What Were the Odds of Paul the Octopus Picking Eight Straight World Cup Matches?

The Oracle of Oberhausen, Paul the octopus
The biggest star to emerge from the just-concluded World Cup has eight legs -- but has never kicked a ball. An octopus named Paul living in an aquarium in Oberhausen, Germany is now an international celebrity following his feat of correctly picking eight consecutive World Cup matches, culminating in Spain's victory over Holland.

What are the odds? Well, according to a San Francisco State mathematician, there are two answers to that -- an easy one and a hard one.

For each World Cup contest, Paul was presented with two buckets of mussels. One bucket was designated with the flag of one World Cup soccer team, and the other with the opposing squad. In each instance, Paul chose the eventual winning side. Assuming each run was independent of the others, the odds of this occurring are simply 1 over 2 to the eighth power -- or one in 256.

Paul didn't see this one coming, though...
Professor Mariel Vazquez, however, isn't quite ready to sign off on the easy answer. Was each of Paul's predictions truly independent? Did he go after a particular bucket? Did he prefer a type of mussel in one bucket as opposed to the other. Did he simply choose the left one over the right one? Since this wasn't a scientific experiment, the level of scrutiny necessary to answer these questions doesn't appear to have been present.

Also, since the World Cup is limited to 32 teams and run every four years, Paul hasn't really been put to the test. "The sample size for the octopus was quite small," notes Vazquez. "If you were tossing a coin eight times, you won't get four heads and four tails. You could have all tails in one experiment of eight [flips]. But if you repeat the experiment a million times, on average, you'll get a 50-50 response."

Not to be a killjoy, Vazquez admitted that Paul's psychic extravaganza has proven "amusing," and she'd been pondering the odds of his feat even before SF Weekly cold-called her. "But you can't draw a conclusion from one experiment."

Actually, this is Paul's second experiment -- he predicted four of Germany's six matches in the 2008 European Championships. He's 12 for 14 overall -- better than most any two-legged prognosticator -- but, Vazquez notes, this is still a very small sampling.

It appears to be the only sampling Paul is going to get. Aquarium officials have announced that he's giving up the psychic racket and going back to being a regular octopus. Vazquez applauds the decision to retire the Oracle of Oberhausen. "Everyone would have wanted to go see him," she says. "This is a good idea, I think."

By the way -- SF Weekly's odds of finding a mathematician in his or her office in the middle of summer turned out to be one in 15. It's not quite as difficult to phone one as predicting eight straight Cup matches -- but it sure ain't easy.

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