Should you have bet on Leicester City?
As you know, Leicester City won the English Premier League this week. At the start of the season, you could get 5000:1 odds on this happening. Twelve people did.
Now, most weeks someone wins NZ Lotto first division, which pays more than 5000:1 for a winning ticket, and where we know the odds are actually unfavourable to the punter. The 5000:1 odds on their own aren’t enough to conclude the bookies had it wrong. Lotto is different because we have good reasons to know that the probabilities are very small, based on how the numbers are drawn. With soccer, we’re relying on much weaker evidence.
Here’s Tim Gowers explaining why 5000:1 should have been obviously too extreme
The argument that we know how things work from following the game for years or even decades is convincing if all you want to prove is that it is very unlikely that a team like Leicester will win. But here we want to prove that the odds are not just low, but one-in-five-thousand low.
Professor Gowers does leave half the question unexamined, though
I’m ignoring here the well-known question of whether it is sensible to take unlikely bets just because your expected gain is positive. I’m just wondering whether the expected gain was positive.
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 »
My late father used to work for a London bookmaker. One of his jobs was to set odds for outlandish bets like the possibility of snow falling in London on Christmas Day or, I’m not kidding here, the likelihood of aliens arriving on earth. In those days I don’t think it was legal for UK bookmakers to take bets on football. If it was, my dad would have been the person setting the odds for Leicester City to win the league.
My Father was a wizz at mental arithmetic and used maths to set odds for horse races based on form. However, much of his work was what he described as “advertising”. Setting the odds on aliens invading meant his firm would get written about by newspapers, which was very good for business.
He told me that the odds for, say, a team like Chelsea or Manchester City winning the league would be was he called an actureal calculation. It would take into account how much money arrived from gamblers and would dynamically change, just as horse race betting would.
My dad would have described the 5000 to 1 on Leicester City as advertising. It seems generous, no team (well maybe Aston Villa) is really that much of an outsider. But in reality the firm wouldn’t get many bets on Leicester, so the actual number would be meaningless in normal business terms.
My guess, knowing how my father worked, is that the bookmaker would have won far more than normal this year. Paying out 5000 to 1 to a handful of small punters would be a fraction of the payout if, say, Chelsea had won.
And, I’m extrapolating here, but I’m willing to bet there would have been newspaper and TV stories about the people who won those bets, each featuring the bookmaker’s name. A sound investment all round.
8 years ago
That’s an excellent point.
So, we can make a good case
(a) that the bookies set the odds too high but were right to do so
(b) that, nonetheless, most people shouldn’t have tried to take the bet, and didn’t.
8 years ago
First of all, I think people have been conflating “Leicester winning the league” with “any unlikely team winning the league”, although the effect of this on their conclusions is probably not huge. If there were other teams at 5000-1 this season, I suspect you’d find around about 12 people with bets on them to win it as well. Probably even more from supporters of a team like Bournemouth, making their debut season in the Premier League.
Given what was known at the start of the season, I’ve seen quite a few analyses (including some that account for point 4 in Prof Gowers’ post) that suggest that the 5000-1 odds were actually low; as are, I imagine, the similar-in-magnitude odds being offered for snow on Christmas and Elvis being found alive. His point 1 is a good one if the odds were only based on a binary outcome of “did this team win the league?”. But the bookies have far more information than that, such as estimates of the attacking/defensive qualities of each team, home advantage, etc, and their models have proven to be quite good at predicting not only the league winner, but the approximate number of points each team will end up on.
I imagine the model — using simulated league tables, not the binomial distribution — gave a probability lower than 1/5000, and as the commenter above says, the bookies then rounded it to a number that would’ve looked good in ads – and lowered their risk in case of a black swan (/ fox?).
What seems to be clear though, is that even if a bet at the 5000-1 odds at the start of the season almost certainly had negative expected value, at some point during the season the expectation of a bet on Leicester became positive, and that is where the bookies lost out. I wouldn’t be surprised at all to see 5000-1 odds being offered at the start of next season for other teams with ‘a new manager and some unheralded new players’. It’ll draw a few headlines and increase business without too much risk. Especially if they’ve learnt their lesson and lower the odds if that team goes on a Leicester-like run.
8 years ago
I think people have been conflating “Leicester winning the league” with “any unlikely team winning the league”
Yes, that’s the point of my analogy with lotto, but as you say, it probably doesn’t make a huge difference.
8 years ago