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.