March Math-ness

The Curious Aztec takes you behind the scenes of scientific investigation and discovery taking place at San Diego State University.

With our beloved Aztecs eliminated from this year’s NCAA men's basketball tournament, we can take a dispassionate and objective look at the mathematical quirks that help statisticians like San Diego State University’s Jim Lackritz make sense of the chaotic world of March Madness. This may seem a bit Stats 101, but the way probabilities play out in what we like to think is a game of pure skill can be a bit weird.

I asked Lackritz, who is an emeritus associate dean in the College of Business Administration, co-founder of SDSU’s Sports Business MBA program and a total college basketball fanatic, about the seemingly counterintuitive nature of upsets in the tournament. For any particular game, a large upset—say, a 14-seed beating a 3-seed—is by definition an unlikely scenario. But in the first round of tournament play, it’s very likely there will be at least one big upset, and usually a few. So what gives?

Long odds...

That’s just the nature of compounding probabilities, Lackritz explained. Get a bunch of unlikely scenarios together and it’s likely one of them will happen.

“If you have four games, and in each of them the favored team is given an 80-percent chance of winning, then there’s a 60-percent chance of an upset happening in one of those games,” Lackritz said.

OK, but what about Kentucky’s magical run of a season: an undefeated 34 wins in the regular season and, at the time this article was written, two wins so far in the tournament. Statistically, what’s the likelihood of Kentucky running the table 40-0, going undefeated from the beginning of the season straight through to cutting down the net?

Determining a team’s probability of winning any of its games at the beginning of a season is heavily dependent on how many players are returning from the previous year, the historical success of the coach, the recruiting season and many other factors, Lackritz said, but most people assumed Kentucky would be really, really good.

...and a long season

For the sake of easy math, let’s assume that in every single game Kentucky played, they had a 95-percent chance of winning. (That’s probably untrue for other very good teams Kentucky played throughout the season, but they were favored to win by Las Vegas odds-makers in every one of their contests so far.)

Over the course of a 40 game season, with a 95-percent chance of winning each game—each game virtually a sure thing—Kentucky still would only have been given a 12.9-percent chance of winning the whole enchilada. Even the extremely good face long odds over a long season, Lackritz said.

I asked Lackritz whether the dizzying probabilities of the NCAA tournament fed into his stats-geek nature, or whether his love of college basketball fostered his love of statistics, and without hesitation he said both were true.

“As a statistician, the tournament is great,” Lackritz said. “It’s one of my favorite times of year.”