## A quick note on the absurd Goldman Sachs World Cup predictions

If you haven’t been on twitter this may have passed you by, but there’s been extensive and widespread panning of this set of World Cup predictions by renowned investment bankers Goldman Sachs. (The track record of Sachs can best be described as spotty). The largest source of scrutiny? Their claim that Brazil have a 48.5% chance of winning the World Cup. I’m here to show that that prediction is probably even more stupid than it may initially look.

To win the World Cup a team has to win 4 knockout matches. Let’s assume that Brazil face four equally talented teams in the knockout round. This isn’t quite true, but for convenience (and to be generous to Sachs) lets assume it is. For the record Sachs have them facing the Netherlands, Uruguay, Germany, and Argentina so it’s not too far off to my eye. For a team to have a 48.5% chance of winning four straight knockout games against opposition teams of equal strength the implied odds of winning a given game is 83.4% (0.834^4 = 0.484). That sounds high to me, so lets provide some context by looking at the odds for Premiership matches in the ’13-14 season.

First we need make some assumptions that I think are generous to Brazil (and thus Sachs):

1) that Brazil will have a home advantage that’s as large as that experienced by Premiership teams
2) the team that was an 83/17 favourite to win in the first 90 minutes will also be the 83/17 favourite to win in extra time/in penalties (this is particularly generous to Brazil)

(Note that neither of these are mentioned in the article as to if/how they’re in Sachs’ model)

You’ll probably notice that these assumptions make it very convenient to just use the odds for each Premiership match. I’ve averaged the odds from eight bookmakers and ignored the odds of a draw. Using just the odds of each team winning we can see, if a given match had to be won by one team or the other (as for a World Cup knockout match), whether one of the teams was at least an 87.4% favourite to do so. The full list is included below (click on the table to see it full size):

They’re not as rare as I expected but it doesn’t take a particularly keen eye to see the kind of matches that are represented here. Good Premiership team against pretty bad to terrible Premiership teams. And here’s where my problem lies with the Sachs’ predictions. Are Sachs really suggesting that the gap in talent between Brazil and the Netherlands/Uruguay/Germany/Argentina is equivalent to that between Arsenal and West Ham, or Chelsea and Villa, or Spurs and Norwich? Does that seem reasonable to anyone out there?