Nate Silver — yes, that Nate Silver, who had predicted Brasil to win the World Cup (see diagram in the post above, courtesy of FiveThirtyEight) — compares his complex (and, dare we say, opaque) statistical methods, like the Soccer Power Index and “Elo ratings,” with simple betting markets in his humble-pie post titled “The most shocking result in World Cup history.” Here is an excerpt (emphasis ours):

The Soccer Power Index (SPI) match-predictor (which uses a poisson distribution to estimate the range of possible scores) gave Germany only a 0.022 percent probability (about one chance in 4,500) of scoring seven or more goals …

Although we don’t have SPI ratings before 2006, we can look at the Elo ratings, which are heavily correlated with SPI and contain data back to the 19th century. The Elo ratings (which we’ve updated manually since the start of the World Cup) had Brasil as a 65 percent favorite before Tuesday’s match, with most of that based on its (supposed) home-field advantage …

Betting markets, which had the game at even odds going in, look a lot better than SPI and Elo in this instance. But there was almost certainly some bad luck for Brasil. [The Brasilians] had more shots than Germany in the match — I would never have guessed that while watching the game — and kept possession of the ball slightly more than half the time. Some of the goals that Brazil keeper Julio Cesar allowed were unavoidable, but he was not exactly Tim Howard in net …

In other words, prediction markets are great, but no one can predict a “Black Swan” like the lopsided outcome of yesterday’s Brasil-Germany match. By the way, what do you think about Silver’s observations about the role of luck? Wouldn’t you expect “luck” (bad and good) to be distributed randomly on both teams during the duration of the match? Also, should FIFA consider a forfeit rule?