Unpacking the Impact of Foul Balls on Strikeouts

In eight of the 12 different count-states, fouls and whiffs come with the same penalty: a strike. In a 1–1 count, for example, it really doesn’t matter whether you look silly swinging and missing at a curveball or just miss a home run by being a few inches wide of the foul pole. In either case, hitters have to come back for another swing, with the count now 1–2.

We all know this. Those are just the rules of the game. But it creates a very interesting hierarchy for hitters. When a hitter swings, only one of three things can happen: He can put the ball in play, foul it off, or whiff. And, as mentioned, for two-thirds of those outcomes — the foul and the whiff — no distinction is even made in eight of the 12 count-states. No wonder that the league-average hitter, by run value, is penalized when he swings.

But fouls have a unique property that makes them wholly different than whiffs: the ability to prolong at-bats. In the same way that you can’t lose on a serve in ping pong, you can’t strike out on a foul ball (bunts excluded). While they carry the same penalty as whiffs in all non–two-strike counts, foul balls manage to be the only safety net for hitters when their backs are against the wall, and to me, it makes for a pretty interesting dichotomy when you break it down that way.

Because foul balls provide this special safety net for hitters, it would make sense intuitively that hitters who foul off more pitches probably strike out less. If a hitter fouls off a lot of pitches, especially relative to the number of whiffs he creates, he is almost certainly going to avoid a K and eventually should get a pitch to put in play. Indeed, there is a pretty strong correlation between foul-to-whiff ratio and strikeout rate:

So obviously there’s a pretty interesting relationship here, but I mainly wanted to include this chart to show off Nick Madrigal, who has somehow fouled off 101 pitches and whiffed on just 14, good for a foul-per-whiff ratio of 7.2. As you can see in the chart, the second-best mark is well behind him: Luis Arraez, with his 4.3 foul-to-whiff ratio. The distance between first-place Madrigal and second-place Arraez is roughly the same distance between Arraez and Hunter Renfroe, who ranks in the 35th percentile in the stat.

If you’re looking for answers to show how hitters limit strikeouts, developing a rough metric with Madrigal at the top is not the worst place to start. Through games on Wednesday, he has struck out in just 5.6% of his plate appearances so far this year, a figure that unsurprisingly leads baseball. But is it mostly Madrigal’s lack of whiffs that keeps him from striking out so much? Is the numerator of a stat like foul-to-whiff ratio largely irrelevant? Is there only a correlation between this stat and strikeout rate because whiffs are included?

The answer to all three of those questions is mostly yes, but it’s also more complicated than that. Whiffs end at-bats. If you whiff on a two-strike count, you have struck out. If you foul on a two-strike count, nothing changes. You just do it all again. This provides the potential for a whole host of outcomes: You could also foul off the next pitch, but you could also still whiff. An extreme example would be if a hitter fouled off 20 consecutive pitches every at-bat before whiffing just once. Said hitter would have a 100% strikeout rate and a foul-to-whiff ratio of 20. At the end of the day, the whiff matters much more than all those foul balls.

Whiff rate, then, is going to correlate much more highly to strikeout rate than foul rate ever will. It’s pretty obvious when you look at the two scatterplots.

First, foul-per-swing rate versus strikeout rate:

And now, whiff-per-swing rate versus strikeout rate:

I highlighted both Madrigal and Kevin Newman here because they perfectly encapsulate the difference between foul rate and whiff rate and their respective impacts on strikeout rate. While Madrigal leads baseball in strikeout rate at 5.6%, Newman isn’t far behind him at 6.5%. Madrigal fouls a fair number of pitches off and Newman does not; that’s why we see Madrigal and not Newman at the top of the foul-to-whiff ratio leaderboard. But both players rarely whiff, and that’s why they are so good at limiting strikeouts.

Case solved, right? Foul balls don’t have a significant impact on strikeout rate because they prolong at-bats rather than yield an alternative outcome. Well, it’s not exactly that simple. When we look at how the two variables interact — fouls and whiffs together, rather than separately — we find that there is a significantly stronger relationship between fouls and whiffs and strikeout rate than just whiffs alone. Here’s the correlation between strikeout rate and regressed strikeout rate from those two variables:

Fouls do matter, and pretty significantly so, but not by limiting strikeout rate. Just by including Foul% into the regression, the r-squared jumps by 10 points. The model including Foul% explains 10 percentage points more variability than the model without it. In this regression, each point increase of whiff rate results in roughly a one-point increase in strikeout rate, but each point increase of foul rate also results in a half-point increase in strikeout rate. This suggests that the opposite of the initial hypothesis may be true: Hitters who foul off more pitches may actually be prone to striking out more, likely because there’s no distinction between fouls and whiffs until they get to two strikes. In all counts, if a hitter fouls off more pitches, he’s going to accumulate more strikes over time, and on average, that will ultimately lead to more strikeouts.

I also ran count-specific analyses looking at the changes in foul and whiff rates once hitters reach two-strike counts versus these same rates in all other counts. There was no relationship (r-squared = .001) between difference in foul rate and strikeout rate, and only a very, very small relationship between difference in whiff rate and strikeout rate (r-squared = .020). Again, while foul balls seem like they have a positive impact on an at-bat, especially when a hitter is up there “battling,” they only prolong it and seemingly don’t have a huge impact on the overall outcome, at least in terms of strikeouts.

In non-two strike counts, foul balls are bad because they add a strike. Hitters who foul off more pitches in general are likely going to be worse off, and even if hitters foul off more pitches in two-strike counts than they do otherwise, they don’t really change their strikeout rates as a result.