Some people call it bracketology. It is the art of filling out an NCAA basketball tournament bracket, and mathematically speaking, it is nearly impossible to do so without making a mistake.
“There are only two possible outcomes for each game,” explained Bobby Winters, assistant dean of the College of Arts and Sciences and university professor of mathematics. “Since you have 68 games there are two to the 68th power possibilities. But there is only one way to get them right. Roughly speaking, that puts your odds at one in 1 followed by 20 or so zeroes.”
What does that look like? A person’s chances of filling out a perfect bracket are about 1 in 100,000,000,000,000,000,000.
While it may be fun to fill out a bracket, the mathematics involved is actually pretty intense.
“It’s called combinatorial (or counting) mathematics, and it actually dates back to the second century,” Winters said. “The basketball bracket, because it’s so well defined, is pretty straight forward. But combinatorial mathematics is meant to allow for multiple outcomes, so these types of problems tend to be some of the most difficult in mathematics.”
So difficult in fact, that Winters normally uses stories to demonstrate combinatorics to students in his introductory mathematics course.
“It’s usually filled with freshmen,” he said with a smile. “And we don’t want to scare them.”
Although Winters can determine the odds of a perfect bracket, he doesn’t fill one out for himself.
“I do a lot of things,” he said. “And the only way I can get them all done is by not following sports.”
When pressed for a selection though, Winters does have a favorite.
“I’ve always been an Oklahoma State fan, so if I had to choose I’d say ‘Go Pokes!’”
©2013 Pittsburg State University