# On the probabilities of winning the world cup

I just read an article on the bbc about sports data company gracenote’s estimates of countries’ winning probabilities for the upcoming soccer world cup. I then looked up the best current betting odds on oddschecker. These are, of course, subject to change. I looked at them on the morning (Pacific Time) of the 7th of June.

I then looked at the expected return to a one Euro bet on the various countries winning the world cup under the assumption that gracenote’s estimates are completely correct. So if you believe in gracenote’s estimates as the abolute truth, what should you bet on?

Well, Brazil is the favorite according to gracenote but also in the betting odds. Gracenote gives them a 21% chance  of winning the world cup, and at current best odds of 9:2 you would win 4,50 Euros if you put 1 Euro on Brazil. This means you would expect to get 4,5 * 0,21 = 0,945 Euros back. So if you are risk averse or risk neutral you should not bet on Brazil at these odds, but if you had to you could put a Euro on Brazil. Germany has similar best odds of 5:1, but gracenote does not rate them so highly, giving Germany only an 8% chance of winning. So you would only expect to win back 5*0,08=0,40 Euros for every Euro you place on Germany. This means that, if you could, you should “short sell” Germany to make money in expectation. This is not so easy to do in sports betting markets so let’s not pursue this here. It turns out that most of the better teams are not rated as highly by gracenote as they are in the betting odds.

So, again, what should you bet on if you believe in gracenote’s estimates? According to gracenote Peru has a 5% chance of winning the world cup. At current odds of 325:1 you would get an expected payout of 325*0,05=16,25 Euros for every Euro you put on them. This is an expected return better than anything you can get on the stock market I would guess. Mexico, Switzerland, Colombia (with expected payout of 3,75, 3,50, and 2,60 Euros for every Euro you put on them) are also high return bets.

I am afraid, though, that I believe in the efficiency of sport betting markets much more than in one sports data company’s estimates, so I will not follow these suggestions myself. If you want to know more about the efficiency or inefficiency of betting markets a good starting point would be a 1988 survey by Thaler and Ziemba.

One day later, on the 8th of June, I noticed that Peru’s odds have gone down to 200:1. Perhaps this was a reaction to the new information provided by gracenote (although I am not quite sure when their estimates were posted). You would, however, still make an expected winning of 200*0,05 = 10 Euros for every Euro you put on Peru if you believe gracenote’s estimates.

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# Intro to Econ: Second Lecture – Arbitrage with Sports Bets

In this part of the second lecture I turn to another area in which the absence of arbitrage – due to people preferring more money over less – implies severe restrictions: sports betting. I begin by giving the students potentially fictional betting odds on three football (soccer) games, given in the following table.

$\begin{tabular}{c|ccc} & Game 1 & Game 2 & Game 3 \\ \hline A & 1,1 & 4,75 & 1,9 \\ x & 11 & 3,6 & 4,2 \\ B & 21 & 1,78 & 5 \\ \end{tabular}$