Drunkard's Walk - Leonard Mlodinow [52]
Let’s apply these ideas to an example I mentioned briefly in chapter 4: the situation in which two companies compete head-to-head or two employees within a company compete. Think now of the CEOs of the Fortune 500 companies. Let’s assume that, based on their knowledge and abilities, each CEO has a certain probability of success each year (however his or her company may define that). And to make things simple, let’s assume that for these CEOs successful years occur with the same frequency as the white pebbles or the mayor’s supporters: 60 percent. (Whether the true number is a little higher or a little lower doesn’t affect the thrust of this argument.) Does that mean we should expect, in a given five-year period, that a CEO will have precisely three good years?
No. As the earlier analysis showed, even if the CEOs all have a nice cut-and-dried 60 percent success rate, the chances that in a given five-year period a particular CEO’s performance will reflect that underlying rate are only 1 in 3! Translated to the Fortune 500, that means that over the past five years about 333 of the CEOs would have exhibited performance that did not reflect their true ability. Moreover, we should expect, by chance alone, about 1 in 10 of the CEOs to have five winning or losing years in a row. What does this tell us? It is more reliable to judge people by analyzing their abilities than by glancing at the scoreboard. Or as Bernoulli put it, “One should not appraise human action on the basis of its results.”19
Going against the law of small numbers requires character. For while anyone can sit back and point to the bottom line as justification, assessing instead a person’s actual knowledge and actual ability takes confidence, thought, good judgment, and, well, guts. You can’t just stand up in a meeting with your colleagues and yell, “Don’t fire her. She was just on the wrong end of a Bernoulli series.” Nor is it likely to win you friends if you stand up and say of the gloating fellow who just sold more Toyota Camrys than anyone else in the history of the dealership, “It was just a random fluctuation.” And so it rarely happens. Executives’ winning years are attributed to their brilliance, explained retroactively through incisive hindsight. And when people don’t succeed, we often assume the failure accurately reflects the proportion with which their talents and their abilities fill the urn.
Another mistaken notion connected with the law of large numbers is the idea that an event is more or less likely to occur because it has or has not happened recently. The idea that the odds of an event with a fixed probability increase or decrease depending on recent occurrences of the event is called the gambler’s fallacy. For example, if Kerrich landed, say, 44 heads in the first 100 tosses, the coin would not develop a bias toward tails in order to catch up! That’s what is at the root of such ideas as “her luck has run out” and “He is due.” That does not happen. For what it’s worth, a good streak doesn’t jinx you, and a bad one, unfortunately, does not mean better luck is in store. Still, the gambler’s fallacy affects more people than you might think, if not on a conscious level then on an unconscious one. People expect good luck to follow bad luck, or they worry that bad will follow good.
I remember, on a cruise a few years back, watching an intense pudgy man sweating as he frantically fed dollars into a slot machine as fast as it would take them. His companion, seeing me eye them, remarked simply, “He is due.” Although tempted to point out that, no, he isn’t due, I instead walked on. After several steps I halted my progress owing to a sudden flashing of lights, ringing of bells, not a little hooting on the couple’s part, and the sound of, for what seemed