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Are you more likely to be killed by a meteor or to win the lottery?

This tweet from the QI Elves popped up on my Twitter timeline:

In the account’s usual citationless factoid style, the Elves state that you’re more likely to be crushed by a meteor than to win the jackpot on the lottery.

The replies to this tweet were mainly along the lines of this one from my internet acquaintance Chris Mingay:

Yeah, why don’t we hear about people being squished by interplanetary rocks all the time? I’d tune in to that!

A couple of other helpful sorts have provided some extra data as context for this fact:

I asked on Twitter if any turbonerds keep a record of every jackpot ever, and of course they do: Peter Rowlett and Tim Stirrup both provided me with a link to Richard K. Lloyd’s comprehensive table, which reckons there have been 4749 winners, of which 3220 became millionaires.

4750 people have ever won the lottery (for a definition of ‘won’ that might not be the one we want, but it gives us an order of magnitude)

And only one person ever has been crushed by a meteor:

I immediately hit the

AMBIGUOUS PHRASING OF ODDS KLAXON

(Hey, QI like to do it to their guests, so why can’t I?)

The statement sounds wildly incorrect on first inspection, so I reckon we’re not talking about the same kinds of odds.

It must be the case that:

  • someone has worked out the odds of being killed by a meteor,
  • someone has worked out the odds of winning the lottery, and
  • someone has compared those two numbers.

I assume at least the first two someones were not QI Elves, and I reckon the third one probably wasn’t either. So, where did QI get their fact?

A search for “meteor lottery odds” got me this story on independent.co.uk published five days before QI’s tweet, so that’s probably their source. That links to “Review Journal”, a generically authoritative-sounding title, which turns out to be the Las Vegas Review Journal, who in 2015 published an article by someone affiliated with gobankingrates.com titled “20 things more likely to happen to you than winning the lottery”. That cheery listicle cites a 2008 article by Phil Plait on his Bad Astronomy blog where he cites Alan Harris’ answer to the Fermi question of working out your odds of being killed by a meteor, directly or indirectly. The “crushed” phrasing, which is a stronger statement than the one Harris looked at, seems to originate with the Las Vegas Review Journal. Maddeningly, Plait doesn’t give a citation for Alan Harris’s calculation and I can’t find a better source on Google, so the search stops here.

After all of that chasing, I’ve got a kind-of reputable source for the “1 in 700,000” odds of being killed by a meteor presented in the Independent article. That’s much better odds than the 1 in 45,057,474 chance of winning the lottery claimed by operators Camelot. We hear about people winning the lottery fairly often, so why isn’t “meteor squish” a journalistic cliché like “bus plunge”?

Well, the meteor figure is your lifetime odds of being killed, and the lottery figure is your odds of winning each time you play. That’s it – they’re measured in different units, effectively. Plait’s Bad Astronomy piece contained a good explanation of what the odds meant, but that got lost when the headline figure was spread in factoid form.

So we can’t compare the two numbers as stated – that’d be like me saying I’m taller than you are old. What can we do to get numbers for meteors and lotteries that we can compare?

One option is to assume both take place once – a meteor hits Earth, and you play the lottery. We know the odds of winning the lottery in one attempt, and one of Harris’s assumptions in his model was that an asteroid impact would kill everyone – so your probability of being killed is 1. No contest – you’re way more likely to be killed by an asteroid that hits Earth than for the lottery ticket you just bought to be a winner.

A more reasonable approach might be to look at your odds within a certain period of time. We’ve already got a figure of around 1 in 700,000 for being killed by a meteor in a 70-year lifespan, so we just need to get the corresponding figure – what are your odds of winning the National Lottery at least once in your lifetime?

Clearly, it depends on how often you play. My personal odds are zero – I’ve never so much as bought a scratchcard. Conversely, if you buy enough tickets, you can guarantee you win, a tactic executed to great success by Voltaire and later on some MIT students. Those strategies both relied on oversights in the rules of their respective lotteries to make them profitable, but if you’ve got a fortune to spare you could buy a National Lottery ticket corresponding to each combination of six balls and guarantee that exactly one of them will win.

For the sake of getting a reasonable number, let’s say you buy one ticket for each draw. There are two draws each week, so 104 draws each year. So your odds of winning the lottery at least once in 70 years is

At this point I wanted to use the fact that you can only play the lottery once you’re 16, and the life expectancy in the UK is 81.2 years, but I’ll stick with 70 years of playing so we can compare with the meteor number.

\[ 1 – \left( 1 – \frac{1}{45057474} \right)^{(104 \times 70)} \approx 1 \text{ in } 6190 \]

That’s a way, way lower number than the meteor number. So you’re vastly more likely to win the lottery in your lifetime than you are to be killed by a world-ending meteor – over 100 times more likely, in fact.

And if a meteor did kill everyone, you’d be unlikely to read about it in the news the next day.

2 Responses to “Are you more likely to be killed by a meteor or to win the lottery?”

  1. Anonymous

    It is a METEORITE, not a meteor, that actually hits the surface of the earth. That’s why nobody has been killed by a meteor. (I suppose it MIGHT just happen if the person were in space orbiting the earth!).

    Reply

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