Thursday night at the National Museum of Mathematics in Manhattan, where 50 would-be mathematicians huddled in a windowless classroom to harness the power of linear algebra and complex computer codes to predict the outcome of each of the 67 games in the N.C.A.A. men’s basketball tournament.
They weren’t there just for the love of the equation.
“There are a billion reasons to be here tonight,” said Tim Chartier, a math professor at Davidson College, who was leading the event, called March (Mo)Mathness.
He was referring to the contest with the $1 billion prize offered by Quicken Loans (and insured by Warren Buffett’s Berkshire Hathaway) for a perfect bracket.
To reach Chartier’s room at the museum, the crowd opened doors with handles shaped like ?, the symbol for pi. Once assembled, Chartier said that theirs was no easy task. He estimated that the odds of picking every winner were one in nine quintillion.
“But there is a chance,” he said.
On Sunday, the N.C.A.A. releases the matchups for its biggest tournament. Chartier was preparing the eager students, who paid as much as $100 at the door, to get a leg up on other sports fans with his first public, in-depth presentation of the mathematical models he uses for choosing winners.
In 2009, Chartier and his Davidson students began developing a bracket program that quickly yielded remarkable results, even though many of the participants had no interest in college basketball. The program can be adjusted for losses early and late in the season, as well as for margins of victory and defeat.
Chartier insists that his program works. Several of his students have finished in the 90th percentile of ESPN’s annual contest, which drew more than eight million entries last year. Three students finished in the 96th to 99th percentiles.
But the outputs are only as good as the inputs. Last year, one student accurately predicted 14th-seeded Harvard’s win over third-seeded New Mexico but was beaten by more than 98 percent of the ESPN entries. “You have to be a bit careful there,” Chartier said.
The underlying math — applied linear algebra — is similar to what the Bowl Championship Series used to produce its rankings, but with a twist. Instead of incorporating past results, Chartier’s math helps predict how the tournament teams will be ranked and how they might fare. The software allows for either a Colley ranking, which is a linear system that uses only wins and losses, or a Massey ranking, which integrates the scores of the games.
For most of the class, only basic math skills were required to follow along, but math majors were also challenged.
“We may be home to Steph Curry,” Chartier said, referring to Davidson’s former point guard, “but also some major bracketology.”
Chartier, 45, has also used math to solve Sudoku puzzles. He has explored the relationship between linear algebra and the physique of Yoda from “Star Wars.” And he has pondered the meaning of Buzz Lightyear’s slogan, “To infinity and beyond.” Chartier is also a mime.
Using simple diagrams that showed various win-loss situations, Chartier broke down the algorithm using systems of only four teams. He then expanded it to a diagram that looked like a spider web indicating the outcomes of nearly 350 teams in about 5,000 games.
Several students gasped.
“Holy smokes!” one exclaimed.
With iPads that had Chartier’s software ready to go, along with printouts of practice brackets that used previous years’ data, students peppered Chartier and two student assistants with questions. What about upsets? How are emotional favorites factored? How much weight is a home game worth? And what about Florida?
At one table, Joan Casazzone and Helen Kramer, high school math teachers from Great Neck, N.Y., worked on their predictions, hoping to bring the science of bracketology into their classrooms.
“I’d love more of the nitty-gritty,” said Casazzone, who described herself as a basketball fiend. “Coding is hot right now.”
She and Kramer said they hoped to fill out several brackets Sunday night, some using math, others using feelings.
“We teach adolescents,” Kramer said. “So we know a lot about unpredictability.”
The Hitchcock family — Mike, Mary and their 14-year-old twins, Katie and Will — were visiting from Winston-Salem, N.C., and made time for Chartier’s seminar between seeing “Matilda” on Broadway and paying a visit to the Intrepid Sea, Air & Space Museum.
As the teenagers worked on brackets on their iPads, the family’s conversation soon drifted toward dividing the jackpot.
Katie said her parents were not guaranteed a share in any winnings.
“Well,” she reminded them, “we do have our own bank accounts."
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