Opinion: As a statistician, I wondered how the FIFA draw method for the World Cup would affect the probabilities. For kicks, my research collaborator and I came up with a fairer approach.
It’s official — Canada has qualified for this year’s soccer World Cup. The last time that happened, 36 years ago, I was a teenager backpacking through soccer-obsessed Europe.
The group assignments will be determined on Friday in a televised event where teams are selected by drawing balls from urns. However, there are various restrictions: each group must include one team from each of four “pots” , no group can have more than two teams from Europe nor more than one from South America, etc.
For example, if every complete assignment were equally likely, then the probability that Canada would be placed in Group A should be 15.4 per cent. However, under FIFA’s method, that decreases to 14.8 per cent. Germany’s Group A probability should be 13.4 per cent, but decreases to 12.5 per cent. And the United States’ probability should be 9.6 per cent, but increases to 12.5 per cent .
Our first method uses a computer algorithm called a “rejection sampler,” which is fast and simple and gives precisely equal probabilities. Unfortunately, it might not provide good drama for a televised draw.
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