Devising a Pitcher xHR/FB Rate
I was pretty successful at developing an equation to estimate what a hitter’s HR/FB rate should be given his fly ball + home run distance, along with the average absolute angle and standard deviation of the distance of those batted balls. My formula resulted in an R-squared mark of 0.649, which seems pretty darn good to me, especially when it completely ignores park factors, which we know play a significant role. On Tuesday, I found that the year-to-year correlation of a pitcher’s batted ball distance is less than half that of a hitter’s. Then yesterday, I discovered there was some correlation between a pitcher’s batted ball distance and his HR/FB rate and ISO mark.
In that last article, I teased that Jeff Zimmerman also armed me with the same angle and standard deviation data he provides me for hitters, but for pitchers. So naturally, my first inclination was to line up all the data and run those three variables to attempt to devise a pitcher version of the xHR/FB rate equation.
Once again, my data set was comprised of 663 player seasons from 2008 to 2014. The best fit equation was thus:
xHR/FB = -0.4211 + (Avg Dist * 0.0013) + (Avg Absolute Angle * 0.0036) +(Std Dev Dist * 0.0016)
Just like in the hitter’s version, angle plays the most important role, followed by standard deviation. Who would have thought that average distance would bring up the rear? Unfortunately, this equation isn’t nearly as good as the hitter’s one:
Adjusted R-squared = 0.276
That’s not terrible, but it’s quite low. Here’s a scatter plot of xHR/FB vs HR/FB:
Because I know this question will be asked, the dot all by its lonesome at the top on the 16% xHR/FB line is Miguel Gonzalez, 2014 version, with a 12.1% actual HR/FB.
In this data set, the actual HR/FB rate ranged from 3.1% to 19.2%, while the xHR/FB rate ranged from 6.6% to 16.0%. This seems like part of the problem with coming up with an equation to estimate it. It’s very fluky, jumps all over the place, and is mostly controlled by the hitter. So even if we thought we knew what HR/FB rate a pitcher should be allowing, it’s not going to end up there the majority of the time due to total randomness.
For those curious, here are three notorious HR/FB rate suppressors:
| Jered Weaver | Matt Cain | Clayton Kershaw | ||||
|---|---|---|---|---|---|---|
| Season | HR/FB | xHR/FB | HR/FB | xHR/FB | HR/FB | xHR/FB |
| 2008 | 8.3% | 8.7% | 6.8% | 9.8% | ||
| 2009 | 8.3% | 7.9% | 8.4% | 10.6% | 4.1% | 9.3% |
| 2010 | 7.8% | 8.4% | 7.4% | 9.8% | 5.8% | 9.4% |
| 2011 | 6.3% | 6.8% | 3.7% | 8.4% | 6.7% | 7.1% |
| 2012 | 8.6% | 7.3% | 8.4% | 9.2% | 8.1% | 9.6% |
| 2013 | 7.8% | 7.9% | 10.8% | 10.9% | 5.8% | 8.3% |
| 2014 | 8.9% | 7.9% | 13.7% | 11.6% | 6.6% | 9.8% |
Looks like Weaver’s HR/FB prevention skills are legit, at least according to this xHR/FB formula. So maybe it’s not just the pitcher friendly ball park. Cain had some magic going on earlier in his career, certainly with some help from his home park, but that magic has seemingly disappeared. Kershaw is obviously not a human, and defies any sort of formula. He’s a true outlier, which formulas aren’t meant to work for.
While this was a fun little exercise, the equation developed isn’t all that helpful. The search continues as we try explaining HR/FB rate differences that aren’t totally chalked up to ball park and luck.
Mike Podhorzer is the founder of ProjectingX IQ, an advanced fantasy baseball analytics platform that transforms projection data and in-season performance signals into actionable intelligence. He is the 2015 Fantasy Sports Writers Association Baseball Writer of the Year and three-time Tout Wars champion. He is the author of the eBook Projecting X 2.0: How to Forecast Baseball Player Performance, which teaches you how to project players yourself. Follow Mike on X@MikePodhorzer and contact him via email.
