A few weeks ago we discussed the creation of a model (Do you want to bet on it?) that showed the probability of different teams winning the world cup, and also showed the probabilities of other events within the world cup. This model has now been used for 3 purposes: – 1 – As part of the entry into an official modelling competition run by the Brazilian Operational Research Society 2 – As part of the entry into a competition within our Capgemini FET group to determine the scores of each match 3 – To assist with getting money from the bookmakers. So how did we fare? Did we beat the Brazilians at their own game? Did OR lead the way with the rest of the team? And most importantly, did we beat the bookmakers? 1. Brazilian Operational Research Society Competition We read about this competition in another entertaining blog! The Brazilian modelling competition is very simple. Each participant only needed to submit probabilities for each of the first 48 world cup games – win/lose/draw. Although this sounds like it should be a good fit for the model, in reality the scoring mechanism that was chosen to mark the submitted models tended to favour models that were blander. For example our model strongly predicted that Spain would beat Switzerland for which we gave the probabilities of 77%/16%/7% (Spain/draw/Switzerland) and the average probabilities were (51%/27%/23%). Due to the scoring mechanism that was chosen, teams were penalised heavily if they strongly predicted a result which did not occur. In this case we scored -0.74 and the average model scored -0.46. The Germany Serbia result was similar, as indeed were quite a few others. For this reason, we finished 10th in the competition (out of 10)! 2. Capgemini FET group Competition The FET competition was also simple. Each player had to predict the actual result for each of the first 48 games. There was a range of scores from 3 for predicting the exact result to 0 for not getting the right result. The table below shows the final position: –

In the end the Capgemini Model finished 3rd, which was way better than the average. However we didn’t win. The reason is that the model predicted the average score. You would expect such a model to do better than the average person picking numbers using no technique, but there will always be some lucky people who for whatever reason pick the right scores. Again, though, the model was not designed with the scoring system in mind. Interestingly two other predictions by OR entrants (in pink) came 2nd and 4th – so 3 out of the top 4 places for OR driven entries. The results from both these competitions demonstrate the importance of designing a model to answer the question that is asked. If the question is not considered then the model produced may give interesting results, but it may not give the best answer. 3. Beat the Bookies The model used in the above competitions was actually developed to answer a third question Is there a difference between the odds offered by a bookmaker and the odds from assessing the chance of the result happening, and can we make money on that difference? The model has been used to look at whole tournament events – such as who will win and who will be in the final, and at the scores in individual matches. As the tournament has yet to finish, for now we can see how the individual match predictions are going. If we take the Portugal vs North Korea match as an example, the model showed that there were a number of places where the probability of various results was better than the odds being offered. These are shown in the table below: –

For each of these results, betting on the result would pay out more than the probability suggested, so a bet was placed on each result. The value of the bet varied according to the odds, so £2 was placed on 3,2 and £1 on 7,0. Of course as you now know the final score was 7-0 to Portugal, and this match netted over £200. In total 6 of the 40matches that have been attempted have produced wins, the value of these wins has far outstripped the amount wagered, currently to the sum of over £300. If we continue to follow the system we will definitely be positive at the end of the tournament. All this for an initial investment of only £200. So we may not have the kudos of beating Brazil at football, or the satisfaction of trouncing our colleagues, but we will be quietly counting our success when the final final whistle blows.