The best equation I have ever developed from an adjusted R-squared perspective is pitcher xK%. That equation yielded a 0.913 R-squared, so it didn’t exactly need any tweaking. However, I was on an xEquation rush recently and decided to develop new ones, as well as update old ones. So we’ll begin with xK% and dedicate my week’s posts to looking at the new version of the metric.
The formula uses the same strike and strike type metrics from Baseball-Reference.com as in the earlier version, with the only difference being updated coefficients. The components can be found by clicking on the “More Stats” link next to the Standard Pitching box and then scrolling down to Pitch Summary — Pitching. Here is the link to Corey Kluber’s metrics. Fun fact — the metrics in this box are all to one decimal place because of me, as they actually used to be rounded to the nearest whole number until I emailed Sean Forman to request the change.
My population included all pitcher seasons from 2011 to 2015 with at least 50 innings, including relievers. That resulted in a total of 1,638 player seasons in my data set. From the commenters, I learned to keep the last season out of the data set and instead use it to test the effectiveness of the equation as an out of sample data set.
xK% = -0.8432 + (Str% * 0.2916) + (L/Str * 1.2689) + (S/Str * 1.5334) + (F/Str * 0.9672)
Adjusted R-Squared: 0.931
Str% — Strike Percentage | Strikes / Total Pitches
L/Str — Looking Strike Percentage | Strikes Looking / Total Strikes
S/Str — Swinging Strike Percentage | Strikes Swinging Without Contact / Total Strikes
F/Str — Foul Ball Strike Percentage | Pitches Fouled Off / Total Strikes
Compared to the previous xK% equation, every coefficient is slightly higher, while the intercept is lower (or, a greater negative number). I don’t know what that means or how to interpret it, but interesting to note, nonetheless. I should also point out that my R-squared rose even higher! That’s cool.
So let’s talk about these four variables, along with some other B-R.com metrics in the same table and begin with their correlations with K%:
As one might imagine, there is an extremely strong relationship between inducing swings and misses (S/Str) and racking up the strikeouts. But would you have guessed it was this strong? It’s far and away the most important type of strike to generate.
Curiously, L/Str (looking strike percentage) has literally no correlation! However, that’s deceiving, because if I leave the metric out of my regression equation and just keep the other three, the R-squared falls to just 0.796. Maybe the more math inclined could explain that one to me.
I also considered incorporating other metrics into my equation, including 1st%, 30%, and 02%. Unfortunately, they didn’t add any explanatory power, plus, I then had to worry about introducing the dreaded multicollinearity. I figured all three of these metrics would be highly related to Str% and it would be silly to include both. I was right:
Just as high as you would think. So none of those made my updated equation, which resulted in the same components as the original.
Now let’s talk year-over-year correlations. How stable are the components themselves and how does that compare with the stability of K% and xK% from year-to-year?
So in my data set, the YoY correlation of xK% was slightly higher than K%, both of which are pretty high. All the strike/strike type components also have high correlations, with swinging strike rate being the most stable skill. You may recall me referencing in past articles that I’m more skeptical of a pitcher’s strikeout rate spike if it’s driven by a jump in looking or foul strike rate, rather than swinging strike rate. This is why.
Now for the tastiest meat of all. How does xK% perform compared to K% in forecasting the following year? Remember, this equation was not built as a forward looking projection, but rather as a backward looking one, or what “should have” been. That said, here we go:
|K% Y1 to K% Y2||0.713|
|xK% Y1 to K% Y2||0.716|
The success here is more than the tiny increase in R-squared suggests. That’s because the best use of the metric is early in the season when the samples remain small. Since the metric uses pitches as the denominator, versus total batters faced for K%, our sample size rises much more quickly and we are therefore presented with a reasonable sample size far sooner. Keep reading to see the proof.
Let’s finish things up by checking in on how the metric performed on the out of sample 2016 data:
|K% 2015 to K% 2016||0.710|
|xK% 2015 to K% 2016||0.714|
Excellent, nearly identical correlations using a data set not included in the equation’s population.
Lastly, I hinted that the real strength of the metric is when working with smaller samples. So I decided to also test correlations from 2015 to 2016 using a data set of just pitchers who recorded fewer than 50 innings in 2015 and any number of innings in 2016. The sample size was just 55 pitchers, but the results were exciting:
|K% 2015 to K% 2016||0.587|
|xK% 2015 to K% 2016||0.632|
While unsurprisingly both correlations fell compared to the group that pitched at least 50 innings, now xK% has a much larger advantage. I would guess that as the sample size shrunk even further, the xK% advantage would continue to grow. And that’s precisely what this metric was developed for.
Mike Podhorzer is the 2015 Fantasy Sports Writers Association Baseball Writer of the Year. He produces player projections using his own forecasting system and is the author of the eBook Projecting X 2.0: How to Forecast Baseball Player Performance, which teaches you how to project players yourself. His projections helped him win the inaugural 2013 Tout Wars mixed draft league. Follow Mike on Twitter @MikePodhorzer and contact him via email.