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Why Paul the Octopus was right
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It is rather interesting to see the two year old Paul the Octopus get all his predictions right. His prediction skills have reached an unprecedented high with the latest correct prediction of Spain beating Germany in the second semi-final. While analysts have gone to town trying to explain Paul's prediction skills, it is essentially simple mathematical probability or chance at work and nothing beyond that. Let us try and understand this through a simple coin tossing exercise. When a coin is tossed there are essentially two outcomes possible, heads or tails. Given this the chance of a coin landing a head (or a tail for that matter) is ½ or 0.5, every time a coin is tossed.
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So if the coin is tossed twice what is the probability of the coin landing a head (or a tail) twice? The answer is very simple. The probability is ¼ or 0.25 ( .5 x .5). Or there is a 25% chance that the coin will land head two times in a row. Similarly if the coin is tossed five times, what is the probability of the coin landing head (or tails for that matter) five times in a row? 0.03125 (0.5 x 0.5 x 0.5 x 0.5 x 0.5). Or there is a 3.125% chance the coin will land head five times in a row. Now what is the probability that the coin will land a head ten times in a row? 0.0009765625 or there is 0.098% chance of the coin landing head ten times in a row. So what does this coin tossing experiment tell us? There is a chance of the coin landing head constantly all the time, even though the probability of it landing head over and over keeps going down, as the number of coin tosses increase. Similar is the case with the predictions of Paul the Octopus. Every match has two results since we are in the knockout stage. Either of the two teams can win. So the probability of Paul the Octopus getting the prediction of an individual match right is 0.5. Now Paul has predicted the results of six matches correctly for Germany? Now what is the probability of getting the results of six matches right? The answer is 1.5625%, which is a rather small probability, but is a probability none the less. So Paul is no oracle, it's just a matter of chance that he has got things right, till now. This phenomenon can be observed in various other facets of life. John Allen Paulos in his rather engaging book A Mathematician Plays the Stock Market gives the example of e of a stock newsletter scam wherein the publisher sends out the newsletter each week predicting the way a common stock market index (like the Sensex or the Nifty) will go. In the first week, the newsletter is sent out to 64,000 people, picked up randomly. To half of these people, the newsletter predicts that the index will go up and to the other half the newsletter predicts that the index will go down. Whatever happens to the index by the end of the week, 32,000 people would have received a correct prediction. The same process would be repeated again, but this time with the half which got the newsletter with the correct prediction. So 16,000 people will get a newsletter predicting the rise of the index and to the rest the newsletter predicting the fall of the index. This process will be repeated a few times more. By the end of the sixth week, 1000 people would have got correct predictions for six consecutive weeks. To these people another letter would go, pointing out the good performance of the newsletter. And from now on if the individuals wanted to continue getting the newsletter, they would need to pay for it. The phenomenon of Paul getting his predictions right is just the same. Nassem Nicholas Taleb, in his book Fooled by Randomness which he wrote before he became famous for writing The Black Swan, explains this phenomenon brilliantly. He says, "If one puts an infinite number of monkeys in front of (strongly built) typewriters, and lets them clap away, there is a certainty that one of them would come out with an exact version of the Iliad".Having said this, Taleb asks "Now that we have found that hero among monkeys, would any reader invest his life's savings on a bet that the monkey would write the Oddessey next?" Calls for killing Paul the Octopus have already begun in Germany, for predicting Germany's loss to Spain correctly. I just hope, Germans turn vegetarians for a while. PS: I am not surprised that Paul has retired from making any more predictions. The owner obviously understands all good luck runs out someday.
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By Sheldone Pillai Aug 12, 2010 It's wonderful the way you link things up. Your deep insights into the behaviour of global markets and the expected repercussions are commendable. I always believe that all systems eventually are led into randomness by nature and sustained and timely efforts are required to reinforce their smooth working and that is the tougher part. :)
Best of luck and please continue writing the way you do. It's wonderful.
By Vikram Madan Jul 16, 2010 If you have infinite monkeys banging away at a typewriter, all the books ever written will come out, exactly as they exist. All the newspapers ever, exactly as they are. Everything that has ever been written. Constitutions, medical books... et al.
And an infinite number of books yet to be written, and news yet to happen. It will all come through.
We have seen parrots, parakeets, monkeys, and last but not least, humans do the predictions before. Octopus is new, that's what made it more interesting. 8/8, 100% for the 8-legged.
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Yeah he has got it all right and retired....
Wonder whether anybody has read the book called SECRET. If you think something WILL happen, the universe will adjust itself to see to it that "it" happens. The fear factor that the losing team will have and the winning team's motivation push them to perform in that direction. THAT IS THE SECRET.
@ Rohitkumar
Even thought the coin doesn't have memory, the probability reduces the second time because of the number of outcomes.
i.e, when a coin is tossed 2 times, there are 4 possible outcomes.
