This post is inspired by the famous book Fooled by Randomness by Nassim Nicholas Taleb.
Imagine a person who wants to play Russian Roulette. It is a game in which the referee (or the executioner?) takes a revolver containing one bullet in one of its six chambers, spins the cylinder, points to the head and pulls the trigger. If you survive, you get a prize – 4 million dollars.
Alive at Age 50
As seen in my previous posts, one can determine the person’s survival chance is 5 in 6 (83%) in one game. This person decides to play this game once a year, starting at age 25. What is the probability that she will become a 100-million-dollar net-worth individual (NWI) by 50? Use the Bernoulli trial that we had discussed in the previous post, and we get a survival chance of about 1% after 25 games [25C25 (5/6)25(1/6)0]. The odds to earn 100 million this way are, indeed, small; no two opinions but to acknowledge her exceptional luck!
Let me complicate the plot: imagine 1000 individuals started playing this game in different parts of the world (different venues, referees, different TV sponsors!). There is a definite possibility of about ten winners (give or take a few) after the 25th season of this deadly game.
A Superhero is Born
Suddenly, these superstars are on the covers of Fortune, in popular TV shows, and parents of young children start pressuring their kids to learn this game. Spiritual gurus proclaim their remarkable moral habits; TV anchors interview their grandmothers; data analysts flood YouTube, fitting their BMI to eating habits to academics with their achievements. Ladies and gentlemen, I am presenting you this evening: the superhero of all fallacies, the Survivorship Bias. It is a selection bias in which reasoning is made by considering only the survivors’ data and not those that have already ceased to exist.
Survivorship bias exists everywhere, far more than what you think. The superstars of the stock market were Taleb’s favourite example. Consistent longer-term performances of fund managers have been the subject of many studies. More often than not, they were no better than Roulette gamers. Then comes the band of ultra-rich business leaders – risk-takers, college dropouts, lonely, full of grand ideas …
Another example is our obsession with the past. You must have heard about extraordinary claims of how prosperous, healthy and long-living our ancestors used to be when living ‘close to nature’ – all these when the average life expectancy was just in the 20s! Of course, the author who wrote the stories included only those who survived their adolescence AND showed some amazing ‘acts of valour’. Try calculating the joint probability of the following: chance of surviving adolescence x having some remarkable skills x being found by the author x getting the king’s approval to include in the book.
Dice Probability Calculator
Human Life Expectancy PNAS
Mistakes due to Survivorship Bias: BBC
