Psychic elephants, math, and getting fooled

Nearly every Euro or World cup football tournament has a news feature about a psychic animal that predicts a country’s results. It was no different a few days ago when news showed up about a psychic elephant that was predicting a German victory against England.

These pieces of news are always interesting as they’re accompanied by a video of this soothsaying animal. They likely provide some comfort to those placing big bets.

They’re also a fantastic example of how we can get fooled by anecdotes into believing something that isn’t true. The reason for this ability to be fooled is the inherent difficulty in understanding probabilities/ratios.

In this case, this elephant made the news because she predicted the results 3 games in a row. How hard is that?

As a game can have 3 outcomes (Win, Lose, Draw), the probability of getting the first result right is 1/3 or 33%. Repeating that in the second game brings us to 11%. Doing it in the third game brings us to 3.7% or 1/27.

3.7% of 1/27 may not mean much. Consider this – during such tournaments, there are hundreds – maybe even thousands – of animals who are encouraged by their owners to indulge in these kinds of games. If one of them does well enough, they could become a celebrity. And, with random chance, 1 out of every 27 of these animals would get it right.

To predict the round of 16, 1 out of every 54 (only 2 possible outcomes – win and lose – at this stage) of these would get it right. Quarterfinals would take us to 1 out of every 108, semi finals would be 1 out of every 216, and the finals would be 1 out of every 432.

So, if 500 random animals around the world did this, one of them would be “psychic” as they’d predict every result right. And, the chances of 500 random animals being asked to do this by owners (across horses, elephants, and even octopuses :-)) is high.