Today sees the start of the World Cup – the premier football tournament in the world. As you would expect, the OR team has been hard at work determining who is likely to win. But for us this is not just a bit of fun - this is also a chance to make some real money at the expense of the bookmakers! So who do the bookies think are going to win*?
If the bookies are offering odds of 4/1 then this means that every £1 you spend, you get £4 back (plus your stake) if the bid is successful. If your team is expected to win 20% of the time then you will break even – 1 in 5 times you will gain £4; 4 in 5 times you will lose £1. Are these odds reasonable? To determine this we created a Monte Carlo model base on historic match data (from FIFA). The model Using the results of past football matches, we created a ranking system and a distribution of results for when teams with different ranks playing each other. These distributions help us predict the likely outcome of any international football match and, as the World Cup is a series of football matches with a set of rules determining who plays who, we are able to model the entire tournament. Having created a model that can ‘simulate’ a single World Cup, we then run the model a large number of times (imagine not having to wait another 4 years...). From this we can see how many times each team wins – and this effectively tells us the probability of that team wining the tournament. We simulated the World Cup 5,000 times - of these England won the tournament 265 times giving a probability of 5.3%. The advantage of this sort of model is that it not only takes into account the relative strengths of each of the teams, but it also incorporates the structure of the competition – for example, what England's chances are given who they are likely to play in the final stages of the tournament. Whereas traditional modelling often gives only worst, average and best case 3-point estimates, a Monte Carlo model such as this one can also give lots of additional information – such as who is likely to win each group, and what are the chances of each team getting knocked out at each round. Our model gives the following probabilities for each team to win the world cup:
The bet So how can we use this information to our advantage? Well the trick is to compare the probabilities with the odds offered by the bookies. By comparing the odds to the probabilities, we can work out the best bet to make. In this case, the best bet is the Netherlands – for each £1 you bet on them at the odds of 9/1 you can expect to win £1.16p. So if you were to bet a large number of times then you would expect to come out on top. Of course the problem is that there is only 1 World Cup, so even though you may have an expected return, it is not guaranteed on a single event. One way to cater for this is to spread your bets on more than one team and place bets on multiple (ideally independent) events within the tournament. Its worth noting that the odds for England are very bad compared to the likely probability of them winning. For every £1 you bet on England you can expect to lose 55p. A reason for this is that the bookmakers are not taking the true probabilities into account when they set the odds. Instead they are considering the popularity of bets and their consequent exposure – as many people from England are betting on their home nation the book makers adjust the odds accordingly. Finally, it’s worth saying that this model is just a bit of fun – we will not be responsible for any bets that you choose to place (but of course will be asking for commission if you win!) * odds taken from Bet365.com 10th June 2010