Joe Enos

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Thursday, January 22, 2009 15:49:52

Associated Press Is Bad At Math

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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.

Tags:

money

Comments:

Comment from Brad Switzer (http://www.classcreator.com):
Friday, January 23, 2009 01:37:03

You know it's funny, I actually found your writeup after doing a Google search for something like this after seeing the same story. I noticed the same thing right away. Obviously the odds of any 2 numbers hitting twice in a row is 1 in 1,000, not 1 in a million. You already know what Day 1's numbers are. You're going to know that number 100% of the time obviously... Thus the odds of whatever number that is hitting again is 1 in 1,000. Good job there AP! :)

Comment from BluesFiddle:
Friday, January 23, 2009 13:58:08

The AP Story is fine. It just depends on what your definition of 'such an occurrence' is.

COMMENT FROM JOE ENOS:
Friday, January 23, 2009 14:07:55

@Brad: Thanks for the comment - I'm glad I'm not the only one who noticed this. @BluesFiddle: It seems pretty clear that their definition of 'such an occurrence' is 'two consecutive days with the same numbers drawn in the same order'. With that definition, odds are 1/1000. I can only think of two other definitions of 'such an occurrence': 1) Two consecutive days where 1-9-6 hit. But they'd run the same story if the numbers were 8-4-9 instead of 1-9-6, so that isn't it. 2) One individual won the grand prize two consecutive days - not a big deal, since the prize is just $500, but it's still cool for that one person. But even that didn't happen - different people won the prize on the second day. Thanks for the comment though.

Comment from BluesFiddle:
Friday, January 23, 2009 16:00:49

http://www.unl.edu/tcweb/fowler/lotterySimulation/ Simulation using Mathematica (shown in pdf and htm formats). 100,000 pairs of three-digit numbers. 118 occurrences of identical pairs.

COMMENT FROM JOE ENOS:
Friday, January 23, 2009 16:05:03

@BluesFiddle: Thanks for the link. It's a little hard to follow, but it does seem to draw the right conclusions.

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