Professor Michael Magazine is upending the logical world of math with a good dose of March Madness.

Magazine teaches a new class called Bracketology at University of Cincinnati, the home of the 10th-seeded Bearcats, where 33 business students are spending the semester trying to make sense out of what can feel nonsensical at times — the art of filling out an NCAA tournament bracket.

“The life lesson is that we make a lot of decisions that are the right decisions,” Magazine says, “but the outcomes don’t always come out the way we planned.”

And that’s why picking the NCAA tournament is so much fun.

Magazine says that, yes, he’s among the millions of Americans who take part in the country’s largest office pool — where all you need is a pen, a copy of the bracket and $10 or $20 to get in on the action.

Real basketball knowledge? That’s optional. Some people pick their favorite mascot, others go based on color, still others just throw darts at a board.

“I always tell people to ignore where they went to school,” Magazine says. “But it’s hard to do.”

He teaches the course with a Cincinnati alum, Paul Bessire, who owns predictionmachine.com, a program that runs thousands of simulations to forecast likely winners of games. Armed with that, along with some mathematical models, Magazine and Bessire hold three sessions — handicapping, assembling brackets, filling out the brackets and seeing how everyone did.

“It’s a pass-fail class,” Magazine says.

Good thing because when it comes to March Madness, the numbers get a little crazy.

According to the website bookofodds.com, if you fill out your bracket by picking the better-seeded team in every game, the odds of that bracket being perfect are more than 35 billion-1. Or, to put it another way, you have an 18 times better chance of being killed by a waterspout this year.

There are more than 9.2 quintillion combinations (a 9, followed by 18 zeroes), and even if you eliminate all those that have a No. 16 seed winning even a single game — which has never happened — you’re still talking about enough paper to build a trail from the Earth to the moon more than 1 million times.

Oh, and about eliminating those No. 16 seeds: Might think twice about that.

This has been the most unpredictable college basketball season anyone can remember, including one stretch where the No. 1 team in The Associated Press Top 25 changed for five straight weeks.

Even in seasons that have seemed more “predictable,” the NCAA tournament has become increasingly unstable over recent years. Butler, enrollment 4,500, has made the Final Four twice in the last three years. In 2011, little-known and even less-heralded VCU transformed itself from a No. 11 seed that barely got into the tournament into a Final Four team. Last year, two No. 15 teams won on the first Friday of the tournament. After the second upset, ESPN reported none of its 6.45 million bracket entries were perfect anymore.

“We messed up some brackets! We messed up some brackets!” senior Kyle O’Quinn exclaimed last year after he led 15th-seeded Norfolk to an 86-84 upset over Missouri.

Tom DeRosa, a former algebra teacher who now runs a website that provides teachers with everyday lessons for their own classes, says there is no mathematically surefire way to figure out which 15 or 16 might break through this year. But you can’t completely ignore them, either.

“You look at the numbers and, yeah, it’s a pretty good bet a 1, 2 or 3 seed is going to win the whole tournament,” says DeRosa, whose March Madness lesson is being taught across America this week. “If you’re making a bracket and you don’t have any ‘1’s in the Final Four or anywhere near the Final Four, you’re probably not going to win your pool. But things get a lot more nuanced the more you read. ‘’

Speaking of nuance:

— Blue has been the school color of 24 of the 40 teams to make the Final Four during the last 10 years, and the hue worn by the last nine national champions.

— Of those 40 Final Four team mascots, 12 have been people (Spartan, Mountaineer, etc.), seven have been canines and five have been birds (mostly the mythical Jayhawk). There have been Warriors at the Final Four and a Gator or two. But the most ferocious — for those who like to pair the mascots off in cage matches — has been, by far, the Blue Devil.

— Las Vegas, which exists because of its ability to get math right, has No. 1 seed Louisville as a 9-2 favorite to win it all, followed by second-seeded Duke and Miami at 8-1. (Warning: Odds can be influenced by betting patterns, and Duke has one of the largest followings in the nation.)

Using a mix of all this information is Glen Calhoun, the head of props for the national tour of the Broadway smash “Jersey Boys.” On Monday, he was busy unloading nine trucks full of wardrobe and scenery, as the show moved from Norfolk, Va., to Houston. Not his only task of the day.

“I’ve got to get our NCAA brackets set up,” he said. “I’ll be sure to squeeze that in.”

More than 50 people are in the cast and crew, and Calhoun figured at least half of them would take part.

“What’s good about the March Madness pool is that anyone can get in there and do well,” he said. “You can study up, and then it all falls apart. I remember one year when Wake Forest got me. Or you can just pick your favorite teams, and that works sometimes.”

Magazine insists that, yes, there is mathematical advice to follow, including some he picked up by reading Nate Silver, the blogger who picked the electoral college count in last year’s presidential election nearly to the number. (By the way, no word yet on whether President Barack Obama will be channeling Silver when he fills out his bracket.)

Silver suggests that Nos. 8 and 9 seeds can sometimes be worse Sweet 16 picks than those seeded 10, 11 or 12 because the winner of an 8-9 matchup is all but destined to play a No. 1 in the next round.

“I tell people, if you’re going to pick upsets, do it in the 10, 11, 12, 13 range,” Magazine said.

It’s OK to use your gut, Magazine says. But, he insists, it’s folly to completely ignore the numbers.

“Sometimes, you predict someone’s better because in simulations, 80 percent of the time they win,” he said. “Well, that means 20 percent of the time they lose. That’s going to happen. That’s been a useful lesson for students.”

And, as any good math professor will remind you, being wrong doesn’t always mean you were, well, wrong — even if the scoreboard says you were.

“It just means it didn’t work out that time,” Magazine says.