Most foul balls in one at-bat

Editor’s note: A version of this article was originally posted to the SABR-L listserv on August 25, 2009. The post has not been updated.

By Ted Turocy

Here’s a summary of what the Retrosheet corpus has on the topic of most foul balls in one at-bat.

The most foul balls in a PA in Retrosheet files occurred 7/23/1988, when Kevin Bass flew out to left field against Steve Bedrosian in the 8th inning after fouling off 15 pitches, with the PA going FBFBFFBFFFFFFFFFFFX.

Three PAs involved 14 fouls, with the most notable among these being Alex Cora against Matt Clement in the 7th on 5/12/2004, when Cora hit a 2-run homer to right after battling BCBFFFFFFFFFFFFFFX.

Overall, the distribution of number of total number of fouls in a PA is:

• 15 fouls: 1 PA
• 14 fouls: 3 PA
• 13 fouls: 5 PA
• 12 fouls: 3 PA
• 11 fouls: 26 PA
• 10 fouls: 59 PA
• 9 fouls: 191 PA

Now, about the data: Retrosheet has pitch sequences for “many” games since 1988; it’s not complete, but the overall coverage of the last 20 years is a significant percentage of the total games played since then. Prior to 1988, coverage is sporadic, except for the treasure of a long run of Dodgers games. Overall, a rough estimate would be that Retrosheet has pitch sequences for maybe 15% of the PAs in history (that’s a real back-of-the-envelope calculation, but should be good enough for what follows).

Given this partial data, what can we expect about what the “real” record is for fouls in a PA? It is extremely dangerous to extrapolate out the tail of a distribution like this, but, hey, I’m feeling saucy this morning. The data above are fit roughly by a model where each long PA is extended by a foul ball about 35% of the time on each pitch. If we start with the 191 PA at 9 fouls and compute forward using that 35% rate, we would predict 8.19 PAs with 12 fouls, 2.87 with 13 fouls, 1 with 14 fouls, 0.35 with 15 fouls, and 0.12 with 16 fouls in the Retrosheet data, which is qualitatively similar to what we see. If we assume that Retrosheet has pitches for 15% of the PAs in history, AND we assume (and this *is* a big assumption) that pitch patterns in the last 20 years are fairly representative of history, then we would expect, in history, that there have been about 55 12-foul PAs, 19 13-foul PAs, 7 14-foul PAs, 2 15-foul PAs, 0.82 16-foul PAs, 0.29 17-foul PAs, and 0.1 18-foul PAs. In other words, given the data we have, it’d be reasonable to expect the record is around 17 fouls.

Again, this is extrapolation, and as such needs to be treated with great caution. There are three key assumptions which could be wrong.

1. The probability a plate appearance is extended by a foul is independent on the length of the PA. It’s possible that when a batter and pitcher have gone through 10 consecutive fouls, one or both of them change their approaches, irrespective of whether it’d be optimal to do so. It’s unclear what effect this would have if true; does it make the PA more or less likely to be continued by a foul? The data are too thin to try to answer this.
2. The probability a plate appearance is extended by a foul is independent of the batter and pitcher. A control pitcher who throws lots of strikes matched up against a batter with great bat control would probably generate more fouls than a power pitcher against a free swinger. To the extent this makes a difference, this would tend to increase our expectation for the record above 17, though how much above 17 is, again, not clear. In order to get the expected record up to 23 fouls, for instance, you would need to assume that there’s around a 60% chance a pitch winds up as a foul once a PA gets to 9 fouls.
3. Modern data are representative. We just don’t know whether this is true or false. On the one hand, we have all these legends of 20+ foul plate appearances, but at the same time, we have all these legends of there being fewer pitches per PA. Those aren’t incompatible per se, if there were a lot more variance across pitchers and batters in the past than today in terms of the changes a pitch wound up being a foul.

Given all this, if I had to bet, I’d put the over-under on the most fouls in a PA at about 19. I think there’s something to my points (2) and (3), and both of those would cause me to revise upwards the calculated prediction of 16 or 17. However, barring a situation where a pitcher and batter conspired to generate lots of foul balls for some reason, it’s hard to see the record being likely to go past 20.

As for these anecdotes about 25-foul PAs, we need to be careful about some selection bias. They were surely long PAs. However, one has no way of knowing when a PA starts that it’s going to be an epic PA. At some point around 10-12 fouls, people might start looking around at each other and asking how many fouls had been hit. In the absence of someone systematically recording pitches, the estimates people will give in that situation will vary; if you asked a small group of people how many fouls there’d been when there really were 10, I’d bet you’d get answers ranging from 7 to 14. So, then, someone starts counting from 14 or 15 at that point, instead of the actual 9 or 10, and if the PA really goes 15 fouls, it gets remembered as 20.

So, in the absence of a systematic record — someone charting pitches, or an audio or videotape to refer to — what will be remembered are PAs which were truly long, but also where the count of fouls was estimated on the high side at some point in the middle of the PA. That could easily account for a PA which really had 16 or 17 fouls — quite reasonable given the data — being remembered as having twenty-plus.

This reminds me of an exchange I had at the convention in DC. As the old saw goes, data is not the plural of anecdote. However, data are, in some sense, nothing more than anecdotes which are systematically recorded. That’s why having pitch-by-pitch for a large number of games is essential to answering this question accurately; otherwise, we wind up selecting out plate appearances which are long, but then furthermore get misremembered as being longer than they were.