March 1, 2006 Combinatorics calculates that randomly picking the outcomes of every game in the NCAA tournament stands one chance of success in more than 18 quintillion. If every person on Earth could fill out a bracket every second, then it would take them roughly one century to fill out all possibilities.
PROVIDENCE, R.I.--The NCAA tournament is the most coveted title in college basketball. For the fans, however, the office pool is a sport of its own. But can math help you improve your picks?
With 64 games determining who's the winner of the big dance you're hoping for the big prize in your office pool. But mathematician Mike Breen, from the American Mathematical Society in Providence, R.I., says the odds of a guaranteed win are not in your court.
The only sure-fire method is to pick every possible outcome using a kind of math called combinatorics. Since there are 64 games and two possible outcomes -- a win or a loss -- that number is enormous. According to Breen, it is 18 quintillion, 446 quadrillion.
"So if every person on Earth could fill out a bracket every second, then it would take them roughly one century to fill out all possibilities," Breen tells DBIS.
Mathematicians say if a dollar bill represented each of the possible outcomes, you could lay them end-to-end and they would make two round trips between earth and the big dipper. While the odds seem out of this world, there is a way to score some points. "One thing is: The number one seeds seem to make it to the Final Four," Breen says. It's not a slam-dunk, but that advice may get you closer to the jackpot.
One other factoid: if you wanted to hit your home with a bean bag from space, you'd have a better chance of hitting your roof than you would of correctly picking all the brackets in the tournament randomly.
BACKGROUND: It's time again for "March Madness," when U.S. college basketball teams compete to win the NCAA Division I Basketball Tournament, and buddies compete with each other by picking winning teams to guess the ultimate outcome of the tournament. But the realities of mathematical probability dictate that it's almost impossible to get your picks 100 percent right.
CALCULATING THE ODDS: Since there are 64 games in the March Madness tournament and two possible outcomes for each team's game -- a win and a loss -- the number of possible outcomes for the tournament is a staggering 2 to the power of 64: that is, 2 multiplied by itself 64 times, or 18,446,744,073,709,551,616. If one dollar bill represents each of the possibilities, and the six-inch bills are placed lengthwise end-to-end, the line would make two round trips between the Earth and the middle of the Big Dipper -- a distance of about 75 light years. In fact, if you put in a dollar for each of the possible ways to fill out the team bracket chart (see link below), you would be able to pay off the U.S. National Debt (about $8 trillion as of March 2004) 2.3 million times over.
THE MATH OF FILLING OUT THE POOL FORMS: Combinatorics is a mathematical theory of counting individual objects, particularly units of a finite set, like a collection of marbles stored in a small pouch. Once primarily a mathematical curiosity, it is vital to many areas of modern technology. For example, it is a useful tool in determining probabilities and the number of structures possessing certain properties as applied to telephone (fiber optic) networks and computers. It can also be used to analyze industrial process schedules, electrical networks, and economics. And it's the math that you'd use if you actually filled out every possible form.