Sunday, June 7, 2009

On Randomness

I'm in the midst of reading Leonard Mlodinow's The Drunkard's Walk: How Randomness Rules of Our Lives, a nifty little tome whose purpose is to ensure us that our instinctual assumptions about probability are almost always completely wrong. It is, in a way, the contrarian counterpart to Malcolm Gladwell's Blink. (Perhaps, with enough public pressure, we can arrange a cage match between the two, involving whiteboards, graphing calculators and a curling iron.)

Anyway, Mlodinow writes a great deal about sports (since it often provides the most literal example of his thesis, as uber-baseball geek and Bill James fanatic Joe Posnanski has ably noted here and here), and at one point, he reveals a simple statistical truth about a seven-game playoff series, which is, essentially, that even seven games cannot truly minimize randomness: Even if we can somehow statistically determine that, say, the Lakers would win 55 percent of their games against the Magic, the Magic would still win the series four out of every 10 times. And even if the Lakers could be expected 66.6 percent of their games against the Magic, Orlando would still win 20 percent of the time (let us call it "The Pietrus Effect.") In the former case, it would take 23 games to achieve "statistical significance," meaning the underdog would win less than 5 percent of the time; in the latter, it would take 269 games, or roughly the temporal equivalent of watching the director's cut of Kobe: Doin' Work.

Here's the point Mlodinow did not make (at least, not yet): In sports, increased randomness is almost always a good thing. This is why the two most exciting times of year in sports are the college football season (where top teams are constantly falling victim to unexpected upsets) and the NCAA tournament (where upsets have become the tournament's entire commodity, and where the application of mathematical processes like the RPI have , in recent years, actually threatened the tournament's wonderful spontanaiety.) And this is why I think football has become an inherently better (and more popular) game than either baseball or basketball, especially on the professional level: Because it is physically impossible for football to play its games in series.

And, yes, I will freely acknowledge that this will never, ever happen, if only for financial reasons: But can you imagine if, for one experimental year, the NBA playoffs (or the baseball playoffs, for that matter) were staged like the NCAA tournament, with the championship perhaps as a three-game series? After all, why should we pretend that a seven-game series will produce a more "authentic" victor when all it does it minimize The Pietrus Effect by a small amount, without rendering it statistically insignificant? Why not allow your best players to throw everything they have into a single game in order to preserve their season (or in baseball, to utilize your entire pitching staff on a single evening)? Maybe it would throw the entire process into chaos. Maybe we'd wind up with a Bulls-Jazz final. But if the Lakers sweep the next three games, who's to say the random result wouldn't be the more interesting one?

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