The Psychic Octopus: How to Be Right 8 Times in a Row by Pure Luck
The short version: a single guesser calling 8 fifty-fifty matches correctly has a 1 in 256 chance. But Paul the Octopus wasn't the only animal guessing in 2010, and with 100 guessers there's about a 32% chance that at least one gets all 8 right. Nobody writes about the 99 who didn't. The same arithmetic makes 'tipsters with a perfect record': start with enough of them, and luck will produce one.
Old Ted from the allotments keeps hens, brews something in his shed that he calls cider and the fire brigade calls "a situation", and has a hen called Doris who predicts football.
Before each Saturday match, Ted puts two bowls of corn in front of Doris, one under each team's name. Whichever bowl she pecks first is the prediction. Doris is six for six. Uncle Gary has started placing bets on her advice. Ted has started charging for consultations, payable in corn or cash, preferably cash, because Doris eats the corn.
Doris has a famous predecessor
In 2010 an octopus called Paul, living in an aquarium in Oberhausen in Germany, was offered two boxes with food before each of Germany's World Cup matches, each box marked with a team's flag. He picked the winner of all seven of Germany's matches and then the final: 8 out of 8. He became world famous. (At the European Championship two years earlier, he'd managed 4 out of 6, which got much less coverage.)
If each pick is a fifty-fifty guess, getting 8 in a row has a chance of 1 in 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1 in 256. That's unlikely for one octopus. But Paul wasn't the only one.
The ones you never heard about
During that World Cup, all sorts of animals in all sorts of countries were picking matches for the cameras, along with countless office sweepstakes, pundits and uncles. Suppose there were 100 guessers, each picking 8 matches at random.
- Chance that one particular guesser gets all 8: 0.39%.
- Chance that at least one of the 100 gets all 8: about 32%.
So a perfect animal oracle was close to a one-in-three shot, and once it happened, the world's press was guaranteed to find it. The 99 animals that guessed wrong got eaten, ignored or both. This is multiple testing: try enough times and something will look miraculous, so the miracle tells you how many tries there were, not how good the winner is.
Chance of a perfect 8 out of 8 by pure guessing
How to make a perfect tipster from nothing
The same trick works on purpose, and it's an old one. Write to 1,024 people. Tell 512 that the home team will win on Saturday and 512 that the away team will. After the match, forget the half you got wrong, and repeat with the other 512, then 256, then 128.
After ten weeks, one person has received ten correct predictions in a row from you, without a single wrong one. To that person you are a genius. They will probably pay for week eleven. You have not predicted anything: you have simply let survivorship bias run a mailing list.
How to check a perfect record
1. Ask how many started. How many hens, octopuses, tipsters or newsletters were guessing? A winner from a thousand guessers is expected.
2. Look at every prediction, not the famous run. Paul's full record was 12 out of 14, still good, but with a less magical ring.
3. Watch the next ten, not the last ten. A record made before you heard of someone was selected by the fact that you heard of them. Only predictions made afterwards are a fair test.
Where it costs you money
Fund managers, newsletter writers and social media traders with a dazzling recent record are drawn from a very large pool. Some of the dazzle is skill; a lot of it is that the pool was big. Before paying for anyone's picks, find their full record, including the funds they closed and the calls they deleted, and judge them on what happens after you start watching. It's why we tested 430 strategies and showed all of them, not the eight best.
The moral
Doris picked the wrong team in week seven. Gary lost $40. Ted explained that Doris had been distracted by a fox, which he has since seen off with a bottle of the cider, and that a seventh-week wobble is well known among professional hens. Doris's record now stands at six from seven, and Ted has raised his prices, on the grounds that she is now more experienced.
Paul's record is as widely reported; the 100-guesser example and the mailing-list arithmetic are illustrative. Doris and Ted are fictional; the cider, unfortunately, is not. Educational content, not financial advice.