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March Madness Math Secrets

A perfect bracket probably isn't in the cards, but a winning one might be


As we head into the first games of the Sweet Sixteen in March Madness, you might be disappointed at how poorly your bracket is doing.  But don’t worry, even though there are tens of millions of brackets filled out each year, there has never been a perfect one.

Nobody’s perfect

In a typical March Madness bracket, you try to predict the winners of each game for the entire tournament before the tournament starts.   Since there are 63 games in total, if you were to randomly choose each winning team (i.e. 50% chance of being right on each guess), the chances of getting them all right is 1 in 263 or 1 in 9.2 quintillion.  Now, given seed numbers and expert opinions, most people will be better than random chance.

“But even if you have, say, a 70% chance of getting each guess right, that’s still worse than one chance in 10 billion of getting a perfect bracket” says Jeffrey Rosenthal, Professor in the Department of Statistical Sciences at the University of Toronto.

Like any game of chance, part of choosing a successful bracket is luck.  The other part?


Bet on math

Although many people consider sports and math to be completely opposite disciplines, there are many ways that mathematical analysis is helping athletes and sports teams.

“One of the things about sports these days is that the data are coming to us in waves,” says Tim Swartz, Professor of Statistics and Actuarial Science at Simon Fraser University in B.C.  In the NBA, for example, high speed cameras capture the location of all 10 players on the court as well as the ball 25 times a second.  “There’s so much data, it has opened opportunities for people doing statistical analyses.”

Prof. Swartz himself uses statistical analysis to determine optimal batting orders for cricket teams or to analyze penalty calls in the NHL.

Keith Willoughby, Associate Dean and Professor at the Edwards School of Business at the University of Saskatchewan, developed a simulation model to determine the in-season probability of a team winning the Grey Cup.  The Canadian Football League regularly features the model results on its website.

“It’s not just fun and games, we’re using theory, statistics, and computing to solve real problems that are of interest to lots of people and teams,” says Prof. Swartz.

March Madness

For March Madness, tournament seeding is a good starting point to help increase your chances of a correct pick.  In fact, the seeding is partially determined by something called the rating percentage index or RPI – more math!  RPI is a formula that combines a teams’ winning percentage and its opponents’ winning percentages into an overall score.  However, there are several criticisms of RPI for ranking teams, one of which is that it doesn’t take into account margin of victory.

So what other ranking systems are there?  Turns out, there’s a lot!

Three years ago, Prof. Rosenthal, was hired by TSN to rank the March Madness teams based solely on statistical analysis.  He found the most important factors for making correct picks were the team’s overall win percentage, the team’s win percentage in non-conference games, and the team’s strength of schedule (i.e. the average strength of the opponents they played).

RPI and the “Rosenthal fit” both use “aggregate statistics” – for example, a team’s wins and losses are lumped together into a single winning percentage.  Laura Albert McLay, Associate Professor in the Department of Industrial and Systems Engineering at the University of Wisconsin-Madison and author of the sports analytics blog “Badger Bracketology”, uses a method that treats each game individually.   “What you have is this connectivity matrix that tells you who played who, so you’re actually looking at the specific match-ups and giving credit for each specific win,” explains Prof. McLay.


Don’t get upset

Of course there are bound to be unpredictable upsets (i.e. a lower seeded team beating a higher seeded team).  Like so many of us, Prof. Willoughby predicted Michigan State as the overall winner.  There was about a 5% chance of them losing to Middle Tennessee in that first round, but it happened.

And although they are irritating, upsets may actually be the key for winning your pool.

Nobody can win if everyone makes the same picks.  Choosing something that differentiates you from everyone else could be your winning ticket.  Prof. McLay picked UNC as her champion.  “UNC seemed like a good mix of likely to win but maybe not as likely to be picked by everybody else,” explains McLay.

“It’s not getting the most points, it’s getting more points than your opponents!”


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Malgosia Pakulska is a freelance science writer, speaker, and blogger. She completed her PhD in Professor Molly Shoichet’s lab studying drug delivery systems for spinal cord regeneration after injury. She is still passionate about research and wants to share that excitement with the public. When she is not in the lab, she is experimenting in the kitchen and blogging about it at Smart Cookie Bakes.