I started.

  5. James Gentile said...

    Great point about the closers. That sounds like an interesting line of inquiry for the future. I imagine someone has looked at which types of pitchers get more called strikes outside the zone. Anyone remember if high velocity (a typical closer trait) has an impact?

  6. Brian Mills said...

    The research I have done on the zone actually shows that—after controlling for count and pitch type, etc.—higher velocity is less likely to be called a strike.

    I suspect this might just be a perceptive thing in that these faster pitches are harder to judge.  But it could be something else or there could be something I am missing in the model.

  7. Philip said...

    bucdaddy made some good points about use of a closer.

    I’ve read some excepts from Sportscasting, too. And while much of what the authors write can certainly be persuasive, I’m not convinced that home field advantage can be explained as simple as the make it: officiating bias.

    For example, while the quality of NHL referees certainly has taken a beating the past twenty years from retirements, expansion and going to a two-ref system, to simply account for home ice advantage as being a ‘‘bias’’ by the officials I think is grasping at straws. Sure, visiting teams get more penalties. And sure, shootouts are almost evenly split.

    But there are other factors where you can’t come up with a statistical accounting for home ice advantage, such as the home team having the last change before a face-off or that the visiting team’s center has to put his stick down on the ice first.

    To simply dismiss other possibilities because it’s nearly impossible to account for them statistically does not make another theory sound.

    James wrote:
    “But sure enough as I filtered the data adding more and more critical game states, I found that advantage did increase noticeably the more crucial the situation…”

    One could also observe that the ‘advantage’ increased noticeably as the sample size decreased significantly.

    I understand that James is limited with the number of situations that exist. But I would question the validity of making a comparison in a “1-run game, 9th inn” situation looking at 23,378 takes to that of a “Tie game, 9th inn, Bases loaded” in which only 304 takes occurred.

    A sample size of 304 is just way to small. There could be a noticeable fluxuation in the data just depending on how often Mariano Rivera was the pitcher in those home and away games.

    And there are the unknowns. How much more often does a visiting batter under such pressure freeze on a third strike that perhaps a home batter swings at?

    Finally, PITCHf/x data itself isn’t 100% accurate. The system tracks a pitched ball as it crosses the front of home plate. SportsVision itself claims that its tracking is accurate to an inch. Considering the strike zone at the front of home plate is 17 inches across, that makes the greatest margin for error nearly 12% (one inch on each side of the plate).

    Furthermore, pitches crosses the plane of the front part of the plate above the strike zone but which dip into it after should officially by the rule be called strikes but for which I understand PITCHf/x would consider a ball. Likewise for curves which catch a piece of the strike zone after initially crossing the front plane part of the plate as a perceived ball.

    Perhaps a more accurate analysis would be to look as the data like we analyze ballpark factors (comparing the same set of players, home and away) to find anomalies. But even with that, we’d be going up against a small sample size.

    In a few years we may know the answer with accurate data, if full strike zone analyses can be tracked. But even with that, we’d still have some bias as how an umpire considers the upper and lower limits of the zone depending on what he believes the batter’s normal batting stance should be.

  8. BenMarkham said...

    When I was a kid I had a third base coach for a few years that always yelled “good eye” to our hitters at the first moment he could tell we weren’t going to swing, before the umpire had time to call a strike or ball. He never admitted to it but everyone assumed he did it to influence the umpire.

    By the same token, I could see premature cheering (like a crowd erupting as a close 2 strike pitch crosses the plate) influencing the umpire a little. He might be a little more likely to give the crowd what it wants in those situations.

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