Luck, Skill, and What Happens When You Toss a Coin 10 Times

Look at this chart– it’s a simulation of 20 people flipping a coin ten times. Let’s call it the World Series of Flipping. Heads are worth +1 point and tails are worth -1 point.

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Just as you would expect, some contestants did better than others. The spread is approximately symmetrical– about 3 people scored very high, about 4 scored very low, and the rest were more-or-less average. Of those, some were above 0, some 0, but they were overall unremarkable compared to the big leaders and big losers.

Suppose the World Series of Flipping is a multi-round game. The winners get to keep on playing, but once a contestant gets caught with a score of -1 or lower, he becomes a loser.  Losers have to collect their things and go home.

So here is what happens when we remove the losers:Screen Shot 2013-12-22 at 1.30.30 AM

Now we expand it to remove the unoccupied negative space:

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The symmetry of the first image disappears, and this paints a very different picture of the outcome. Rather than an even distribution of some failures, some successes, and most mediocrity, we just have a few winners with the rest being non-winners who are still in the game.

Why is this misleading? Consider this: if you were to take the results of the first round, remove the losers like we did, and run it again, remove the losers again, and so on, you would end up with just one or two winners. You would then be inclined to look at one of the long-term winners and, judging by their impeccable track records compared to their failed competitors, logically conclude that they are more skilled at tossing coins. You might even be tempted to suggest that he is more likely to toss heads in the future than the others.

But that’s obviously wrong– this was a purely probabilistic exercise. No one competitor is any more skilled than another. Each one, regardless of his track record, has a 50/50 chance of flipping heads next round, and hence a 50/50 chance of coming up as a loser in the long run. But that’s not always how it seems.

Like the World Series of Flipping, life is a game made up of many rounds. The lucky ones, as long as they keep living, get to keep on playing, and the unlucky ones get weeded out.

We have a tendency to look at successful people and try to emulate them, and we look at less successful people and we try not to do what they did. And why not? We’re only trying to learn from our environment.

But in doing this we fall victim to a significant fallacy. We make the mistake of assuming that past performance is an indicator of future success. And the real bitch of it is that sometimes past performance really does indicate a propensity for future success, but generally we have no way of identifying when that’s true. Sometimes success is the result of competence, and sometimes it’s luck. I think usually it’s a combination, but in any case we can’t tell the difference by observing.

It gets worse: We can’t tell the difference between luck and skill when observing other people, but we also can’t tell the difference in ourselves and in our own histories. Are you successful because of a series of favorable coin tosses, or are you talented in some unknown and useful way? How could you possibly answer that?

The truth is that being lucky feels a lot like being talented. The foolish person assumes that his accomplishments are the result of hard work, dedication, and his own innate skill. But the smart person takes the opposite approach– he assumes it’s always luck and starts each day with the assumption that there is at best a 50/50 chance of absolute failure. The smart person acts accordingly in the face of this uncertainty.