1) First one is heads and 2nd one tails
2) First one is tails, 2nd one heads
3) Both are heads
4) Both are tails
so landing on tails in a row or heads in a row has the probability of 1 in 4, ie 0.25.
how can this paul predict? i did not understand how he can predict. anyway i am not in a mood to oppose him. paul, keep it up.
Yes, what Jack said is right. ANIMALS have a greater sense of reality and they are easily able to access information fields in the cosmos, which enables them to time travel into the future. If Paul were on Facebook, I would be his follower.
1.5625% is NOT the correct answer because 3 of the 6 matches had 3 possible results! The correct answer therefore is [(1/3)^3]*[(1/2)^3]. Moreover, one could argue that in those 3 matches that had 3 possible results, not each of the results had the same probability.
@The answer is 1.5625%, which is a rather small probability, but is a probability none the less.
This is a very weak argument and the article is a very amateurish attempt to prove/disprove Paul's predictions. The way i see it, you have used a Coin Toss event as an analogy to drive home the point that Paul's predictions were a chance. Fair enough!
The second part of the article is rather interesting read. Thanks for introducing the book "A Mathematician Plays the Stock Market". Will check it out.
The first and the second part of the post are loosely connected.
This is illogical. How do you compare Mr Paul's predictions with the newsletter's predictions? Paul has been pretty famous before the World Cup. Whereas for the newsletter, the number of people who receive the right prediction decreases each time the letters are sent, in Paul's case, the number remains the same.
To Rohitkumar:
The chance of the coin landing a head (or tail) in a row is not equal to the chance of the coin landing a head (or tail) second time. You cannot equate the result of 2 combined events with one selective event.
The octopus proved there is a supreme power in the world.
Your maths is wrong, as pointed out by others also. Probability will not change for n coin tosses, and it will be .5 for each toss as they are independent events. Please correct your post.
i just read the part about taleb and a monkey writing the iliad and i can say boldly that it's a total lie and if i find that monkey, i will invest my whole life on him because i know he can write more than Odyssey. probability and randomness could only make sense for so long as putting 50 words in reasonable sequence and if it makes any sense? that's another question.
am pushed to say "whatever" but then i won't. even the logical presentation here is faulty because if there are only two possibilities and a prediction tilts towards the right answer at 90% accuracy then even science will try to tilt and since science is stiff-minded, it pushes it to para-science which is the medium through which scientists express their growing beliefs in alternative realities without getting off government payroll.
I am confident it's just a coincidence, nothing more than that. Paul's final match prediction is going to be wrong.
Vivek the "Kaul" Vs Octopus the "Paul" ;)
Hey guys, heard about a parrot in India who's also predicting something about FIFA matches?
I think Paul should become a freelance financial adviser and buy himself a little secluded bay in the South of France.
I agree with Jack.I believe that Paul the Octopus's ability to predict is due to its ability to access the field information in the Cosmos. Time Travel? Sounds funny and impossible to human beings. Can we just make more extraordinary assumption that the Octopus in fact was a very intelligent and more civilized creature from the other side of outer space where millions of years ago its origin/kingdoms were destroyed by the 'big bang'? This makes me sound more ridiculous... hehehe... well, the Octopus might be one of the survivors from the big bang which managed to escape via its own spaceship and later crash landed on our planet Earth, ironically, into the Ocean, and had to evolve to some kind of octopus. Who knows? Maybe Octopus in the previous form is just like us, human being.
"Now Paul has predicted the results of six matches correctly for Germany? Now what is the probability of getting the results of six matches right? The answer is 1.5625%, which is a rather small probability, but is a probability none the less."
You're right about this: rather small probabilities are still non-zero probabilities, which strictly speaking means they aren't IMPOSSIBLE, but that just as strictly speaking means that they're IMPROBABLE (and may thus mean that the explanation is implausible). It generally suggests that something other than random chance is at work.
One could say as you've said for any result and, if one does as you've done here, render any hypothesis based on probabilistic evidence unfalsifiable. ("YOU say he opened the door and walked through it, but *I* say that he [quantum] tunnelled through it. The probability of him doing it is really small, but it's a probability nonetheless.")
By Rudra Chattopadhyay Jul 9, 2010 I believe that the selections Paul makes are based entirely on the Flag's "appeal to him". Now this "appeal" can be influenced by various factors, like hunger (reddish flags of Spain & Germany give a feeling of presence of blood) or even peace & quiet (if he goes to whiter flags). But another major influence as rightly mentioned by Jack is the cosmic waves that people produce as he begins to move. Maybe the people around sensed that Spain should be a deserving winner & they were looking at Spain's flag; this might have caused the octopus to go Spain's way... at least this is what I think ;)
Even though I feel that the comparison of the soothsayer octopus oracle with a random flip of a coin or to infinite monkeys playing with a typewriter is preposterous to say the least, nevertheless, it made for interesting reading.
You also overlooked the fact that out of 6 predictions in a row, 4 were favourable and 2 were unfavourable. Assuming the order of prediction was LWWWWL (W-Win, L-Loss), there are 6!/(4!.2!) ways in which we can have 4 wins and 2 losses. So the probability reduces even further.
