Foul Balls Again
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.
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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.
If there are an average of 15 games a day for 162 days in the season, thats 2430 games a year for the entire MLB. Wouldn’t that mean that someone should catch two consecutive foul balls once ever 1,371 years? 3,333,333/2430=~1371). Didn’t really think that all the way through, but is that correct?
If you have a 1 in 3,333,333 chance of catching two foul balls in a row, and there are 1371 games, then what you have to do is calculate the odds of not catching a foul ball which is (1-(1/3,333,333) to the 2430 power and then it’s 1 – that number. Which is about 1 in 1428.
I don’t think that means it’s going to happen once in every 1428 years. It means that you specifically have those odds of catching two foul balls in a row, if you went to every game. To have a 50/50 shot at catching a foul ball, you would have to attend nearly 2.3 million games.
So, it’s probably not going to happen to you. But it is going to happen to someone. Much like winning the lottery.
The Number’s Guy at the WSJ did a similar analysis but came up with a number that is much more frequent. personally I think his analysis is more accurate and you make it sound like it is much less likely than it actually is.
http://blogs.wsj.com/numbersguy/a-pair-of-lucky-baseball-fans-337/?mod=WSJBlog
Chris: I’m actually quoted in that article. I didn’t even know he did a piece on it after I talked with him.
We’re really talking about different things. The chance of predicting you, specifically you, will catch two foul balls in a row is 1 in 3 million (I’m not writing out the 3’s), or there-abouts, or even the much much lower odds that Dave Studeman came up with.
The 1 in 10,000 was once in every 10,000 games. I’m not saying it will happen once in every 3 million games.
Whoops, I read it a couple of days ago and didn’t realize you were mentioned. I now see why I thought the numbers seemed much less probable than I expected. Your criteria is that it happens to you, and it happens consecutively, correct?
I was wondering, what are the chances that any one fan catches two balls during a game?
at one particular game i attended in Oakland, i saw one fan catch two foul balls on consecutive pitches. he sat in the second deck behind home plate. and in catching the two balls, they both came directly to him – there was no needing to go and get the balls. he had his glove, and just raised it up to catch both of them. the second one he was kind enough to give to a boy who was sitting near him.
I’ve never caught a foul ball at a game, but whenever I find my seats the first thing I do is look around for the closest kid so I’ll know — if I do catch one — exactly whom I’m going to give it to.
If the odds of one fan catching a foul ball in a game are 1 in 3,333,333, and total baseball attendance for a year is about 79 million, I’d expect it to happen about for about 24 fans a year.