Monday, October 18, 2010

Lucky pennies and constrained roulette

In a recent post about progressive taxation, Jonathan Cohn says the following about economic fairness:
One is that it fails to account for the power of luck. Almost by definition, people who are successful have benefited from some measure of good fortune. That fortune can take the form of obvious, material advantages -- like access to advanced technology and good schools. Or it can take the form of more subtle, but still important, assets for moving forward in life--like good health or loving parents.
There's no arguing with the basic thrust here, but it presents a very narrow view of luck. You can get a broader and more interesting view if you think in terms of probability distributions.

The idea of luck is closely tied to the idea of beating the odds. Having an unlikely positive outcome is more or less equivalent to the informal concept of being 'lucky,' but this often leads into one of those areas of probability that give people trouble.

There's a natural and entirely rational impulse to look for explanations when we see something unlikely. Unfortunately, there's also a natural tendency to get confused when we go back and assign probabilities after the fact.

One of the best known examples comes from Burton Gordon Malkiel in his classic A Random Walk Down Wall Street. Malkiel draws an analogy between a successful investment fund manager and a lucky coin-flipper.

Imagine a coin flipping competition. You start with a thousand coin-flippers. Every round consists of one flip. At the end of every round, those who came up tails leave the game. The contestants go from 1,000 to 500 to 250 to 125 to 63 to 31 to 16 to 8.

"By this time, crowds start to gather to witness the surprising ability of these expert coin-flippers. The winners are overwhelmed with adulation. They are celebrated as geniuses in the art of coin-flipping, their biographies are written and people urgently seek their advice. After all, there were 1,000 contestants and only 8 could consistently flip heads."

As presented here, this seems absurd but if you spend some time watching CNBC or browsing the business section of your local book store, you'll realize it's not exaggerated.

Related to the lucky coin-flipper is the grand prize winner.

We have a roulette wheel numbered 1 to 100, 100 spaces on the table and 100 players. On a first come, first serve basis, each player picks a number. Whoever is sitting on the number that comes up gets everyone's chips.

The winner can argue that he or she had some special skill at number picking, and that's entirely possible, but there's no way of confirming that claim by looking at the results of the game. Someone had to win and whoever won could make the same argument.

Just as it's not difficult to find lucky coin flippers, it's also easy to find CEOs and business leaders who benefited greatly from landing on the right number.

Consider Michael Eisner.

Eisner was CEO of Disney from 1984 to 2005. By any standard it was a good run, marked by growth, major acquisitions, prestigious and popular products. Eisner deserves credit for a lot of good decisions, but the single biggest factor behind Disney's resurgence came from a turn of the roulette wheel.

In the late Eighties, with the format war settled and VCR reaching saturation levels, parents discovered that the easiest (and often the only) way to keep a small child quiet was to pop in a video (I recall Robert Altman saying in an interview that Popeye was his most profitable film for just this reason). Suddenly Disney was sitting on the most valuable film library in the world.

It is true that Eisner pushed to speed up release of some of the studio's classics, but the home video division had started years before he got there and given the size of the market that opened up, it's hard to believe that even the most cautious of executives would have held back the films much longer.

Michael Eisner simply found himself sitting on a lucky number.

If a sock puppet had been appointed CEO of Disney in 1984, the home video market for kid-friendly shows would still have exploded and the company still would have made a mint. It might not have managed a Little Mermaid or a Lion King but it still would have had a fantastic run and you'd have no trouble finding numerous books exploring the business genius of Argus McArgyleSock.

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