probability

Predicting Every Fixture at Euro 2016

In a frankly bizarre move, the Vote Leave campaign has offered a £50m prize to anyone who can predict the result of every fixture at the upcoming Euro 2016 tournament.

Now, I’m not quite sure what the purpose of this is in terms of politics, although the referendum takes place during the tournament.

I’m told it’s all for fun, but the absurdity of this “competition” is astonishing.

Seemingly the Vote Leave camp has had two donors provide the backing for the competition, and the prize is insured by Lloyds underwriters.

But let’s do some maths to show how mad this all is.

First of all, you don’t have to get the score right – just the result. So for every fixture that will be either a win for Team A, a win for Team B or a draw. There are three outcomes per fixture then.

The tournament has 51 fixtures in total (I’m glad to see that there is no pointless 3rd/4th place playoff).

Calculating the precise odds will be hard, although a bookie should manage it. But let’s simplify things enormously and assume every fixture is equally likely to go one of the three possible ways. In other words you have a 33.3% chance of getting the result right.

This is effectively a 51 fixture accumulator, so we need to know one third to the power of 51 (ie 0.33351) to get the probability of picking the right answer. [See update below]

This is a small number.

0.00000000000000000000005%

Put another way, it’s a 2,153,693,963,075,670,000,000,000 to 1 shot.

Or 2.2 septillion to one!*

Simply speaking, this won’t happen. Indeed, if everyone on the planet entered the competition, it still wouldn’t happen.

In fact, every person on the planet would have to make 302 trillion guesses each, with everyone’s guesses different from everyone else’s, for there to be a winner.

Let’s put it another way. The odds of winning the jackpot on the UK national lottery are 45m to one. That’s why you haven’t won yet. The odds of winning the jackpot three times in a row in three consecutive draws is only 93 sextillion to one – still lower than these odds.

I imagine the underwriter at Lloyds only really had to charge for their time in drawing up a contract. The only cost to Vote Leave is building a website.

I know that companies have run prediction based competitions in the past. For example, in 2010 Toshiba ran a promotion in which you were refunded the cost of a new TV if England won the World Cup. That’s a calculated risk. Again it’s insured, but the premiums will have been more substantial and probably came from a marketing budget. But in a 32 team tournament, so there is a chance that your team will win. Perhaps the insurance might have cost £5m based on £100m of TV set sales.

Look this particular competition is a stupid thing for a slow news day. But I don’t understand the point of a competition that isn’t just unlikely (Leicester City winning the Premier League), but is categorically NOT going to happen.

And I wonder what it says about a populace’s understanding of probability that anyone even came up with such a scheme.

[Update: I later realised that after the group stages, there are of course, only two outcomes for the 15 knockout stage matches. So in fact, the number should be 0.33336 x 0.515 = 0.00000000000000000002033%, or a 1 in 4.9 sextillion chance. Much more likely, I’m sure you’ll agree!]

* A septillion is a thousand times a sextillion, which is a thousand times a quintillian, which is a thousand times a quadrillion, which is a thousand times a trillion, which is a thousand times a billion, which is a thousand times a million… You get the idea. It’s a big number.