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Tired of K/BB? K%-BB% Gap? Fall into zGAP!

I'm a pretty cool guy, so lately I've been thinking and reading a lot about the merits of various measures of strikeout and walk rates for pitchers. By now, we probably all know that K/9 and BB/9 are flawed because they have innings as the denominator, when batters faced is preferred. I also recently had my life flip-turned upside down when I read Glenn DuPaul's article demonizing K/BB - a metric I had until recently considered pretty cool - in favor of the gap between a pitcher's K% and BB% (which I will henceforth refer to as "GAP" for lack of a snazzier shorthand).

On one hand, Glenn had some good points, and I largely now agree that K/BB is flawed. He tossed around some R-squareds, which are like candy to me, and he proved that K/BB's predictive value upon Runs allowed per 9 (R/9) paled in comparison to GAP to the tune of 9.9% to 17.9%. Pretty convincing that there are better ways of measuring this phenomenon than K/BB.

On the other hand...well, let's use Cliff Lee and Max Scherzer as examples. Scherzer led the majors with a K% of 29%, and had a BB% of 8%, for a 21.7% gap. Scherzer's K% is obviously excellent, but the 8% for walks is mediocre; a bit below average. Compare that to Lee who has K-24% (which is also excellent, 11th in the majors) and BB-3% (which by far led the majors) for a 21.1% difference. I'd say Lee has an excellent K% as well AND an amazing BB%. So basically, Scherzer is an A+ strikeout pitcher and a C+ control pitcher, while Lee is maybe an A- strikeout pitcher and an A+ control pitcher. Do you really think Scherzer's gap lead tells the whole story? Would you want Scherzer over Lee this past year if you had the choice?

For this reason and more, simply using the difference between the two percentages doesn't pass the stink test for me. I think the biggest problem with "GAP" is that it assumes that K% and BB% are weighted equally, or the same scale. In fact, the range for the two is very different - the K% range is 20% (Henderson Alvarez' 9.8% to Scherzer's 29.4%) and the BB% range is just 10% (Lee's 3.3% to Edinson Volquez' 13.1%).

So basically, the difference between an average BB pitcher and an amazing one is about 5%, whereas the difference between an average K pitcher and an amazing one is closer to 10%. Put another way, GAP favors K% heavily over BB%, and I don't know that this is a) OK, and if it is I b) don't know whether it is being favored in the correct ratio.

If a pitcher is 6% better at striking out batters than another (which is meaningful, but not a lot, probably about 25 percentile points) but 6% worse at walking (which is a WHOLE lot - around 60 percentile points) then he will be rated the same as the other pitcher GAP-wise, but he does not make up for this in actuality because he is not as much BETTER a K pitcher than he is WORSE a BB pitcher.

GAP implicitly weights the influence of K-rate to BB-rate at a ratio of 2:1. It may be the case that this ratio is accurate/meaningful, but I don't think that has been established at any point.

You can't do this - K% and BB% are simply on different scales. It would be like subtracting your IQ from your weight and acting like that number was a meaningful amalgam of intelligence and health. You have to convert them so that they are on a common scale.

What I think would probably solve this issue is to weight K and BB equally, and use z-scores for each and use the gap between the z-scores. This would give us a more accurate representation of the difference between percentile rank for each statistic.

For the uninformed, a z-score is synonymous with a standardized score. It is calculated (x-mean)/standarddeviation, where x is an individual score. The result is "the number of standard deviations an observation is above or below the mean," and as long as a variable is normally distributed, you can standardize anything and compare it pretty validly to anything else that has been standardized. 0 means average, about 68% of observations are between -1 and 1, anything more extreme than 2 is in the 5%, and more extreme than 3 is in the 1% and should probably be considered an outlier.

Since it's Saturday night, and as I said, I'm a pretty cool guy, I decided to fire up the ole SPSS engine and run the analyses myself. I took all 88 ERA title-qualified pitchers from 2012 and calculated R/9, K%, and BB%, and then calculated standardized scores for the whole gang.

From DuPaul's article:

R-square of K/BB: .099
R-Square of GAP (K%-BB%): .179

Using the gap between the z-scores of K% and BB% to predict R/9 in a linear regression analysis, we get an R-square of .335 for "zGap". This is pretty good. In fact, it is almost twice as good as GAP.

Why is zGAP so much better than GAP? Well, it comes back around to what I mentioned earlier - the fact that K% is arbitrarily weighted 2:1 to BB% since we never bothered to check if that was correct. The fact that we converted the two variables to a common scale and then re-measured and yielded a much higher R-square strongly suggests that this 2:1 ratio is incorrect.

To see whether the 2:1 ratio is correct, I ran another regression analysis - I just looked at K% and B% as separate variables in the same regression analysis (i.e. no gap, K% and BB% --> R/9). This yielded a .485 absolute value standardized regression weight for K% and .411 for BB%, which is about a 1.18:1 ratio, way lower (and more accurate) than the 2:1 that GAP uses.

What would probably work even better would be to multiply the K% z-scores by 1.18 and then take the gap between 1.18*zK% and zBB%. When we do this, we get an R-squared of .338, which is only very slightly higher than just using the z-scores. It's a bit more accurate, but probably not enough higher to justify all the extra work. The 18% difference exists, but it is probably just easier to consider that K% and BB% are roughly equally predictive of R/9 than to fiddle around with such a small difference.

So, to summarize, K% and BB% are roughly equally influential on R/9 (K being about 18% more influential, which is meaningful but probably not enough to justify making a statistic more complicated). Using the gap between K% and BB% is a better idea than K/BB, but we do need to adjust the GAP formula because GAP incorrectly weights K% as twice as important as BB%, so we need to edit the formula to put them on the same scale. To do this, transform each of K% and BB% to a z-score by taking (x-mean)/standarddeviation, then subtracting zBB% from zK% to get "zGAP".

Just for fun, here's the 2012 top ten list in my "zGap" statistic:

Pitcher zK% zBB% zGAP Weighted zGAP
Cliff Lee 1.29 -1.95 3.24 3.47
Max Scherzer 2.58 0.24 2.34 2.80
R.A. Dickey 1.40 -0.68 2.07 2.32
CC Sabathia 1.09 -0.93 2.02 2.21
Cole Hamels 1.42 -0.58 2.00 2.25
Justin Verlander 1.45 -0.42 1.87 2.13
Joe Blanton 0.32 -1.49 1.81 1.86
Chris Sale 1.42 -0.27 1.69 1.95
Felix Hernandez 1.11 -0.58 1.69 1.89
Clayton Kershaw 1.55 -0.07 1.62 1.90

This passes the sniff test for me - all of these guys are elite pitchers except for Blanton, and he was an excellent control pitcher in 2012 if nothing else. Using regular GAP, Max Scherzer comes out ahead of Cliff Lee, and I think we all know that Lee is better than Scherzer.

- Deej Simons

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