All I am trying to say is the predictions cannot be dismissed as pure mathematical probability. There is certainly an element of mystery, something that is beyond the comprehension of human beings. We human beings suffer from the ego problem that we can understand and explain anything and everything under the sun using the mathematical models known to us. We need to accept that our cognitive powers also have their own limitations.
Well, your analysis has some basis, but just think about this. Each team Germany played, 11 out of 12 times, its predictions were correct. And, every prediction process is 0.5 times. Have you ever thought of probability of the probability of selecting wrong prediction, that's also huge, But that it is being avoided by Paul each time (11 out of 12 times) is somewhat mind boggling. And, that's the real mystery. Though it can be justified by mathematics. But, life and events are not outcomes of just statistics always. And, your calculations of coin toss are anyway wrong. I would like to learn from Paul how to select the right choice 11/12 times. If I can do it, I would be the king, perhaps.
By Trent Boyett Jul 9, 2010 There are more than 2 chances, what about a draw? This blows your theory out of the water. Sorry.
The owner probably is mixing something in one of the containers which is attracting the octopus towards it.
It is not about Mathematics, Animals have greater sense of reality and they are easily able to access the information field in the cosmos which enables them to time travel into the future.
You are kidding, right... 1.56% is impossible to predict even with a peta byte super computer. The answer is not in probability but in time and space.
Even if one uses the most powerful computer known to man, predicting 6/6 wins in the World Cup by any means is not only extraordinary but also illogical. Mathematics cannot solve the mysteries of world.
Human beings have lower psyche than animals. Anyway, the powers that be, Illuminati, would suppress the octopus or even kill it or send out wrong information to discredit it... This information is too vital for the powers that be to come out.
Each time a coin is tossed, the chance of its landing a head (or a tail) is 0.5, because each toss is a separate act, and the coin has no memory of the result of a previous toss. Then how the chance of its landing a head (or tail) in a row (second time) is reduced to 0.25?
By Avinash Ram Jul 8, 2010 "what is the probability of getting the results of six matches right?" cannot be calculated only based on the octopus's prediction. You would have to consider the probability of Germany winning or losing as well. So, you would have to calculate the probability of the octopus's prediction and the match's outcome being the same.
If you would assume the match's outcome to be random, then the probability of getting that order in winning and losing matches would be the same as the probability of the octopus prediction which is 1.5625% (or 0.015625).
So, the probability of we witnessing a perfect correlation between the octopus and Germany's matches is 0.015625 * 0.015625 (= 0.000244), which is 1 in 10,000.
The fact that we witnessed the one octopus out of a million of them is enough reason for its popularity.
If you consider all the matches that the octopus has predicted (including the Euro Cup), the probability gets much lesser than 1 in a million.
I really thought it was obvious that there was a link to probability in the octopus episode until I read this article... Hard to believe people consider it to be an oracle.
You overlooked the fact that Paul also correctly predicted 5 out of 6 German games in UEFA Euro 2008. This means the probability of this occurring is that of correctly predicting 11 out of 12 matches.
This gives us a binomial distribution with p = 0.5 and n = 12. The probability of 11 successes then is 0.29%, significantly less than your estimate.
I don't think Paul has psychic powers, but you still have to marvel at the sheer unlikeliness of this 1-in-300 even, especially given the paucity of predicting octopi in the world.
I do feel there is a tricky side to it. But my gut feeling is that Paul's owner would have placed something in the container which attracts the octopus. I think the owner makes a calculated prediction, based on which he would have placed the bait in the container which he feels could win. If it be so, Paul's owner has done wonderfully well to have predicted correctly.
By Edouard Goudenhoofdt Jul 8, 2010 I would like to comment on this.
I agree that the perfect prediction of Paul the octopus is only due to luck. However, if we consider that it is not really Paul but a human that made the prediction, then the probability of a perfect prediction is a little higher. Indeed, football teams are not coins and Germany has a higher probability to win against weaker teams and a higher probability to lose against stronger teams. So the probability of a perfect prediction would be about 20%.
Paul is not one of the millions of octopuses doing prediction. So the monkey comparison is not relevant. If the good skills of Paul were presented after the World Cup, then it might have been the case.
By Benjamin Opoku Wireko Jul 8, 2010 Paul is a great guy, he allowed destiny to take its own course. Germans don't have what it takes to win the World Cup. They got to this stage through luck. THEY SHOULD LET PAUL BE.
even then it was only a 1.56% probability. by this logic chances paul would have gone wrong were (100-1.56)= 98.44 which is 63 times more than his probability of getting things right.
By Tatunmen khan Jul 8, 2010 one thing is clear... that you are a jerk!
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Yeah...my mother feels the same about me :-) ...thanks for reading and commenting
By Rakhi Sahay Jul 8, 2010 Super... I just love your blogs and am a regular reader. Though I don't have the talent to write like you, but I will tell you a small prediction that I made today, similar to our Paul-y... I somehow knew you would write on Paul :-) Keep it up! Best.
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Thanks for reading and commenting....
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