Foul Balls Again

by
May 15, 2008

In his excellent Ten Things I didn’t Know Last Week column, Dave Studeman speculates on the odds of two fans sitting next to each other catching a foul ball. I was asked about the LA Times article (where two fans sitting next to each other caught back-to-back foul balls) in an e-mail last week and the math to solve this problem became a huge topic of conversation over my weekend.

We previously calculated the odds of catching a foul ball/home run at about 1 in 1000, assuming that everyone in the stadium had access to all foul balls and home runs (which isn’t exactly true).

So let’s say that each foul ball hit into the stands is an independent event and they’re randomly distributed. And let’s say that where you’re sitting you have the ability to catch a foul ball. And let’s say there are 10,000 fans sitting in an area where you can catch a foul ball.

Your odds of catching any one foul ball hit into the stands is 1/10000. Now if there are 30 balls hit into the stands each game, your odds of catching a foul ball have increased to 1-((9999/10000)^30). Which is about 1 in 333.

Now your odds of catching 2 consecutive foul balls in a game is considerably worse and we’re going to assume that both these foul balls are catchable. (Dave Studeman in his evaulation does not assume that and that’s a major difference). Catching two consecutive foul balls would be (1/10000)^2, which is 1 in 100,000,000. But you have 30 chances, so the odds are 1-((99999999/100000000)^30), which is about 1 in 3,333,333.

Those are your odds of catching two foul balls in a row at any one particular game if all things were completely random.

Update: The Numbers Guy over at the Wall Street Journal did a piece on this earlier in the week and Carl Bialik (The Numbers Guy) is who sent me the initial e-mail.





 

David Appelman is the creator of FanGraphs.

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joser
15 years ago

But foul balls aren’t randomly distributed, of course. Thanks to the nets behind the plate, overhangs from upper decks, and other stadium configuration issues there are places foul balls will never (or very rarely) go. And then of course the very act of fouling off a ball doesn’t result in a random distribution — far more end up in the areas just behind the dugouts than land out by the foul poles. There’s probably a couple of thousand people at most who sit within arm’s reach of areas where foul balls land almost every game. I’m sure if we plotted a season’s worth of foul balls onto a stadium diagram we’d see certain areas that were foul rich and others that were deserts. Even without that level of detail, there are obviously areas where you can sit to maximize your chances, and two people sitting next to each other in those areas are certainly more likely to both go home with a ball.

I recall watching a Mariners’ game a couple of years ago where two line drives were hit just foul down the 3rd base line. The lower box seats jut out towards the line there, just past the bases, and both the balls went right into those seats — and right into the glove of the same fan. The announcers were remarking on how unlikely that was, but it really wasn’t… particularly since the fan with the glove was the only one trying to catch them while everyone around him was trying to get out of the way of those rockets.

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