# How to Win \$1 Billion on NCAA Basketball: A Mathematician's Tips

Rankings expert and college professor Tim Chartier explains how he uses math to come up with an almost-perfect March Madness formula.

Last Thursday, the underground classroom at the National Museum of Mathematics in New York was filled to capacity for a college professor’s PowerPoint-aided lecture. But this was no ordinary class, and the “students” ranged from college kids to an elderly woman who listened as attentively as anyone. The goal, the energetic professor explained, was not an "A" but something far more enticing: a perfect March Madness bracket and a \$1 billion prize.

The lecturer was Dr. Tim Chartier, a Davidson College professor who specializes in ranking methods. For the past several years, he has preached and taught a math-heavy form of bracketology—the science of predicting the annual NCAA college basketball tournament. Chartier’s formula, an evolving code-based matrix that ranks each of the 68 tournament teams, has helped several Davidson students score in the 96th percentile (or higher) in ESPN’s bracket challenge.

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This year, Chartier’s goal is to help someone win the \$1 billion prize offered by Warren Buffett and Quicken Loans to anyone who correctly predicts all 63 games of the men’s tournament. Even with such a lucrative payout, the odds are absurdly long. If every game were a 50/50 proposition, the odds of a perfect bracket would stand at roughly 9.2 quintillion to 1.

Of course, not all tournament teams are created equal—a No. 1 seed has never lost to a No. 16 seed, for example. A recent Deadspin article quoted a DePaul University math professor who estimated the practical odds of a perfect bracket at roughly 128 billion to 1. And as Chartier noted in his presentation, Buffett is offering \$100,000 each to the top 20 finishers in his tournament, perfect bracket or not. With more than \$10 billion spent annually gambling on March Madness, there are spoils to be won even if the perfect bracket remains a wistful dream.

I spoke to Chartier prior to his presentation and picked his brain about the right blend of math and instincts, key tips for the casual fan, and who the math says will win it all this year.

How does one become a bracketologist?

My academic research is in ranking methods. We look at things like the page-ranking algorithms of Google, and we also look at sports rankings. In 2009, my collaborator [and College of Charleston professor] Amy Langville said: “You know what? ESPN has this huge online bracket tournament. Let’s create brackets with our ranking methods, just to see if it’s creating meaningful information.”

One of the brackets we created that year was in the 97th percentile out of 4 million brackets on ESPN, and all of the brackets we create using our method did quite well.

When you began formulating your method for March Madness, what factors did you focus on?

At the time, we were primarily working with recency. Nate Silver uses it in his analysis of polls—a more recent poll will count more than an earlier one. Generally we see a more recent game being predictive of how things will play out in the tournament than a game further back [in the season].

We used interval weighting, where we break the season into intervals. The season was broken up into two-week segments, and in each two-week segment the games were weighted the same. The segments where the wins and losses aren’t as important can be weighted at half a game, for example. If a block is really important, you can weight each game at more than one.

So then your formula accounted for the concept of momentum.

Yes. You can literally just tell our software that on Day 1 of the season a win equals X, on Day 2 it equals Y, and so on. People can use that to weight games played later in the season more highly.

But that was what you were doing in 2009—let’s talk about the bracketology method you’ve settled on now. What does it emphasize?

We have two methods. One is the Colley Method, named after [astrophysicist] Wesley Colley. He developed a method used by the BCS for college football. His basketball method only counts wins and losses, not margin of victory. We also use the Massey method [created by sports statistician Kenneth Massey], which does integrate scores.

What’s new about your method this year?

One thing we’ve changed is that we’ve made it easier to cap the size of a win [when using the Massey method]. We often use a 15-point margin of victory as a cap, because there is a lot of variability in blowouts, and the size of the blowout can impact your rating of a team. A coach might put in the second squad, for example. Of if you don’t play as hard against a team you’re already beating and only beat them by 20 instead of 40, it can actually raise the rank of the weaker team that was blown out. Capping point differential at 15 eliminates a lot of the noise we see in the data, and we find that it tends to be more predictive.

Another thing we’re trying to do that’s not yet in a Web format is to run our method once, get our ranking of teams, and then input teams’ ability to beat opponents that are very close to their ranking—how good are tournament teams at beating teams that are about as strong as they are? Then we run the method again with the updated rankings. It may not get you the \$1 billion, but it can make you a better bracket.

What other factors are you trying to tackle?

We’ve been doing some preliminary work trying to determine how much upset-ability, if you will, that there is in the tournament. There’s always the upsets that are difficult to predict, but some years lay themselves out in a much more predictive manner, especially with our method. You can really see that reflected in the ESPN bracket challenge scoring from year to year. The winning score from year to year can change greatly, and some years even the best bracket misses a good amount of games.

What’s the “upset-ability” look like this year?

Based on our work to date, it looks like this year could have more upsets, because the teams are more closely matched than previous years we’ve studied. Not just the teams at the top, but the teams in the middle of the pack as well.

What advice do you have for pickers trying to account for bracket busters, like Florida Gulf Coast last year?

At one level, you’re not going to know. I’m not sure anyone can pick it up with a formula or a method. Last year, when Harvard beat New Mexico, none of us predicted that — it was shocking. So some of this is what we love about sports, the random effect that can’t be predicted and makes it fun.

That said, one thing that we have looked for in bracket busters is unheralded teams with a top player and good supporting cast [like the Stephen Curry-led Davidson team in 2008 that made the Elite Eight as a No. 10 seed]. Another thing we look for is when a team is more likely to play above its expected level. If you look at a team’s Pythagorean winning percentage, it can tell you that a team is lucky and wins more than it should, or vice versa. And if a team can beat strong opponents towards the end of the season, that’s a big predictor of tournament success.

Enough details. Which team does the math say is going to win it all?

Florida. A couple weeks ago, Arizona was coming up as the team to beat, but for the last week or so Florida has been our favorite.

How should we fans who aren’t math whizzes combine formulas and instinct when filling out our brackets?

If there’s something that you think might play into March Madness that’s not in the formula, you can incorporate that along with the math when filling out your bracket. For example, our methods do very well in the first and second round, but it can be harder to predict as you move on. A team like Davidson, or Virginia Commonwealth in 2011 [which made the Final Four as a No. 11 seed], they can grow in confidence as the tournament goes on. That’s why I often tell my students to be careful, because the math is not going to totally tell you everything. If it did, I’d be retired.

What is one prediction your model has made in past years that you’re really proud of?

We had a student who correctly picked Butler to go to the Final Four [in 2010], because she put into the formula the ability to recognize sustained winning streaks.

OK, my head’s spinning. Let’s boil it down: What would your advice be to the casual fans who are filling out brackets in their office pools and trying to beat the system?

One, figure out the math that you’re going to do and trust it. Combining math and your intuition is not a bad idea. It will mean that there’s more variability in your picks, but there’s also variability in the tournament.

Two, don’t get too hung up on any specific allegiance you might have for—or against—a particular school. I’ve seen students who have really bad brackets using my method because it pops out a team that they’re not willing to pick to win.