There are more than 9.2 quintillion ways to fill out the N.C.A.A. men’s basketball tournament bracket, and as March Madness gets underway, more than 100 million Americans are determined to get it exactly right.
Jeffrey Bergen, a DePaul University mathematics professor, has calculated that with some knowledge of team rankings, player statistics and other basketball matters, the odds of hitting the perfect bracket are one in 128 billion.
For everybody else, the chances are even more dismal. But that matters little to people who place bets on the bracket, according to Dae Hee Kwak, an assistant professor of sport management at the University of Michigan.
In a paper published in The Journal of Gambling Studies, he argued that the illusion of control makes people believe they can win.
Previous studies have shown that people who bet on the lottery, in which winning is purely a matter of chance, believe they have better odds if they pick their own numbers instead of relying on those randomly assigned by a computer.
The odds of picking the victors in each of the 63 games in the N.C.A.A. tournament are much worse than the odds of winning the lottery. But when people get to make their own choices, Dr. Kwak said, they are more likely to believe they have control over the outcomes.
Before the 2012 tournament, Dr. Kwak divided 81 undergraduates into two groups. He asked one to fill out the brackets with their best guesses; the rest were given blank brackets but told not to fill them out. Then Dr. Kwak and his colleagues asked members of each group how confident they were in their ability to make accurate predictions.
There were no differences between the two groups in perceived knowledge of basketball or in the number of previous bracket contests they had participated in. But those who went through the motions of filling out the bracket thought they had a 60 percent chance of winning, while those who did not thought their odds were about 30 percent.
The act of filling out the bracket somehow doubled the participants’ confidence in their accuracy, Dr. Kwak concluded.
“The illusion of control is the strongest driver of enjoyment,” he said. “The more you believe in this illusory control, the more likely you are to attribute your wins to your skill and your losses to bad luck.
"The more control you think you have, the more you’re going to enjoy it and the more you’re going to bet.”
Try your chances at a special poll for risk-takers. No money required: NYT NCAA bracket, here.