Wednesday, June 4, 2014

Soccer, Math, and small multiples

NYT's The Upshot has published an intriguing piece about the upcoming World Cup this morning. According to Kevin Quealy and Gregor Aisch, authors of the charts and the accompanying article, the selection method used by FIFA to build the World Cup groups is unfair, so they propose an alternative based on the work of Julien Guyon, a French mathematician. Guyon has explained his calculations here.

The charts at the bottom of the page are probability distributions based on thousands of simulations that follow either FIFA's method (light blue curves) or Guyon's one (dark blue curves.) The Y-axis is probability (%) and the X-axis represents levels of difficulty. FIFA's method leads to a much larger variance than Guyon's: the light blue curves are flatter and wider than the dark ones. This means that a mediocre team can easily find itself in a tough group, and a strong team can end up surrounded by shaky rivals. You can clearly see this if you play with the draw simulator on top of the page. Click several times and you'll notice that very strong and very weak groups are much more likely to appear using FIFA's method.

The Upshot deserves praise for several reasons: (a) the terrific integration of copy, simulator, and graphics; (b) the beautiful small multiple array of probability distribution charts (I still believe that this kind of graphic is too unusual in the news;) (c) the fact that The New York Times is not afraid of challenging its readers with such a geeky discussion. This could be a reminder for other news organizations: Readers aren't dumb.


  1. I loved the analysis and the presentation of it, but I worry about the unstated assumption that FIFA rankings are equivalent to team quality. Typically these would under-represent the strength of the host (Brazil played fewer competitive fixtures as they don't need to qualify) and over-state the strength of a country like the USA, who qualify from a weaker confederation.

    Playing with the simulator I turned up a Very Weak Group A of Brazil, Greece, France & Cameroon and Strong Group B of Colombia, Italy, Costa Rica and Algeria. If these groups played each other in rank order, I would expect the weak group to win more than they lose.

    I'd like to do a similar exercise with an alternative ranking system (maybe the Elo ranking system) and compare the effects on the team allocation, as my gut instinct is that doing this would change the distributions again. It also adds fire to the off-field debate of the merits of different ranking systems. If I get the time, I'll post a link here

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