# Predicting pitchers’ strikeouts using xK%

Expected strikeout rate, or what I will henceforth refer to as “xK%,” is exactly what it sounds like. I want to see if a pitcher’s strikeout rate actually reflects how he has pitched in terms of how often he’s in the zone, how often he causes batters to swing and miss, and so on. Ideally, it will help explain random fluctuations in a pitcher’s strikeout rate, because even strikeouts have some luck built into them, too.

An xK% metric is not a revolutionary idea. Mike Podhorzer over at FanGraphs created one last year, but he catered it to hitters. Still, it’s nothing too wild and crazy like WAR or SIERA or any other wacky acronym. (A wackronym, if you will.)

Courtesy of Baseball Reference, I constructed a set of pitching data spanning 2010 through 2014. I focused primarily on what I thought would correlate highly with strikeout rates: looking strikes, swinging strikes and foul-ball strikes, all as a percentage of total strikes thrown. I didn’t want the model specification to be too close to a definition, so it’s beneficial that these rates are on a per-strike, rather than per-pitch, basis.

The graph plots actual strikeout rates versus expected strikeout rates with the line of best fit running through it. I ran my regression using the specification above and produced the following equation:

xK% = -.6284293 + 1.195018*lookstr + 1.517088*swingstr + .9505775*foulstr
R-squared = .9026

The R-squared term can, for easy of understanding, be interpreted as how well the model fits the data, from 0 to 1. An R-squared, then, of .9026 represents approximately a 90-percent fit. In other words, these three variables are able to explain 90 percent of a strikeout rate. (The remaining 10 percent is, for now, a mystery!)

In order for the reader to use this equation to his or her own benefit, one would insert a pitcher’s looking strike, swinging strike and foul-ball strike percentages into the appropriate variables. Fortunately, I already took the initiative. I applied the results to the same data I used: all individual qualified seasons by starting pitchers from 2010 through 2014.

The results have interesting implications. Firstly, one can see how lucky or unlucky a pitcher was in a particular season. Secondly, and perhaps most importantly, one can easily identify which pitchers habitually over- and under-perform relative to their xK%. Lastly, you can see how each pitcher is trending over time. Every pitcher is different; although the formula will fit most ordinary pitchers, it goes without saying that the aces of your fantasy squad are far from ordinary, and they should be treated on an individual basis.

(Keep in mind that a lot of these players only have one or two years’ worth of data (as indicated by “# Years”), so the average difference between their xK% and K% as a representation of a pitcher’s true skill will be largely unreliable.)

It is immediately evident: the game’s best pitchers outperform their xK% by the largest margins. Cliff Lee, Stephen Strasburg, Clayton Kershaw, Felix Hernandez and Adam Wainwright are all top-10 (or at least top-15) fantasy starters. But let’s look at their numbers over the years, along with a few others at the top of the list.

Kershaw and King Felix have not only been consistent but also look like like they’re getting better with age. Wainwright’s difference between 2013 and 2014 is a bit of a concern; he’s getting older, and this could be a concrete indicator that perhaps the decline has officially begun. Darvish’s line is interesting, too: you may or may not remember that he had a massive spike in strikeouts in 2013 compared to his already-elite strikeout rate the prior year. As you can see, it was totally legit, at least according to xK%. But for some reason, even xK% can fluctuate wildly from year to year. I see it in the data, anecdotally: Anibal Sanchez‘s huge 6.7-percent spike in xK% from 2012 to 2013 was followed by a 5.5-percent drop from 2013 to 2014. Conversely, David Price‘s 5-percent decrease in xK% from 2012 to 2013 was followed by an almost perfectly-equal 5-percent increase from 2013 to 2014. So the phenomenon seems to work both ways. Thus, perhaps it shouldn’t have come as a surprise when Darvish couldn’t repeat his 2013 success. To the baseball world’s collective dismay, we simply didn’t have enough data yet to determine which Yu was the true Yu. I plan to do some research to see how often these severe spikes in xK% are mere aberrations versus how often they are sustained over time, indicating a legitimate skills improvement.

I have also done my best to compile a list of players with only one or two years’ worth of data who saw sizable spikes and drops in their K% minus xK% (“diff%”). The idea is to find players for whom we can’t really tell how much better (or worse) their actual K% is compared to their xK% because of conflicting data points. For example, will Corey Kluber be a guy who massively outperforms his xK% as he did in 2014, or does he only slightly outperform as he did in 2013? I present the list not to provide an answer but to posit: Which version of each of these players is more truthful? I guess we will know sometime in October.

Name: [2013 diff%, 2014 diff%]

And here some fantasy-relevant guys with only data from 2014: