Was Paul the Octopus Lucky or Skilful (and how about Richie McCow)?
Guest post by Tony Cooper
Paul The Octopus is famous for picking the winner in 8 out of 8 games at the FIFA World Cup in 2010. How did he achieve this amazing feat? Was he skilled or was he lucky?
To get 8 out of 8 games right where each game is a 50-50 guess the probability is 0.5 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5 = 0.0039 (or one chance in 256). This seems too incredible. An octopus can’t be that good.
Where is the flaw in this probabilistic reasoning?
The answer is that the probability that Paul got a game right was not 0.5 but more. Much more. In fact the probability was much closer to one. Here is the explanation:
Paul, a German octopus, was only used to pick German games, usually picked the German team, and the German team usually won. So the chance that Paul picked the winner was more than 0.5 for each game. That accounts for 5 of the 8 games.
What about the games that Germany lost and the game where Germany didn’t play? Let’s take a guess.
This tournament was not Paul’s first time at playing the game. He had learned previously that there was always food under the German flag. Paul – with some ability to distinguish the flags of different countries – usually went for the German black, red, and yellow. He might have had monochrome eyesight which is why he picked Serbia as a winner in the game against Germany because in monochrome the Serbian and German flags look similar.
For the final Germany wasn’t playing so Paul went for the most German looking flag – that of Spain (red, yellow, red). He seems to have a preference for that flag since he also predicted the win of Spain over Germany in the semi-finals. All flags picked by Paul had horizontal stripes.
So Paul was lucky but not as lucky as the 1 in 256 chance suggests. His main luck was that his team was one of the best teams in the tournament and that some of the other good teams had similar flags.
Will Richie McCow be successful at picking the winner of the All Black games in the Rugby World Cup? Possibly – as long as he keeps picking the All Blacks and the All Blacks keep winning. Will the All Blacks keep winning? That’s a story for a later article.
Tony Cooper, formerly of the Applied Mathematics Division of the DSIR, is a Quantitative Analyst with Double-Digit Numerics of Auckland. He consults mainly in the investment, finance, and electricity industries. His research interests include risk and volatility prediction, alpha generation, data mining, statistical learning, and time series analysis.
The problem is one of selection bias. If we set a raft of these animals going; Paul the Octopus, Peter the Poteroo, Dave the Dingo, Andrew the Aardvark, Yvonne the Yak, … then if we consider enough of them then one will appear to display amazing predictive powers. And then we never hear of Yvonne the Yak’s very mixed record.
David Brillinger appeared in a very good article in the New York Times on this subject when Paul the Octopus was at the peak of his fame.
13 years ago
I talked about selection bias when I was interviewed by TV3 about Paul. Bias seemed likely especially as there was talk that there was more than one Paul the Octopus.
But at that time Paul had picked 4 out of 4 games. He went on to pick another 4 more correctly. No selection bias there (but still the possibility of octopus swapping!).
13 years ago
The other issue here is the alternative hypothesis.
I can only think of three possibilities, in order of prior probability:
1) Chance (augmented by selection bias)
2) Some of the games are rigged, and the octopus/cow/etc owner knows this and is consciously or unconsciously leaking the information
3) Very large chunks of our knowledge of zoology, neurology, and physics are completely wrong.
Anyone that actually didn’t believe in (1) should be taking the psychic octopus problem much more seriously. Especially investigative journalists.
It’s pretty clear that the people writing the stories don’t actually believe them and don’t really care whether they are true or not. That is, in the technical sense of philosopher Harry Frankfurt, Richie McCow is bullshit.
13 years ago