Breaking down 1-in-147.5 quintillion odds of predicting the perfect March Madness bracket

It says it’s March on our calendars, but fans of the Aztecs and college basketball know this time of year affectionately as March Madness. Forget wildflower blooms and daylight saving time. Historic upsets and thrilling buzzer-beating shots that flip the men’s and women’s NCAA Tournaments upside down are now signaling the start of spring.

The San Diego State women’s basketball team earned a 16 seed in the NCAA Tournament by winning the Mountain West Conference Championship for the first time since 2012. They have a first-round matchup with 3 seed Louisiana State University (LSU) on Saturday.

The men earned an at-large bid and are one of the “last four” teams in the tournament. They’ll square off with the University of North Carolina on Tuesday with the 11 seed up for grabs, and if they win, they’ll go on to face 6-seeded Ole Miss (University of Mississippi) on Friday.

Whether your alma mater is in the Big Dance or not, chances are high that you’ll be invited to participate, online or on paper, in a tournament bracket challenge where you attempt to guess the results of the 68-team tournament for glory or a prize.

Last March, Fowler College of Business statistics lecturer Chris O’Byrne helped SDSU NewsCenter understand just how hard it is to submit a mistake-free bracket. This year, we’re attempting to break down that number to show just how grand it is.

First, a refresher on the math: The chances of picking a perfect bracket are 1 in 2 to the 67th power. That comes out to 1 in 147,573,952,589,676,412,928. For simplicity’s sake, let’s just call it 147.5 quintillion, or nearly 20 times the number of grains of sand on Earth. This assumes each participant has a 50/50 chance of winning. Since the tournament is seeded, this changes the odds a little in the bracket filler’s favor, but the fact remains that is how many different or unique brackets can be created from 68 teams.

There are tons of fun ways we can use math to help bring those odds to scale.

For example, Snapdragon Stadium’s fan capacity is 35,000 while Viejas Arena holds 12,414. SDSU would need to sell out both venues every day for 8,527,274,620,910 consecutive years to reach a total attendance of 147.5 quintillion. That’s more than 8.5 trillion years. SDSU would need three sellouts a day to work that number into the billions.

What if we put that number in terms of travel distance?

It would take 496 million round trips to the sun to travel 147.5 quintillion meters.

Now, for an application of calculations as it relates to SDSU’s travel schedule during March Madness.

SDSU’s women’s team is traveling to Baton Rouge, Louisiana, to play LSU on their home floor at the Pete Maravich Assembly Center. That’s about 1,750 miles away from Viejas Arena in San Diego.

If the Aztecs win, they would go on to play at Florida State University (FSU) in Tallahassee, Florida, or at George Mason University in Fairfax, Virginia. A trip to FSU would add around 2,170 miles to the Aztecs’ odometer, while a trip to George Mason would add about 2,630 miles.

For the women’s team to travel a total of 147.5 quintillion feet, they would have to fly from San Diego to Baton Rouge and back, then to Tallahassee and back, and then to Fairfax and back (that’s three round trips), 2,132,489,012,260 times.

The men have to travel to Dayton, Ohio, for their game against UNC. If they advance, they’ll play Ole Miss in Milwaukee, Wisconsin, and if they stay hot, they’ll advance to the South Regional in Atlanta, Georgia. For the men’s team to travel 147.5 quintillion feet, they’d have to make three round trips to those locations roughly 2,029,908,883,927 times.

We all binge-watch, right? According to Netflix, you use up to 7 GB (7 billion bytes) per hour for 4K Ultra HD streams. So if all 500,000 of SDSU’s living alumni banded together on a mission to consume 147.5 quintillion bytes, each alum would need to watch roughly 21,071 two-hour movies in 4K. 

We can start once March Madness is over.

"These mathematic exercises are a fun way to show the enormity of your odds when it comes to predicting NCAA Tournament outcomes," O'Byrne said. "March Madness brings people together by bridging math and basketball, which I think is really unique."

The good news is that you don’t have to be perfect to win your bracket challenge. You just need a little luck on your side.