This World Cup seems full of surprises. The defeat of Argentina against Saudi Arabia and today the defeat of the Germans against Japan. Nobody ever predicted it, it is said on social networks. Neither did we, but we said it could happen. The probability we gave of Arabia's victory was 17.8%, close to that of rolling six on a die. It's unlikely, but we've all rolled a six. Something similar happens with the probability of victory for Japan, our prediction was Japan with a 33% probability. One in three, the probability of rolling five or more on a die.
Despite the fact that we are not aware, we all have an expected probability that things will or will not happen. Those with the most accurate distribution can bet better and make better decisions. The bookmakers have an expected distribution and according to it they give the returns of the bets. If you have a more accurate distribution there is an advantage that you can exploit. Next we take the bookmaker returns, maximize the expected value of the bet return according to our model, and assess how we are doing so far.
A person who bets a dollar on each game following our advice right now would have $24.58, not bad.
By: Pablo Lemoine