Statistics question: asteroids versus tornadoes

On the History Channel recently, there was a program about asteroids and the people who monitor them. At one point, the assertion was made that a person has a 1 in 50,000 chance of being killed by a tornado and a 1 in 20,000 chance of being killed by an asteroid.

The hell? People die every year from tornadoes. It’s been what, a hundred million years since anything was killed by an asteroid? But certainly no people. What’s the obvious thing that I’m missing here?

I think either someone dropped a zero, or they’re figuring, OK tornados kill people, but not that many, though there are lots of tornadoes. Just one asteroid could kill everybody.

Lies, damn lies and statistics.

These guys give about the same figures:

So, the probability of being killed by a tornado are easy to calculate, while the probability of being beaned by a rock from space are mostly just guesses, but when it happens, it’s going to kill a lot of people at once.

But is that how statistics are supposed to work? Do they realize that they are comparing events with two different modals? One is an epistemic certainty, and the other is a metaphysical possibility.

Not at all. That’s specious reasoning. If the sun exploded, it would likely kill everyone on the Earth. That doesn’t mean that the odds of being killed by a Solar Explosion are 1:1.

The assertion that your more likely to be killed by an asteroid than a tornado is utterly preposterous. And in the absence of any explanation for how they came up with the figure of 20,000 to 1, I can only conclude that they made it up out of thin air. (**Beowulff **cited a source that purports to back that figure, but I read the linked article and found nothing of the sort.)

How do we calculate the odds of something happening? The simplest way is to count the instances of something occurring and dividing it by the number of people in the sample. So if 42,000 people died in car accidents last year, and the US population is roughly 300 million, that means the odds of an average American dying in a car accident this year are roughly 7,200 to 1.

Fifty years of data from the NOAA gives an average of 57 Americans killed by tornadoes each year. So even if we make no effort to account for changes in population, or the fact that living in a tornado zone like Kansas makes you more vulnerable than someone living in Vermont, the odds of the average American being killed by a tornado are 5.2 million to 1.

What are the odds of being killed by an asteroid? In recorded human history, the death toll from asteroids is exactly zero. The cumulative death toll from meteorites is zero. The death toll from falling space junk is zero. That’s not to say that none of those things could ever happen, but the fact that it hasn’t happened, ever, suggests that the odds of it ever occurring are extremely large – exponentially larger than 20,000 to 1.

Thank you, Anson2995. That makes sense to me.

I haven’t seen the show in question, but I presume that the producers somehow based their conclusion on the work of astronomer Stephen Schultz of Princeton, who works with the Sloan Sky Survey. He and his team have spent considerable time trying to estimate the total number of asteroids in the asteroid belt. (Actually counting them is largely impossible, because there are so many, they are so far away, and they are moving). Schultz garnered some attention in 2001 when he published an article saying that his research concluded that the number of large (>1 km) asteroids in the solar system was about 700,000 – much less than previous estimates of 2 million. He guessed that this meant the chances of a large object impacting the Earth during the 21st century was roughly 5000-1, not 1500-1 as had been previously reported.

Of course, all that people heard was the 5000-1 figure, and taken out of the context of Schultz’s article, it seemed like a Doomsday prediction. In truth, it was just the opposite. Schultz himself explained that he believed an Earth-Asteroid collision was an event that would occur once every 100 million years, based on the one time it was believed to have happened 65 million years ago.

The folks on the History Channel seem to be proving they know as little about science as they do about history.

What do you mean “the one time?” There are several known impact craters, including at least one even larger than Chicxulub, which is theorized to be one possible contributor to the Permian mass extinction, 250 MYA.

I thought this was going to be a tornado v. asteroid cage match thread.

Oh, an asteroid would totally kick a tornado’s ass.

Now a meteorite caught in a tornado, that could hit a lot of individuals.

I have seen photos of cars and buildings hit by meteorites. The damage looks more than enough to kill a human. Has that never, ever happened?

Not insofar as anyone knows, however, there are at least two known cases of a person being struck by a meteorite, neither fatally. One was a woman in Alabama in 1954, and in 2004, a woman in Suffolk, England was struck.

Useful fact to remember.
96.3% of all statistics are made up.

Here is the applicable passage:
A 1 kilometer asteroid probably strikes the Earth every few million years, while a global killer on the order of 5-10 kilometers strikes the Earth every few hundred million years. A 100 meter asteroid may strike the Earth every thousand years (Cooke, 2004). In fact, in 1908, a 60 meter asteroid exploded in the upper atmosphere over a remote area in Eastern Siberia (Tunguska) and flattened trees for thousands of square miles. A high-velocity impact of a 2 kilometer asteroid with the Earth could kill a billion people. A ten kilometer asteroid impacting the Earth could extinguish us as a species (Foster, 2005). The odds of the Earth suffering a catastrophic collision with an asteroid over the next century is roughly estimated at 1 in 1500 to 1 in 5000 (Schultz, 2001). The probability of being killed by an impact event is very small on the order of 1 in 10,000 to 1/100,000. Driving and overeating are far bigger risks to the average individual.

Bolding mine.

