The Value of Fouls

Stop me if you've heard this one before, but a strike is a strike, right?

Continuing my quest to be the world's greatest expert on the subject of strikes, let's turn our attention to the batter. This post investigates whether the type of strike makes a difference in the outcome of the plate appearance. In other words, is a batter more successful if they foul off strike one than if they swing and miss?

This is part one of a two part series. In this first post, we're going to examine the question retrospectively. That is, we'll look back at plate appearances that end at various counts and see if the outcome differs based on whether the strikes were called, swinging, or fouls. Part two will take a forward-looking approach - looking at each pitch as it happens and seeing whether things progress differently depending on the type of strike.

Let's look at a few different tables. The first one lists the wOBA for plate appearance that ended on a given count. The rest break that down further by looking at the type of the strikes (c = called, s = swinging, f = foul). I'm using wOBA as my measure of effectiveness since it's a nice rate stat that incorporate the run value of each plate appearance. All data is from 2000-2007 and ignores plate appearances by pitchers.

A couple things to note right off the bat. I've ignored any plate appearances that ended with no strikes, since they're not really relevant to the question at hand. I've also ignored any foul balls beyond the first two strikes. I think those most likely do have an impact on the end result of the plate appearance, but I'm also assuming they're spread fairly evenly across all the different ways of getting to the two strike count. Finally, I'm assuming order of strikes doesn't matter. Whether the batter goes swinging strike followed by foul ball or vice versa doesn't matter.

So what do these results tell us? Well, the wOBA is a lot higher with 3 balls and a lot lower with 2 strikes. Makes perfect sense, since you can't walk without getting to 3 balls, and can't strike out without getting to 2 strikes. We'll come back to that later.

Looking at the raw results, it looks like there's some benefit to fouling off a pitch versus any other type of strike. Is it meaningful? Using the formula SQRT(wOBA * (1.1 - wOBA)/PA) (found here) for the standard deviation, looking at the 1 strikes counts, and hoping I'm doing this right (I'm using the smallest number of plate appearances as my sample size), we reach the 95% confidence level for 0-1, 1-1 and 2-1. 3-1 doesn't even really demonstrate the pattern in our sample, but I think that might be dampened by the number of walks at the 3-1 count.

So I feel pretty safe in saying that there's some advantage to fouling off the ball rather than swinging through it or taking the strike. Or, in the reverse, good hitters tend to make some sort of contact on strikes.

Teasing out some kind of meaning from the 2 strike counts is beyond my level of skill, but eyeballing it, it looks like there's something there too.

I'd like to filter out strikeouts and walks, since I was really most interested in whether the strike type indicated anything for balls put into play. So let's look at the same set of tables, showing wOBA on contact only.

The results are pretty much the same. Still significant positives for foul balls at 0-1, 1-1 and 2-1, while not necessarily so for 3-1. And the 2 strike counts are still outside my realm of statistically competency, but appear to demonstrate a similar, if muted, effect.

What conclusions can we draw from these results? It appears that there's a correlation between fouling the ball off (as opposed to swinging and missing or taking a strike) and success in the at-bat. One possible explanation is that good hitters are more likely to foul off the ball. I'm not sure how true this is (see Adam Dunn), but it should be easily testable. Another possibility is that fouling off the ball indicates a near-miss and therefore suggests better contact when the ball is put into play.

The big assumption in looking at things this way is that there's no difference in how a plate appearance proceeds based on the type of strike. I don't think that's really the case. If a batter rips the first pitch into the seats just outside the foul pole, I'm betting the pitcher will respond differently than if the first pitch was swung on and missed by three feet. To check that assumption, part two will look at the same question as the at-bat unfolds, and will try to identify the effects of the various strike types on the whole at-bat, not just the ultimate outcome. I'll try to get the post out next week but there's a good chance it will slip a little bit.