How predictive is it? Is there a statistical significance when you use a formula like this:
xHR/FB Year n+1 = Constant A + (Avg Dist Year n * Constant B) + (Avg Absolute Angle Year n * Constant C) + (Std Dev Dist Year n * Constant D)
It’s projection season, so this is a lot more useful than using in-sample testing. I assume that doing an xHR/FB for year n+1 would also include prior HR/FB rates in some capacity, too.
I haven’t done the work on its predictive value.
Also, the variance we’re seeing could be that a guy like Kershaw is allowing certain players to elevate the ball against him, and against other, more powerful hitters, he’s using more energy/pitches, as well only throwing low strikes, in order to keep the ball on the ground. We know it’s possible for pitchers to “kick it up a notch” against better hitters, since this is essentially what gives the natural advantage to relievers; they’re able to kick it up a notch against everybody they face.
That’s just pure speculation, who knows what Kershaw does. Well, relievers throw harder on average, and fastball velocity correlates well with strikeout rate. I don’t think it’s because relievers kick it up a notch.
Well yeah it’s only speculation and not tested. I’m speculating on things to test to then rule them out. And throwing harder would be one way that relievers “kick it up a notch”. It’s not a coincidence that they throw harder.
Basically, I’m wondering if certain players are able to do what guys like Wade Davis and Luke Hochevar do in the bullpen vs rotation. But they are able to do the equivalent of a bullpen-style approach for great hitters and a starter-style approach against everybody else. If so it would help explain why certain pitchers are able to beat their xMetrics.
Relievers throw harder because they don’t have to pace themselves to go 6-7 innings. They could go max effort since they’ll only be out there for an inning.
Yes, exactly. They make a conscious decision to throw harder. I’m wondering if some starting pitchers may be able to do that, to some degree, for brief periods of time (high leverage PAs and/or against a great hitter) in the midst of a full game as a starter. It’s not a revolutionary idea, but identifying if pitchers are able to do that may help close the gap between things like FIP and xFIP, for example.
So, speculating again, maybe we could expect a guy who constantly throws max effort just to get to 90 MPH as a starter and doesn’t have enough control to nibble around the plate and low in the zone (maybe a guy like Edwin Jackson), could be expected to be worse than his xFIP since he can’t turn it up to 11.
Whereas a guy with impeccable control and who throws at maybe 90% effort most of the time, would be able to be better than his xFIP (and xHR/FB, etc) because when Miggy or Trout come up, or if the bases are loaded, then he IS able to turn it up to 11.
It may be as simple as comparing K% or FBV splits of Low vs High leverage situations. I vaguely remember looking into this a bit a year or two ago and not finding much, but I’ll probably do a little more poking around.
Throwing harder would increase strikeout rate, which is accounted for in FIP/xFIP. It wouldn’t explain a gap between those two metrics and ERA.
Interesting finding concerning Jered Weaver. How is he doing it then? Does his extreme piching from the 3B side of the mound approach have an oversized influence on flyball angle?
Very interesting work.
actually He’s below average on all 3 metrics. I have no idea how he accomplishes it.
What is it then that causes Weaver’s xHR/FB to be roughly as low as his actual HR/FB?
By below average, I meant lower than league average, meaning a good thing.
I wonder if the distance measures are due to Weaver’s high rate of IFFB / FB or whether he also suppresses distance even after one strips out the IFFB.
Popups should be excluded since the distance is strictly from homers and fly balls.
I wonder what the xHR/FB rate is for Gio Gonzalez?
He seems to have done a good job of suppressing HRs since he’s come over to the NL.
The park helps of course; I think it usually ranks in the bottom 10 for HRs yielded.
Gio looks like this, with actual HR/FB listed first:
7.4% 10.0%
8.9% 8.6%
5.8% 9.7%
9.7% 9.9%
6.6% 8.9%
I should clarify the last row is 2014