Can you win a million dollars?
As Betteridge’s Law of Headlines says, the correct response to any headline ending in a question mark is “No”.
From the Herald: “Kogan Mobile – a relative newcomer to NZ – is offering $1 million if you can correctly pick the result of every game in the first six rounds of the new Super Rugby seasons.”
This is a good deal for Kogan Mobile. They get coverage in the Herald and on NewstalkZB (albeit at 5:20am), and they get a lot of email addresses, many of which will be genuine. There will be people who hadn’t heard of the company last week who now have heard of them.
I shouldn’t think the publicity is worth a million dollars, but they’re very unlikely to have to pay out. As I told Chris Keall and Kate Hawkesby, if you typically average 2 out of 3 correct predictions (roughly what StatsChat’s David Scott gets), you’ve got one chance in ten million of getting forty correct predictions — to be precise, (2/3)40
It’s actually a bit worse than that. David gets two out of three correct, but there are easy picks and hard picks, and he does better on the easy ones than the hard ones. Variation in difficult makes it harder to get all the picks right — imagine someone who was 100% wrong whenever the Hurricanes played the Chiefs; they could still average two out of three, but they couldn’t get 40 out of 40.
The variation in difficulty doesn’t make that much difference. Suppose you had a 50:50 chance for 29 of the games and the other 11 were so easy you had a 100% chance. That averages close to 2/3, and the variation is more extreme than really plausible, but the chance of getting all forty correct is (0.5)29×(1)11, or one in 500 million, only lower by a factor of 50.
If Kogan Mobile get a million entries, which seems quite a lot for New Zealand, they’d still have probably less than one chance in ten of paying out. They might have decided to wear that chance, or they might have bought insurance — in 2003, when Pepsi offered a billion dollar lottery-style prize, they insured the risk of paying out, for less than $10 million.
So should you play? Sure, if you feel like it. You just shouldn’t expect much of a chance of winning.
Thomas Lumley (@tslumley) is Professor of Biostatistics at the University of Auckland. His research interests include semiparametric models, survey sampling, statistical computing, foundations of statistics, and whatever methodological problems his medical collaborators come up with. He also blogs at Biased and Inefficient See all posts by Thomas Lumley »