Associated Press Is Bad At Math

blog@jtenos.com (Joe Enos) — Thu, 22 Jan 2009 15:49:52 GMT

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On Tuesday, the "Pick 3" drawing in the Nebraska Lottery came up with the numbers 1, 9, and 6. The significance of this: those same three numbers came up in the same order the previous day. According to the Associated Press, this is some kind of a big deal. And of course, where AP leads, hundreds of other news sources follow - the same article was present in many other news sources, from local to national news.

From the article:
Lottery spokesman Brian Rockey says one of two lottery computers that randomly generate combinations picked the numbers 1, 9 and 6 - in that order - for Monday night's drawing. He says the other computer picked the same three numbers Tuesday in the same sequence.

The odds of such an occurrence? One in a million.

One in a million. If you read that quickly enough, you might actually believe it. After all, there's a 1/1000 chance of hitting 1,9,6 on day 1, so (1/1000 * 1/1000) is 1/1000000. But take a step back - they're not making a big deal that 1-9-6 was hit twice - they're making a big deal that the same number got hit twice. The odds of that: 1/1000, meaning it will happen on average every few years in every Pick 3 in the country. Hardly newsworthy.

If you're not quite sure, here are a couple different ways of looking at it:

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Day 1: Suppose you draw 3-4-5 on Monday. That's a given - it's already happened.
Day 2: What are the odds that you draw 3-4-5 on Tuesday? Answer: 1/1000.
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Here's the same problem on a smaller scale: Suppose instead of 1/1000 odds of winning, the odds were only 1/10. I have two buckets, each with 10 balls. By their math, then the odds of hitting the same win twice in a row are (1/10 * 1/10), or 1/100. Suppose I pull a ball from bucket 1. What are the odds that I pull the same number out of bucket 2? Clearly it's not 1/100 - it's 1/10, since there are only 10 balls in bucket 2.
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Now if you want to talk about the odds of the exact sequence 1-9-6 coming up twice in a row, then we're at one-in-a-million. If one individual person bought a ticket on Monday with 1-9-6 and another ticket on Tuesday with 1-9-6, then the odds from that individual person's point of view are 1/1000000. But that didn't happen. So there's absolutely nothing newsworthy about this story, other than someone is horribly bad at math. Either the lottery officials are bad at math (that's a scary thought), or the writer and editor at the AP are both bad at math, or they are having such a slow news day that they found something that they could trick people into reading.

By the way, I took a quick look at the numbers: This occurrence has happened twice in the last 3 years just in the Nebraska lottery. It's happened 3 times in the past 10 years in the Arizona Lottery. So when you consider how many "Pick 3" lotteries there are in the country, combined with how often this happens, it seems ridiculous to make this a national story.

Of course, you could say that me reporting on a non-story is just that much more meaningless. I'd have to agree with you.

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Associated Press Is Bad At Math