Everyone's talking about March Madness! Especially us, since it combines basketball AND math.
Teams in the NCAA tournament are seeded 1-16 in one of four regions (East, South, Midwest and West), with a lower number indicating a “better” team – typically the 1 seed in each region is the most likely to win, followed by the 2 seed, and on down to 16. They are then matched against each other for the opening games, so each region has a 1 vs 16, a 2 vs 15, etc. (See bracket details here.)
Of course, the higher seed doesn’t always win. So if you want to win your bracket, you need to pick some lower seeds to win. How do you choose? Math to the rescue!
Math can’t tell you which teams are most likely to win, but we can use expected value to figure out how many of each seed we should pick. There are 4 games in the first round for each seed (a #1 vs #16 in the East, South, Midwest and West). How many upsets should we pick in each pair?
A small disclaimer: a few years ago I talked about how a #1 seed had never lost to a #16 seed. Then it happened when UMBC beat Virginia. Let’s see what kind of chaos happens this year!
#2 seeds have won 93.9% of the time. So if you multiply 94% times 4 games, you would expect 3.8 wins. Since your picks have to be counted in whole numbers, you’ll need to choose either 3 or 4. I’m going with 4, but you may feel differently. The rest of the matchups look like this:
So if you’ve picked 3 upsets out of your 4 vs. 13 games, you might want to pick another favorite or 2.
In the past few years, one of the most interesting groups of 4 games in round 1 happened in 2019. The four-team slate was #7 Cincinnati vs. #10 Iowa, #2 Tennessee vs. #15 Colgate, #1 North Carolina vs. #16 Iona, and #8 Utah State vs. #9 Washington. Given those matchups, we correctly predicted an approximately 94% chance of seeing an upset in one of those four games:
There you have it. The next time someone asks you when they'll need to use math in "real life," you'll have one more example to share!
John Franco graduated from the University of Pittsburgh with a BS in Economics in 2000 and an MBA in 2007. Prior to joining Carnegie Learning in 2014, John spent 14 years as a Customer Support Manager between ComponentOne and the University of Pittsburgh. John currently leads the Customer Support team at Carnegie Learning, ensuring that administrators, teachers and students have the best possible experience.Explore more related to this author