On Monday night, I had the privilege of attending a game in which the Reds’ best left-handed starter, Andrew Abbott, faced the Phillies’ best left-handed hitter, Bryce Harper, three times. Abbott got the better of Harper, who went 0-for-3 with a strikeout against the Cincinnati starter and 0-for-5 overall. But the qualities of each player got me thinking.

When Harper swings the bat, one of two things happens. In scenario no. 1, he squares it up and hits it so hard it causes bruising on the deceased ancestors of the workers who stitched the ball together at the Rawlings factory. Sure enough, Harper tagged Abbott’s teammates for three home runs just 24 hours later.

Otherwise, Harper misses it. He can miss it by a lot, in which case he just swings through it, or he misses it by a little. Those swings manifest themselves either in balls fouled straight back to the screen, or in fly balls that go straight up in the air and stay there long enough for the outfielder to take out his phone, and queue up Meat Loaf’s “Bat Out of Hell,” so the ball lands right at the climax of the second chorus. You know the part: “Like a sinner / before / the gates of Heaven / I’ll come crawling on back to you.” The loud one, like five and a half minutes into the song.

Abbott is an interesting matchup for this kind of hitter, because he lives and dies by “misses it by a little.” His style of pitching is like the angled armor on a main battle tank, which is designed not to absorb the impact of an incoming projectile but to deflect and disperse it in a direction where it can’t do any harm.

For example: The third-inning fly out Abbott induced against Harper, which came off the bat at 95.4 mph. Last regular season, Harper put 160 balls in play at 95 mph or more; 92 of them were base hits, 47 extra-base hits, and 21 were home runs. This one, which came off a hanging curveball, traveled an innocuous 244 feet and became an out, because Harper just got under it.

It was that kind of night for Harper, who saw 20 pitches and fouled off five of them. But it got me thinking: Is there something to that just-missed-it foul ball? It’s an article of baseball faith, after all, that a pitch that’s fouled straight back is closer to being hit on the screws than most balls that are actually put in play. Is there a correlation between how good a hitter (or a pitcher) is and how many foul balls he produces?

An in-depth study would involve testing multiple hypotheses using multiple forms of data. I had Baseball Savant, Microsoft Excel, and somewhere between six to eight hours to get this idea from conception to editorial doneness. Blog is Life.

For the purposes of this exercise, I chose to study all pitches from the 2023 regular season, the 2023 postseason, and all major league regular season action through April 1. And I limited the sample to pitchers who had thrown 750 or more pitches (there were 391 of them in total) and batters who had seen 750 or more pitches (371 of them in total).

Here are the top 10 pitchers and hitters in foul ball rate.

See a pattern? I don’t, really. There are good pitchers and bad pitchers, good hitters and bad hitters. The hitters do tend to be free swingers, and short, for what it’s worth. Perez is the only hitter in the top 10 with a listed height greater than 6-foot.

But that gets into a problem with measuring raw whiff rate. Because you have to swing in order to swing and miss, more aggressive hitters will hit more foul balls. In kind of a fishing expedition, I found the correlation coefficient between foul ball percentage and a number of plate discipline stats and overall offensive metrics. If this were an academic paper — and you can tell it’s not, because there was a Meat Loaf reference above the break — I’d give you a table with all those values in the name of scientific transparency. But because this is a less formal publication, I won’t bother.

Trust me, it’s just a bunch of zeroes, for both hitters and pitchers. The only stat that comes out with a strong correlation is swing rate. So let’s account for that. Does foul balls per swing predict any measure of offensive quality?

The hitters are at least getting up over 0.10 in some of these categories, which is probably just noise, but at least it’s not a slam dunk for the null hypothesis.

Let’s look at the leaderboards for foul balls per swing and see if that tells us anything. Here’s the top 10 for both hitters and pitchers:

And the bottom 10:

We’re getting closer, but there are good and bad pitchers on both of these lists. The hitters with high foul-per-swing ratios tend to be aggressive hitters who do a lot of damage — you can see some of the holdovers from the swing plane revolution in there — while the ones who don’t foul off a lot of pitches are just free swingers, period. In fact, if there’s a unifying trend on the bottom 10 hitters list, it’s guys whose wRC+ ought to be about 20 points higher than it was last year: Báez, Jiménez, Chisholm, Castellanos.

Let’s try one last ratio: Fouls per whiff. Not only does this null out the aggressiveness factor, a higher foul-to-whiff ratio would mean that a hitter isn’t missing by much. Conversely, pitchers who allow relatively few foul balls per whiff are not only missing the barrel, they’re routinely missing the whole bat.

Now we’re getting somewhere. This indicates a fairly strong linear relationship between pitchers’ foul/whiff ratios and their results. Specifically: When they allow more foul balls per whiff, they allow a higher opponent wOBA and xwOBA, and the opposite. Conversely, hitters who foul off a lot of pitches per whiff have a higher barrel rate per batted ball event, but a lower HardHit%. Both relationships are fairly strong, but they go in opposite directions.

That’s about to make more sense. Once again, let’s look at the top 10 and bottom 10 in this ratio.

The top 10 hitters in foul balls per whiff are either Punch-and-Judy hitters or the absolute S-tier bat control freaks. Of course there’s a negative correlation between foul balls per whiff and HardHit%; the hitters with the highest foul-to-whiff ratios are going up there playing a finesse tennis game and hitting .320 on a diet of soft line drives. Aim small, miss small.

Conversely, the list of pitchers with the lowest foul-to-whiff ratios is just a list of the nastiest relievers in baseball, and the accompanying list of hitters is a bunch of guys who swing from their heels. Perhaps that’s a little unkind; you can be a good hitter overall while not fouling many pitches off. Rooker was an All-Star last year, and Aaron Judge missed being on the end of this list by three spots. And again, when it comes to results for hitters, foul balls per whiff is pretty agnostic when it comes to performance.

As much fun as this was, measuring hitter or pitcher quality by tracking foul balls is a bit like determining the weight of land-based animals by measuring the width of their ears. You’ll end up pointing in the right direction, just because the top of your list will be dominated by elephants, but there are much simpler ways to get to the right answer.

Nevertheless, I still believe there’s a correlation between quality of contact and fouling the ball straight back. With more detailed data — and in the hands of a more capable statistician — there might be some valuable insight to be gained.