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I’ve never caught a foul ball. I’ve been to a couple of games where I was in the right section and came close to snaring one, but I never got a chance to make a play on a batted ball off the bat of a major leaguer, even if it was one that went the wrong way.

Once when I was 10 or 11, I was sitting at the end of a row in the lower deck of Cleveland Municipal Stadium when a member of the Twins lined a ball foul off to the side, directly up an aisleway. (Thankfully, no one was in the way!) The ball ricocheted off the facing of one of the concrete stairs that led to the concourse and it bounded back down the aisle, where it landed on the step one row behind me. I jumped to snare the pearl but was beaten to it by about half a second by a guy in his 30s. Had I been a few years younger, I might have been more spry, or perhaps I could have pulled the “cute kid” trick and the guy might have given me the ball. But alas, the ultimate baseball raffle prize has never fallen from the sky into my outstretched glove.

In baseball, we don’t like to talk about foul balls. They’re kind of annoying. They don’t really do anything. With two strikes, they don’t even move the count along. They are just a null space in which a pitch was thrown, but nothing technically happened. About the closest we ever get to acknowledging foul balls is when we talk about a player with a good “contact rate.”

What could possibly be interesting about foul balls? It's not true that foul balls are completely devoid of meaning. We know that the batter swung and that he didn’t miss, and maybe that’s something worth knowing about.

Warning! Gory Mathematical Details Ahead!

The first thing that we need to know is that not all foul balls are created equal, both in the rule book (the ones with zero or one strike put a strike into the count, but the two-strike ones … never happened), but also in the information that they tell us about a player. Past research has shown that while two-strike foul balls are (no surprise) a marker of a player with good contact skills, early count foul balls tend to be associated with a lower contact percentage.

I’ve also found that, among batters, foul ball rates for early count fouls tend to correlate very poorly with two-strike fouls, suggesting that the two are largely independent skills. That doesn’t mean that a player who hits a lot of one will hit relatively few of the other. It simply means that knowing one number tells you almost nothing at all about the other.

But let’s see what a foul ball tells us about what’s going on in the game. Let’s start with early count foul balls. Here's data from 2016 for all plate appearances, except for pitchers at bat and intentional walks. We’re going to focus on plate appearances which started with an 0-1 count (the first pitch was a strike). However, there are three ways in which that strike could have gotten there.

AVG

OBP

SLG

K%

BB%

Single %

HR %

All plate appearances

.256

.321

.420

20.7%

7.8%

15.2%

3.1%

All 0-1 plate appearances

.226

.270

.357

28.5%

4.8%

14.4%

2.5%

First pitch was swinging strike

.206

.255

.328

34.1%

5.3%

13.0%

2.4%

First pitch was called strike

.229

.273

.359

27.5%

4.8%

14.7%

2.5%

First pitch was foul ball

.229

.272

.367

28.0%

4.5%

14.4%

2.7%

We see pretty clearly that starting out with an 0-1 count is a bad idea (for a batter, anyway), but we also see that not all strikes are created equal. Note that a foul first strike is very different from a swinging first strike (and about equal to a called strike.) A first-pitch foul even suggests a greater chance that the plate appearance will end in a home run. A similar analysis of plate appearances that started 1-0 and then went 1-1 produced the same pattern.

But wait! You clever reader, you are thinking to yourself, but what if the foul ball is simply the sign of a high-contact hitter, the kind who likes to hit a lot of singles anyway? Or maybe the kind of pitcher who would get a swing-and-not-a-miss is the kind who doesn’t have strikeout stuff, so it’s not surprising that we’d see a downturn in strikeouts from the foul-ball group? Well … we can control for that. And I did.

I looked at all plate appearances that started off 0-1 and controlled for the outcomes that we usually see from that hitter and pitcher. And the effect of how that foul ball made its way onto the scoreboard still remained. If a plate appearance starts off with a foul ball, even allowing for the pitcher and hitter tendencies, we see a notable improvement in outcomes, at least compared to a swinging strike. Swinging and not missing is important.

Let’s look at what happens with two strikes then. I found all plate appearances in 2016 (no pitchers hitting) that went to two strikes. It may or may not surprise you to know that this included more than half (51.4 percent) of all plate appearances.

AVG

OBP

SLG

K %

BB %

Single %

HR %

All plate appearances

.256

.321

.420

20.7%

7.8%

15.2%

3.1%

All 2 strike counts

.179

.251

.281

40.3%

8.0%

11.0%

1.9%

Fouled off at least one 2-strike pitch

.198

.291

.320

35.7%

11.0%

11.5%

2.2%

Fouled off no 2-strike pitches

.170

.232

.263

42.5%

6.6%

10.8%

1.7%

Fouled off exactly one 2-strike pitch

.194

.282

.310

37.1%

10.2%

11.5%

2.1%

Fouled off more than one 2-strike pitch

.205

.308

.339

33.0%

12.4%

11.5%

2.5%

Once again, we find that it’s a really bad idea to go to a two-strike count in baseball, but spoiling a couple of pitches is good for the soul. And the batting line. In fact, take a look at the size of the effect of fouling off just one ball compared to not doing so.

Once again, we worry about whether this just means that a hitter who makes a lot of two-strike contact is one who just doesn’t strike out quite as much. Again, controlling for batter and pitcher tendencies, we see that the effects continue to stand. Fouling off at least one pitch really does boost a batter’s expected outcomes.

And You Thought They Were Just Souvenirs!

Let’s take stock of what we have here, particularly with two-strike foul balls. Intuitively, we knew that making the pitcher throw another pitch was going to have some positive effect. He’s a tiny bit more tired. The batter has already had a few chances to time him up. We can see the splits, and we can start to rule out some of the cause-effect problems that we might start to worry about. On top of that, we know that two-strike fouls tend to be fairly consistent. We know which hitters tend to spoil two-strike pitches on a consistent basis, although does anyone ever really bother to look that one up?

Maybe they should, because we know that a lot of plate appearances get to two strikes, and while it’s better to avoid those two-strike counts, it’s nice to have a backup plan in case things don’t work out. And I think that’s why this one is hidden. Fouling a pitch off doesn’t get us back to league average, and so we might look at the slash line of .198/.291/.320 and think blech, who wants that? Well, someone who is stuck in a situation where the expected slash line is .170/.232/.263, that’s who. But if we have a player who is good at cutting his losses, then that’s extra value for which potentially no one is looking.