Toronto professor claims FIFA draw contains hidden bias that skews the odds

Jeffrey Rosenthal, a professor of probability in the University of Toronto's Department of Statistical Sciences, watched Friday's World Cup draw with more interest than the average Canadian soccer fan.

Together with Britain's Gareth Roberts, his Liverpool-obsessed colleague, he's been trying to correct a hidden bias in FIFA's self-made, sequential method: It doesn't give equal weight to all possible team combinations, effectively skewing the draw.

Rosenthal and Roberts have come up with not one but three perfectly fair fixes, but none was in effect when a collection of the game's greats began drawing names on a stage in Doha, Qatar.

"Every possible way of fitting those teams together should have the same chance of occurring. With the FIFA way, that's not the case," Rosenthal said following the draw. "It's subtle. It's not a huge difference. But it's enough of a difference."

Like soccer itself, the World Cup draw is more complicated than it first seems. Thirty-two teams must be assigned to eight groups of four. In an attempt to balance the groups, the teams are seeded into four pots of relative strength, based largely on their international ranking.

On Friday, however, host Qatar was assigned the first spot in Group A despite being ranked 51st in the world, gumming up the competitive works from the start. Then came a cascade of further challenges, each compounding the others.

Every group had to have at least one team from Europe. Because there will be 13 representatives from UEFA in Qatar, five of the groups now necessarily boast two European sides, but no group could have had three. No other confederation could see more than one team in the same group. Canada couldn't have been pitted against the United States, for instance, because they are both CONCACAF qualifiers.

After the teams from top-seeded Pot 1 were assigned their groups, FIFA's selectors emptied each successive pot in order, and teams were assigned to the first group that wouldn't violate any preconditions. Canada was drawn last out of Pot 4 and fit neatly into the one remaining spot in Group F, alongside Belgium, Croatia, and Morocco. 

But FIFA's sequential method still had — and will continue to have, so long as it's used — an effect on the probabilities of any one team being drawn into a particular group.

In the case of Friday's draw, England (Pot 1) and Germany (Pot 2) were unknowingly at a statistical disadvantage. Rosenthal and Roberts determined that the pure probability of those historic rivals finding themselves in the same group was 10.6 per cent. Using FIFA's method, the odds of their being drawn together increased to 11.8 per cent. (The 88.2 per cent chance against their meeting ended up holding.)

Conversely, Canada should have had a 15.4 per cent chance of playing the Qatar team; using FIFA's algorithm, Canada had a 16.5 per cent chance of achieving that dream draw. The United States received an even bigger bump in relative probability. What should have been a nine per cent chance of the Qataris and Americans facing off rose to 12.5 per cent, a 39 per cent increase.

Neither Canada nor the U.S. got lucky, but that doesn't negate the fact that the odds were tilted however slightly in their favour. The balance of this year's groups might also seem to speak well for the current method, but by Rosenthal's reckoning, the tightness of the pots — Pot 2 was the mathematical ideal, containing the ninth through 16th best-ranked teams in the world — meant that FIFA was its own kind of fortunate.

Rosenthal and Roberts have devised and proposed three alternative selection methods, each of which offers a perfectly uniform draw. Playing with their online simulator is weirdly satisfying, like watching a skilled artisan fit invisible mitre joints into place. Pick after pick, the eight groups are filled out, purely and objectively.

Their most stylish and exciting method still includes the use of lottery balls — which, let's face it, are kind of fun. A computer algorithm gives equal weight to each theoretical candidate for a group, while also meeting all of FIFA's constraints. Selectors could then be offered a collection of balls containing those names to draw manually.