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NCAA & Math

Much hullabaloo is being made of the fact that, by and large, sports writers did an abysmal job of predicting the NCAA Tournament outcome. In particular, folks are pointing out that virtually none of these jokes nailed who would be in the Final Four and who would walk away with the trophy (or belt, or medal, or year's supply of beef jerky, or whatever it is they give the winners).

Well, I don't know nuthin' about no basketball, but I do know a tiny bit about probability -- enough to spot the fallacy in this line of reasoning. The argument, in a nutshell, goes a little something like this: "Of 100 sports writers, only 5 accurately predicted who would win the Tournament; therefore 95% of sports writers are poor are predicting who will win the Tournament." Makes perfect sense, right? But the problem with this criticism is that it's just another case of Monday morning quarterbacking. Remember, the sports writers were announcing who they thought was likely to win, not who was certain to win -- that's what prediction is all about, nailing the probabilities. And there were quite a few upsets this year, such as Duke getting the heave-ho early on. So it's entirely possible the the sports writers were correct in predicting who would likely win, it's just that fate took an unexpected turn.

Confused? Here, let me toss in an analogy, free of charge. Say you have a bunch of mathematicians and a coin. Throw in a fifth of vodka and you got yourself a party right there. You tell them that you are going to flip the coin ten times, and ask them to predict how many times "heads" will turn up. Each and every one of them is going to say "five". Now, you flip the coin ten times and, by some quirk of fate, you gets tails ten times in a row. Aha! Those mathematicians were full of hooey, right? No, of course not -- they were dead on in predicting what was likely to happen. It just ... didn't.

Saying "nearly all the sports writers were wrong" actually weakens the argument that they're lousy predictors. After all, if they were all 100% accurate at figuring out the probabilities they would all make the same predictions, and at the end of the Tournament they would either all be right
or all be wrong (just as each and everyone of the mathematicians was wrong in the above example). In this case, most sports writers made similar guesses as to how things would turn out. The fact that reality didn't conform to conventional sports writer wisdom doesn't necessarily mean they were incorrect (although it doesn't rule it out either).

You see? You don't? Well, that's okay -- when it comes to probabilities there's also, like, a three outta five chance that I don't have the slightest idea what I'm talking about. At any rate, one thing is certain: I just gave myself a headache thinking about this.

Update! The great thing about the Internet -- and by "great" I mean "terrifying" -- is that if you don't have the slightest idea what you're talking about, and you decide to announce this fact via the World Wide Web, you will be put back in your place instantaneously! O Brave New World.

Moments after I made the above post, Bryan Curtis, author of the cited Slate article, dropped me a line:

You know much more about math than I do, but allow me to add more information on the unique brain structure of sportswriters. The very un-mathematical idea behind this experiment was to see how well sportswriters could predict the NCAA Tournament. And, since I had little faith they could do it well, reassure the amateur bracketeers out there that the "experts" were just as confused and ill-prepared as they were.

If I read your analogy about who would "likely win" correctly, then the sportswriters' job should have been easy. The NCAA seeds all 64 of its teams and they could have just picked the higher seed in each game--at least, until they reached the Final Four and had to choose between four No. 1 seeds. But they didn't. Overwhelming majorities of writers picked underdogs in certain games. For example, they picked No. 11 Pennsylvania to beat No. 6 California. Pennsylvania--at least in the minds of the seeding committee and Las Vegas bookmakers--wasn't more likely to win. But the writers picked them anyway. So it seems to me that the writers weren't just playing the averages--though they largely did that, advancing three out of four No. 1 seeds to the Final Four. They were trying, as we all do, to fill out the perfect bracket--which, every year, means picking the right upsets in the right games.

Plus, we don't need sportswriters to tell us what's likely to happen; we can determine that simply by glancing at the seeds or the betting line.

I'm reasonably sure that there is a mathematical theorem that renders everything I've just written completely false.


Bryan, I strongly doubt that I "know much more about math" that you, but you certainly know more about sports than I. For instance, I haven't the slightest idea how they get those seed numbers. You mean they are cooked up by people who are really REALLY calculating the probabilities? Well hell -- that puts a Ford-Expedition-sized hole in my argument now don't it?

All I know about NCAA basketball is that I gave some guy $3 a few weeks ago and, the other day, he gave it and a whole bevy of other three-dollar bills to someone else who had more stars on their March Madness Pool Sheet that I. And if I can't have my three bucks then, by God, at least I'll have this dubious mathematical argument as to why my utter failure to rake in the big bucks in no way proves that I wasn't 100% correct in my predictions.

Posted on April 03, 2002 to