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March Mathness

Tim Chartier presents "March Mathness" as part of the 
MAA Distinguished Lecture Series in 
MAA Carriage House.

When Tim Chartier applies his mathematical study of ranking to bracketology—the art of predicting how the NCAA Basketball Tournament will play out—he gets a reaction. Audiences outside Atlanta decry PowerPoint slides—those that show the Altanta Falcons losing, anyway—as propaganda. Students uninterested in sports thrill at the chance to finally—using math!—best uncles and brothers in family pools. TV crews clamor for interviews.

And MAA taps Chartier for its MAA Distinguished Lecture Series. On February 28, the Davidson professor presented “March Mathness” to a Carriage House crowd that—according to this author’s nonscientific hunch—skewed a little younger and more male than usual. Although Chartier is quick to note that he and his colleagues “don’t actually do research on how to do great brackets,” the performance artist in him—Chartier is a professionally trained mime—recognizes that the bracketology application of his work in linear algebra makes for a good show.

With the glitter of Oscar night a recent memory and the race for the Republican presidential nomination dominating the headlines, it’s obvious that, as Chartier said, “Ranking is an ever-present part of…our society and culture.” Of course sometimes—like when constructing a bracket—we care about more than who will come out on top. We ask ourselves questions like “Who’s No. 8?” “Who’s No. 13?” We want to know, given a pair of teams, which would prevail on the court. 

Improbable as it sounds, Tim Chartier can leverage math to foretell such outcomes, to “predict how 18- to 22-year-old young men will perform in high-pressure situations.” The basis of Chartier’s mathemagic is the Colley Method, named for its developer, Wesley Colley

Chartier outlined the derivation of the Colley Method, starting with Laplace’s rule of succession and performing manipulations—decomposing wholes into halves, adding and subtracting the same quantity—that he admitted can “seem like hand-waving” or “feel like math of the worst kind.” 

“That’s exactly why it’s called the Colley Method,” Chartier said, “because for some reason…[Colley] played enough that he was actually able to work this out.” Math and mathematicians, in other words, work in mysterious ways.

Tim Chartier presents "March Mathness" as part of the
MAA Distinguished Lecture Series in 

MAA Carriage House.

Chartier dispelled the mystery a little, though, by describing how to derive from team statistics—number of wins, total games played—values that, slotted into a massive 350 by 350 matrix, represent a system of equations that can be solved to yield team ratings. To make a bracket based on these ratings, you just assume that the higher rated team always wins.

You can, of course, “usurp the math and make your own decisions,” Chartier said, but consider the Colley Method’s none-too-shabby track record: When Chartier entered a Colley-generated bracket in the 2009 ESPN Challenge, it beat 62 percent of the more than 4 million entrants. In 2010 Colley outperformed everyone from LeBron James and Davidson alum Stephen Curry to Dick Vitale and Barack Obama.

But there’s room in the Colley Method for both improvement and exercise of bracketeer autonomy. Chartier’s students don’t all algorithmically produce and submit identical brackets, after all. For although what Chartier calls “straight Colley” takes into consideration only a team’s number of wins and the total games played between pairs of teams, prognosticators of championship performance might want to fold into their figurings such factors as the timing of games and their scores.

One way to incorporate the former, Chartier explained, is to weight the games based on when in the season they occurred. Perhaps you think a defeat in the season opener should count as only half a loss, that a victory leading into the tournament testifies to such promising momentum that it ought to count double. “You pick a function that models the way that you see the timing of the games telling you how…[the teams] will play,” Chartier said. “That function is your function and that function creates your bracket.”

Chartier closed his talk by soliciting audience input to produce with the help of some Java code a Carriage House Interval Ranking of NCAA teams based on available data. One member of the audience suggested breaking the season into seven intervals, and seven others—including MAA’s Executive Director Michael Pearson—chimed in with weights to attach to each season subdivision. The result? The top three teams will be Syracuse, Kentucky, and Duke in that order, with Ohio State and Wichita State rounding out the top ten. —Katharine Merow


 Listen to the full lecture (mp3)

 Listen to an interview with Chartier and Ivars Peterson (mp3)

  Watch the full lecture on the MAA YouTube Channel

Related:

Tim Chartier’s Bracketology 101 Webinar — the Math You Need to Pick the Winners

Math Improves March Madness Predictions (Inside Science Television)

Got March Madness? Try Math! (The Huffington Post)

Math Students Demonstrate Success with March Madness Brackets Using Teacher's Method (Inside Science Television)

 

This MAA Distinguished Lecture was funded by the National Security Agency.

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