Your method is valid if there are a large number of events in the sample. It is not valid if there are a small number of events, and very not valid if there are zero events in the sample. Yes, a large asteroid striking the Earth in the immediate future is a low-probability event, but it’s not a zero-probability event, and there’s a world of difference between the two. A zero will stay a zero no matter what you multiply it by, but a small number can become a reasonable-sized number if you multiply it by a big number. In this case, the big number is the population of the Earth. The chances of an asteroid hitting are low, but if it does, the consequences are huge, and when you multiply them together, you get a higher expected consequence than for tornadoes.

This reminds me of the story of the 2 statisticians who went duck hunting. When the bird was flushed, the first statistician’s shot missed by 5 feet above the duck, the second’s shot missed by 5 feet below. They high-fived each other and said “We got him!”

There is also the case of the 2 statisticians who were watching an elevator…

2 people got in… a few minutes later 3 people got out…

one statistician turns to the other and says :“The elevator now contains negative 1 people…”

I didn’t mean to say that an asteroid had only hit the earth once, I simply meant that the conclusions from the Princeton study were based on a single occurrence, the one which occurred sixty-five million years ago. What the article said was:

No it doesn’t, and even if you approach the data that way, it’s intentionally misleading. The implication is that we need to be more concerned (and thus more prepared) for asteroid strikes than tornadoes. Of course, that’s silly.

If an asteroid that destroys all life on the planet hits the earth once every 100 million years – that’s the number the Princeton folks came up with – and the average population of the US over those years is 300 million, that’s an average of 3 US deaths per year from asteroid impacts. As I cited previously, NOAA cited the average number of Americans killed each year from tornadoes as 57. That’s almost 20 times as much.

But the root problem is that “average deaths per year” is not the correct way to assess the risk of an exceedingly rare event like an asteroid collision. We’ve got 100 million values of zero and (theoretically) one value of 4 billion. In such a case, you can’t use the average value as a measure of probability.

This is not a complete analysis. The single-datum point (the 1-per-100-Myr impact frequency) is for a 10km impactor, which would certainly be an extinction-level event but, as you point out, is rare enough that the expected number of deaths per year is still low. What the recent asteroid surveys are trying to determine is the size distribution of smaller asteroids: those in the 100m-10km range, still large enough to do a lot of damage (though probably not an ELE) and probably impacting much more frequently than larger ones, thus possibly resulting in higher numbers of expected deaths per year.

Astronomers typically fit power-law curves to these size distributions. The recent results quote power laws n ~ D[sup]-2.3[/sup] or so [this result is a fit from SDSS data, and has a shallower slope than models predicted]: i.e., frequency proportional to the inverse 2.3 power of diameter; the power-law fit is not actually very good over broad ranges of D, but it’s good enough for this discussion. So if a 10km asteroid hits every 100Myr, then a 2km asteroid should hit every 2.5Myr or so. This is still large enough to cause global catastrophe (see here, especially Table 1 and the surrounding discussion) with billions of deaths. If we assume a global death rate of 1/3, that’s 100 million US deaths every 2.5 million years, or 40 per year.

Well of course you can; they are both (attempts at estimating) long-term averages, so they are comparable quantities. Obviously they aren’t the whole story, but it is not nonsensical to compare them. I’m curious as to what measure you propose to use instead.

But (although your numbers are not quite right because you haven’t considered <10km impacts), your main point is that these are very different types of statistical events. I agree; any rational policy will deal differently with these two types of threats. And deciding on a rational policy requires knowing a lot more than expected death rates: in particular, the full costs of the problem and of solving the problem. At current technology, stopping an asteroid impact is basically infeasible (lots of expensive ideas, but none ever tested), so a current policy for avoiding asteroid impacts probably looks something like “Improve technology and hope for no impacts in the next 50 years.” There are other parts of the problem, such as detecting likely impactors, which are feasible (and being done, at least to some extent) today. Since they require a nontrivial amount of time (to compute the orbital elements) it makes sense to do these steps well before you’ll be ready to do anything about them.

But a cost analysis cuts both ways, too. If one places a value on the species’ existence or on modern civilization, then this is an additional cost of an asteroid impact (since tornadoes are never going to threaten extinction).

The SDSS folks said there’s a 5000 to 1 chance of an asteroid 1km or larger hitting in the next 100 years, which means that they figure it’s a once every 500,000 year event. And just so that everybody’s clear of the scale of time we’re talking about, homo sapiens have been around for about 200,000 years.

I guess I take issue with two things. First, the intentional confusion between the “average deaths per year” from an asteroid and the estimated odds of an asteroid striking the earth. They are very different measures, and saying that “the odds of a person being killed by an asteroid are 20,000 to 1” is deliberately misleading.

Secondly, I take issue with the comparison between theoretical assumptions about asteroids and actual observations of tornadoes. It’s clearly an apples and oranges comparison.

I suppose. I’m not sure that we have any good ideas for stopping an inbound asteroid even in theory, so I’m not sure we ought to be investing a whole lot in developing a solution to such an unlikely event. I mean, 800,000 people a year die from malaria. Roughly 400,000 die each year from measles. Those things are much easier to address than stopping a 10km asteroid, and the actuarial tables are much less theoretical.