Should we be upset about upsets?
Math hysteria: NCAA tournament brackets are built to be busted
Oh, the carnage: With upsets by Dayton and Connecticut, just 0.19 percent of the more than 11 million brackets in ESPN's Tournament Challenge called all of Saturday's NCAA games correctly. And then came Sunday, with wins by Stanford (picked by only 4.1 percent of entrants to reach the Sweet Sixteen), Tennessee (4.9 percent) and Kentucky (29.3 percent).
It's not just that there's nobody left with a perfect bracket, either at ESPN or in Warren Buffett's Quicken Loans Billion Dollar Bracket Challenge. Hardly anybody is even close.
To which statheads have this sophisticated response: Duh. A perfect bracket is virtually a mathematical impossibility -- and that's precisely the way the NCAA wants it.
There's a certain kind of awe in watching millions of people get wiped out of any contest so quickly, and it's fun to talk about how close you came (or didn't) to winning $1 billion. But as we all try to figure out how our predictions went wrong, keep this in mind: There's nothing magic about college basketball or this time of year that makes good teams prone to upsets by Cinderellas. Brackets get busted by something called the power of compounding.
Say you could pick the winner of NCAA games with 90 percent accuracy. You would have an 81 percent chance (0.90 x 0.90) of getting two games right, a 72.9 percent chance (0.90 x 0.90 x 0.90) of choosing three winners in a row, and so forth. With 32 games in the NCAA tournament's round of 64, your odds of selecting all of them correctly would be 0.90 to the 32nd power, or just 3.4 percent. That's just to get to the round of 32, and has nothing to do with which teams are playing. It's just the probability that something will run off the rails somewhere, even though there's only a 10 percent chance you will get any individual game wrong.
And of course, you probably can't choose games 90 percent accurately. The way the game of brackets is set up, there are just too many chances to go wrong.
Moreover, as the rounds progress, games get much harder to predict; you're faced with Iowa State-North Carolina instead of Wisconsin-American. So suppose you pick with 70 percent accuracy throughout the entire tournament. Your chances of selecting a perfect bracket would then be about one in 5.74 billion, which means the Tournament Challenge would have to run for more than 500 years before we could expect anyone to get all their games right.
The NCAA wants to get its most popular schools on network TV for as many games as possible while luring fans with unpredictability.
You might have seen even longer odds quoted, of 9.2 quintillion to one. That assumes every pick has just a 50 percent chance of being right. We'll say you're better than a coin flip.
An Indian legend from about 1,000 years ago says that when a mathematician named Sessa invented the game of chess, the local king was so happy that he let Sessa name his own reward. The mathematician asked for one grain of wheat for the first square of the chessboard, two for the second, four for the third, doubling each time. It seemed like a humble prize -- until the king's advisers figured out the total would reach 18,446,744,073,709,551,615 grains of wheat. That's the power of compounding. And instead of wheat grains growing exponentially from one to 64 squares, your odds of a perfect bracket decrease exponentially as 64 teams play to one.
We might be seeing trends toward more upsets, making it even harder to pick a perfect bracket. For one thing, as overall talent improves and disperses around the country, even very weak conferences can produce a team, like Stephen F. Austin out of the Southland, capable of knocking off a Goliath.
For another, smart underdogs might be learning how to use NCAA tournament games to adapt to opponents and improve throughout March, like VCU in 2011 and Florida Gulf Coast in 2013.
And this year in particular, the NCAA selection committee had a hard time figuring out what to do with power-conference teams that were obviously strong but piled up double-digit losses, such as Kentucky, Oklahoma State, Pittsburgh and especially Tennessee. These are squads our Giant Killers project identified as "wounded assassins," who fell short of initial expectations but still packed some punch. They ended up with middling seeds, yet a couple have broken into the Sweet Sixteen.
But the Wildcats aren't a typical 8-seed -- they're the seventh-best team in the country, according to ESPN's Basketball Power Index. And there's a similar disparity for the Vols (an 11-seed, though ranked 24th). If you seed teams too low, lower-seeded teams are going to win more games.
While this has been a pretty good year for upsets, the essential cause of busted brackets is structural. After all, the NBA runs a springtime basketball championship, too. But its playoffs are a grind of seven-game series, which helps ensure the best team wins its title.
In the tournament, one reason for the early rounds is that the NCAA wants to get its most popular schools on network TV for as many games as possible while luring casual fans with the promise of unpredictability. So it stages a single-elimination tournament with a huge field and no byes. That's a format that generates a lot of excitement, with plenty of chances for overdogs to stumble -- and it guarantees nobody will have a perfect bracket.
You might call it the method to March Madness.
2014 NCAA TOURNAMENT
Of the 68 teams that started the Big Dance, 16 remain. Which will end up in Arlington, Texas?