It’s that time of year (or every other year) when a big football tournament is kicking off and one of your colleagues suggests a sweepstake.
Should you venture £1 on this?
Let’s leave aside questions of team bonding, the evils of gambling and the likelihood that the eventual winner will spend their winnings on biscuits for the team. Reality Check is interested only in the odds.
Consider a World Cup sweepstake in which it’s £1 to enter, all 32 teams are drawn and the person who draws the eventual winner gets all the money.
Their effective odds will have been 31 to one (because when you bet with a bookmaker, you get your stake back if you win).
Compare that outcome with a situation in which you draw the name of one of the 32 teams out of a hat and then go and put £1 on that country to win with the best available odds at a bookmaker.
What you want in a sweepstake is to end up with better odds than you would at the bookies, so we’re interested in how many teams you could draw for which that would be the case.
As the tournament kicks off, the answer to that question is nine. There are nine teams for which there are odds in the bookies of less than 31 to 1 against them winning. For example, if you draw Brazil in the sweepstake and they win the World Cup then you get £32, while if you’d bet that pound on Brazil at the bookmakers you’d be struggling to get more than about a fiver.
The nine countries are:
So if you are the first person drawing in the sweepstake then you have a nine in 32 chance, about 28%, of picking a team for which you’d have better odds than you’d get at the bookmakers.
Under the circumstances, you would be considerably better off choosing a random team and putting £1 on it at the betting shop. For example, if you’ve drawn Iceland in the sweepstake and they somehow manage to win the tournament, then you’ll win £32 via the sweepstake when you would have won £200 or £300 if you’d made that bet at the bookmakers.
This is partly because the World Cup is structured with its seeding system in a way that favours highly ranked teams, making it relatively unlikely for two of them to have to play each other before the quarter-finals, and harder for an outsider to win the tournament.
But there are complicating factors here.
If you are not the first person drawing in the sweepstake, then the odds change every time a team is drawn. So, if you see Brazil or Germany going, then your odds deteriorate. Whereas if a succession of sporting minnows are drawn, your odds improve.
If you are organising a sweepstake, then this is why you need the draw either to be secret or to make sure everybody has paid you before anyone draws. Nobody is going to enter a sweepstake if only Panama and Saudi Arabia are left in the hat.
Many sweepstakes are not organised to be winner-takes-all, which complicates matters somewhat. Perhaps you’ll give £16 to the winner, £10 to the runner-up and £6 to the team that is knocked out first.
Although this spreads the winnings, it does not do enough to your expected outcome to make it statistically worth entering the sweepstake.
This is not to say that picking a team out of a hat and betting £1 on it is a particularly good idea either.
Maybe the Reality Check team is just missing the point here, or maybe the author of this piece is feeling bitter because he drew Costa Rica in the office sweepstake.