Paul - the soothsaying cephalopod

As of the 23rd May 2022 this website is archived and will receive no further updates.

was produced by the Winton programme for the public understanding of risk based in the Statistical Laboratory in the University of Cambridge. The aim was to help improve the way that uncertainty and risk are discussed in society, and show how probability and statistics can be both useful and entertaining.

Many of the animations were produced using Flash and will no longer work.

Article in today's Times included below. I should have included the important observation that even if Paul's final two predictions are correct, it does not change my total belief that he is not psychic and the results are just chance. Essentially when a hypothesis has zero initial probability, no amount of surprising evidence will shift that belief. Oh dear, what a closed-minded person I am.

It’s definitely time to retire. I and all my profession are being humiliated by the apparent ability of Paul the psychic octopus to predict the results of Germany’s World Cup matches. I’ve collected an alphabet of letters after my name from 35 years of analysing statistics and making predictions, and yet some soothsaying cephalopod, doubtless with few GCSEs, has got 6 out of 6 correct including the two defeats.

No interviews with Paul are currently available and so we don’t know his thought processes when his Delphic tentacle reaches out and picks the winning team, but he is probably not analysing the data on past performance which forms the basis for most football prediction systems. I recently tried my hand at this and suffered the derision of John Humphreys for my subsequent failure, and analysts at major banks also took time off from their money-making to make World Cup predictions. JP Morgan predicted England to win the Cup (although put Netherlands and Spain as 2nd and 3rd), while UBS, Goldman Sachs and Danske Bank all put Brazil as the most likely winner. Sadly this performance is unlikely to affect their bonuses.

That octopus is destroying my life’s work. I work in a team concerned with improving ‘risk literacy’, who go into schools and explain how lotteries are unpredictable whatever your Aunty says, and that just because red has come up on roulette 4 times in a row, it does not mean that somehow it is black’s turn. And that rather remarkable ‘coincidences’ happen by chance alone, such as in a class of 35 children there is an 81% chance of two having the same birthday, or that if you flip a coin 20 times there is a 75% chance that you will get a run of at least 4 heads or tails in a row. Also, when Derren Brown flipped 10 heads in a row, it was only after he had been flipping for 9 hours and they only showed the bit of film when he finally succeeded.

Most remarkable predictions turn out to due to this kind of selective reporting, and at first I assumed we were only hearing about Paul’s success and not about the hundreds of other sea-creatures picking North Korea as the World Cup winners. But now Paul’s predictions are being publicised beforehand, without any Nostradamic ambiguity. The pressure is on – can he perform under the full media spotlight or will he do a Rooney and disappoint? For some bizarre reason I can’t help hoping that he does get the next predictions right, even though it will mean my erudite lessons in chance will in future be greeted by derisive sneers of ‘OK prof, how do you explain the octopus?’



Perhaps the octopus likes the colour red, and is more likely to pick flags with a lot of red on them. This would seem to explain his usual preference for the German flag, until a flag comes along with more red, like the Spanish. This could be one way the independence assumption is violated, but of course there are many others.

Great article! Very funny. And don't worry: statistically Paul is already overdue to cross the rainbow bridge to paradise reef. You will have years to find adequate explanations.

Well, 8 out of 8 right now. What is your opinion on that, Prof? ;)

Well, the WC is over and he predicted 8 out of 8 games right. Biologist PZ Meyers thinks that we might observe the "Clever Hans effect".

Compare the colours of the flags. I've heard, that octopuses were colour-blind, but it's particularly noticeable, that it always picked the team whose flag contains yellow (or the larger area of yellow). The only exception was Germany/Ghana, but both flags contain yellow. Regards from Germany, Mario

Now, I know octopuses (or should that be octopi?) aren’t psychic, but, with a probability of 2^7 (if my math is right), the odds on that are 1 in 128. Not statistically significant in the big scheme of things, but newsworthy. Apparently he also did the 2008 European Championships and got a more probable 4 out of 6 correct. Which presumably wasn’t newsworthy.

Re: "What a close-minded person I am." Reminds me of the anchoring and adjustment models of decision-making under uncertainty e.g: Ef=f(CEi + (1-C) g (E1, E2...Ej...En) where final estimate (Ef) is a function of the confidence (C) in initial estimate (Ei) plus residual confidence (1-C) times a weighting function (g) to subsequent estimates (E1, E2..etc). C takes values between 0 and 1. g can assign weights in various ways e.g. to E1 (early news) or En (latest news) or Ej (trusted source of news). For instance high C repesents the bigot or highly confident, low C deciders rely on (g) function to generate final estimate (eg fad follower), whereas middle C's (eg .5) represent procastinaters and worry worts. Unfortunately the model makes no provision for changes in C.

Has anyone commented on the 2008 market meltdown reportedly related to flawed models of risk generated by acadenics and 'sold' to investment bankers?