Odds and Ends

No #1 seeds made it to the Final Four—a big news story. (Well, not Iraq or Ukraine.) But do your probabilities more or less right, and it's not so odd. I figure the odds of a #1 seed making it to the Final Four is 21%, and of winning the whole shebang is 6%. My assumptions are that a #1 seed has a 95% chance of winning round #1. A 70% chance of winning round #2. Then: 60%, 55%, 50%, 50% in the subsequent rounds. That yields the 21% and 6% above. George Mason's odds of getting to the F4: around .0003, or three in ten thousand. (My assumed per game odds for a #11 seed aiming for the F4 are 30%, 10%, 10%, 10%.)

My interest in this actually has to do mostly with organization design. Six victories wins the NCAA tournament—and it ain't easy statistically no matter how talented you are. Hence, let's consider a 6-layer organization making a decision—evaluating the right and wrong choice at each rung of hierarchy's ladder. And let's be generous, and imagine each level has a whopping 80% chance of making the right decision. So the odds of eventually getting the thing right are 0.8 to the 6th power—and that's 0.21, or 21% (just like emerging in the F4 if you're a #1 seed). Not so hot. It's like the communications game in which 10 people whisper a simple message to the person next to him or her. We start with "Jack's a smart guy to consider the middle-age market," or some such. Ten dilutions later, no malice involved, we end up with a simple, "Jack's an idiot"—or something quite close. It's a heck of an argument for de-layering in any situation.

Probability buff that I am, I was reminded of all this while reading a review of ex-neocon policy guru Francis Fukuyama's latest book, America at the Crossroads. The neocons' mistakes that have led to exceptional foreign policy over-reach, per Fukuyama, were based to a significant degree on overestimating the lessons associated with the end of the Cold War and the Soviet collapse. New York Times reviewer Paul Berman puts it this way: "The neoconservatives, [Fukuyama] suggests, are people who, having witnessed the collapse of Communism long ago, ought to look back on those gigantic events as a one-in-a-zillion lucky break, like winning the lottery. Instead, the neoconservatives, victims of their own success, came to believe that Communism's implosion reflected the deepest laws of history, which were operating in their own and America's favor—a formula for hubris."

The point of this Post—combining neocons, org decision-making, and the final Four—is the absurdly common tendency to get the odds of sequential events totally and dangerously wrong. "Six layers of management? Hey, our guys are all smart as a whip. We'll get it right." Well, if "smart as a whip," per me, is 80% odds of getting a decision right at any level—then the overall success odds end up, when calculated more or less correctly, quite discouraging. Mis-appreciation of realistic odds, particularly based on a simplistic story line ("smart as a whip," No.1 seeds are invincible, "Reagan won the Cold War single-handedly because he listened to the theories of thus and such neocon theorists") are incredible dangers to the Las Vegas bettor, the corporate chief, and the foreign policy planner alike.

Viva George Mason. (Hey, you can beat long odds—about once every half century, anyway.)