Warming Up For the World Cup

The group draws for Brazil 2014, which starts next week, are not quite balanced, and I’m writing my usual ill-advised predictions for the group stages. As I wrote in December, there was much whining in England, but the USMNT has by most quantitative measures the most difficult group in the tournament. Indeed, the strengths of the eight groups are so asymmetrically distributed, the crime here isn’t that there is a group of death (because there’s two), but that there’s at least one “group of life”: Group E by the linked account (Switzerland, Ecuador, France, Honduras):

Group E is an absolute joke. As mentioned with respect to parity, Group E provided teams like France and Honduras a chance to advance to the Knockout Round when few other groups would have allowed such an opportunity. Yes, it is the World Cup and anything is possible. But, can you honestly say it is fair and desirable to have nations working four years to be a top contender to find they may need to win 2 out of 3 just to reach the Knockouts? Additionally, should there really be groups with no one favored because no one is genuinely a World Cup Title contender?!

That breathless language overlooks the true contender for the group of life at this tournament: Group H (Belgium, Algeria, Russia, South Korea). The 2014 World Cup includes one group with both finalists from 2010 (Spain and the Netherlands), one group where all four sides made the last 16 (Group G: Germany, Portugal, Ghana, USA). Both outcomes would make sense if the quality of the teams or their qualitative relative rankings did vary that much in four years time, and that the group draws were based on a true competitive methodology.

But this is FIFA, so they’re not. Rather, as I pointed out in December:

If the goal of seeding teams is to ensure roughly equal competition across all the groups, there should not be appreciable qualitative distinctions in strength. FIFA does not operate that way, of course. The top eight were seeded, ensuring they’d be kept apart, but then the remaining “pots” were based on geography.

Or, to quote another voice:

The global parity has created group disparity. There is no reason why in a tournament field with such quality there are only 2 groups with an average ranking of less than 20. Additionally, with 2 groups having an average over 25 makes the tournament unbalanced. It warrants FIFA reconsidering the format of dividing pots by region. Why not simply rank the teams 1 to 32 and then divide them into 4 pots accordingly? Parity makes for better viewing pleasure and gives those countries that have deserved to be a top 8 nation more of an opportunity to progress.

In the NYT today, “A Fairer World Cup Draw” outlines a method proposed by a French mathematician named Julien Guyon. The abstract to his paper that the NYT piece draws on brings attention to a much underused term, potgate:

The recent ‘potgate’ which dominated the build-up to the final draw of the 2014 FIFA World Cup Brazil attracted my attention both as a football fan and as a probabilist, and calls for a change of the rules. It is actually symptomatic of more fundamental flaws that are linked to the way FIFA enforces the geographic constraints that they put on the draw. In this paper I investigate these flaws and suggest three new possible sets of rules that produce fairly balanced and geographically diverse groups, and use a small number of bowls and balls, in the hope that for the next editions FIFA will adopt one of these fairer systems, as I believe that the biggest sporting event in the world deserves the utmost level of fairness.

Both the FIFA and Guyon method is simulated 10,000 times for each of the 32 teams in the tournament to explore how lucky (or unlucky) each national side was in its draw. What is plain by those distributions, in addition to the bit where the US was always likely to get screwed regardless, is that FIFA needs to adopt a better system for drawing the groups for Russia 2018 (in addition to a better system for drawing the host for Qatar 2022).  To quote Guyon directly from his conclusion:

In this article I investigated the flaws of the current rules of the FIFA World Cup final draw and I was able to suggest three new possible sets of rules that produce eight balanced and geographicaly diverse groups. The last two sets of rules are even totally fair, meaning that all the acceptable results of the draw are equally likely.

Oh, hang on, he just used the phrase “totally fair” and FIFA in the same paragraph.

Nevermind.