Are Foul Balls Good or Bad? Pt. II (A: They’re Good)

Back in June, I tried to tackle the age-old question: are foul balls good or bad? I tried to determine the “worth” of a foul ball by grouping plate appearances by their number of foul balls (from zero to four-or-more) and looking at two outcome metrics: strikeout rate (K%) and weighted on-base average (wOBA). Unfortunately, my endeavor turned up mostly duds. There are some interesting nuggets – a pitcher’s wOBA allowed improves by nearly 30 points in two-strike counts if he allows at least one foul ball – but most other splits were meaningless. Similar attempts to quantify the effect of a foul ball on the subsequent pitch were similarly fruitless.

I stepped back from the research to let it breathe. Intuitively, I knew there should be value here – I just wasn’t sure how it would present itself. Then, one day (specifically, June 27), inspiration struck in the form of Bryse Wilson’s third career start, during which he incurred nine swinging strikes but also 20 (twenty!) foul balls on 56 four-seam fastballs, amounting to a 16% swinging strike rate but also an absurd 36% foul ball rate (Foul%). The coincidence of many whiffs and also many fouls struck me as fascinating and extremely relevant to my previous research. It encouraged me to reframe the question at hand:

How does foul ball rate correlate with other measurements of success by pitch type?

Never one to shy away from an opportunity to employ a regression model, I took a different approach than the one I used previously. Using Statcast data dating back to 2015, I calculated foul ball rate, swinging strike rate, strikeout rate, and expected wOBA (xwOBA) for each pitcher’s pitch (for example, Clayton Kershaw’s curveball). I set a minimum per-pitch threshold of 500 pitches thrown in order for each observation to be sufficiently large without limiting the number of such pitches that exceed the threshold. For four-seam fastballs and sliders, I specified models with minimum thresholds of 2,000 and 1,000 pitches, respectively, because we enjoy the luxury of pitchers throwing so many of them.

The results – characterized by r², a measurement of correlation from 0 to 1, where 0 is nonexistent and 1 is perfectly correlated – are summarized below and color-coded from cold to hot for your convenience.

As Wilson demonstrated, foul balls are extremely beneficial to four-seamers and moderately beneficial to two-seamers by pretty much any common sabermetric measure. That’s certainly superior to what I determined (or, rather, failed to determine) back in June.

One problem with using r² to characterize the strength of a relationship between two variables is it obscures the directionality of the relationship. Incidentally, while foul ball rate and strikeout rate bears a statistically significant relationship for sliders, the relationship is actually negative. The higher the foul ball rate, the worse the strikeout rate, on average.

It seems to me as simple as: partial contact with a (typically) straight pitch means, on average, it is tougher to hit, whereas partial contact with a (typically) bendy pitch means it is easier to hit. The observation only holds true for sliders, though, which may say more about the frequency with which they are thrown (and, thus, a hitter’s ability to adequately anticipate them) than anything else.

I haven’t investigated the predictiveness of fouls balls yet, but I imagine you could use a pitcher’s four-seam or two-seam foul ball rate as a leading indicator of swinging strikes, and, thus, strikeouts. Even if that conjecture turns out to be unsubstantiated, fastball-incurred foul balls do bear a nonzero relationship with positive pitcher traits. And that’s better than nothing.