Here in Georgia, it’s almost impossible to avoid regular news reports of how much money the MegaMillions lottery is worth, and with the jackpot at over a half a billion dollars, it’s even worse than usual. It’s like they’re conspirators with the lottery organization, trying to drum up more business. If that’s not bad enough, most of the reports have been full of stupid probability comparisons.

According to the back of the play ticket, the current probability of winning the MegaMillions jackpot is one in 258,890,850, usually shortened to one in 259 million. (You can calculate it yourself. Here it is: 75*74*73*72*71*15/(5*4*3*2). If you want, you can express it this way: 75!*15/(5!*70!) where “!” is the factorial notation.) Lately the news reports have been adding that you are more likely to be hit by an asteroid than win the lottery.

Is that true? I decided to look into it. There are a number of Web sites that indicate that it’s true. For example, Wired says the odds of being hit by an asteroid are one in 250,000 (They should really express odds as 1:249,999, which is one chance in 250,000, but that’s way too abstruse.) But Wired provides nothing to back up that probability.

The Economist quotes the chance of an asteroid impact of 78,817,414/1 (the apparent source is the National Safety Council; National Academies in Britain, presumably, and also presumably an impact that results in one’s death). So maybe that’s a good number.

On the other hand, NASA’s Jet Propulsion Lab should have a pretty decent idea about the probabilities of an asteroid hitting the Earth. According to their Web site, although the Earth has been hit by quite a few large asteroids (Apparently a body smaller than one kilometer would be a meteorite if it hit the Earth. A larger one would be considered an asteroid. But that’s way too abstruse.), “no human in the past 1000 years is known to have been killed by a meteorite or the effects of one impacting.” They note that there are ancient Chinese records of such a death. The say that as best they can tell, there is no large asteroid (the kind that causes widespread destruction and mass deaths) that is likely to strike the Earth in the next several hundred years. That seems to imply probabilities far, far lower than winning the jackpot, at least when calculated over reasonable time spans, like a human lifetime.

The requirement for calculating over a reasonable period brings up another point. I’ve been trying to decide whether the comparison between the probabilities is right or wrong, but I think the asteroid comparison is not just wrong, it’s worse than wrong. It’s actually meaningless. The lottery is a single event, one that takes place once at a specific time, and so the probability applies only for the event. The probability that I will win the lottery before the drawing is zero. So is the probability that I will win after the drawing. But the probability of being hit by an asteroid can only be specified over a period of time. The probability that I will be hit by an asteroid within the next second is vanishingly small. The probability that I will be hit by an asteroid within the next 20 years is also small, but different. So saying that the probability of being hit by an asteroid is larger than the probability of winning the lottery is meaningless unless a time period is specified. But, for the news media, that’s way too abstruse.

Even if you grant that they actually mean that the probability of being hit by an asteroid over the remainder of your lifetime is greater than winning the next lottery, they’re still wrong. I think you can get a pretty good idea of that from a purely intuitive sense. Consider that the population of the United States is about 314 million. To my knowledge, no one has been killed by a meteorite this year, or last, or the one previous to that, for as long as I can remember. The population of the Earth is about 7 billion, and still, according to the JPL, no one has been reported to have been killed by an asteroid within the last 1000 years. If the probability is greater than the lottery probability, I am pretty sure there would have been reliable reports by now. And since there have been none, I am pretty sure the probabilities are not as great as the news reports are saying.

But still, the probability of winning the lottery is very small. It’s so small that it’s hard to come up with a comparison that has makes any intuitive sense. I always say that your chance of winning the lottery is essentially the same whether you buy a lottery ticket or not. Of course, that’s not really true. But it might as well be.

Admission:

Despite the irrationality of playing a gambling game with odds so absurdly skewed towards the house, Leah and I do buy lottery tickets, and have since we started dating. My mother played the lottery even before that and for a long time I refused to buy her tickets for her. I thought it was just a waste of money. We recognize that it’s basically a tax on the mathematically illiterate, but we explain it on the same basis as a lot of people – it lets us fantasize for a while about what we would do if we won. I’ll let you know how it turns out.