During the summer, Davidson's quiet walkways mask the bustling work of undergraduates collaborating with faculty on projects that expand their knowledge and test the limits of their imaginations.
Among them in a computer lab in Chambers building this year were five students working with Associate Professor of Mathematics Tim Chartier for eight weeks on a host of questions, answers, possibilities and probabilities concerning math problems old and new.
Several of the students also collaborated with Professor Amy Langville of the College of Charleston on improving sports ranking systems. Sarah Klett '15 and College of Charleston students Steve Gorman and Tyler Perini attempted to improve the accuracy and consistency of the two most frequently used sports ranking systems-the Massey Method and the Colley Method.
"Both methods are used by the Bowl Championship Series to pick football teams," explained Chartier. "We adapted and expanded them for more sports, and to answer more questions."
They ended up developing a weighting system that used the Massey Method to improve the results of the method itself.
Weighting systems consider which variables are most significant in predicting the result of a game. The date of the game turns out to be an important factor when college basketball teams are ranked prior to March Madness. For instance, how a team is doing in November is less indicative of how they will do in the tournament than how they are doing in the months closer to the tournament. In addition, whether a team is playing a home game or an away game also has a statistically significant impact.
The students developed 12 different ratings systems based on the Massey Method, incorporating a number of variables that influence rankings. They also factored in March Madness data from the previous eight-year period. "With more data points, you get a more accurate system," said Gorman. "Prior to 2008 our system wasn't doing as well. But the year it first did better we improved outcomes by 300 games for the season."
Chartier said the team also explored a question posed by Peter Keating of ESPN Magazine - could these methods tell you at March Madness if you were ripe for a lot of upsets? "That's a difficult one," Chartier said. "We have answers to it, but not a definitive answer. Some of the methods the students developed arose when they tried to answer that question."
The students incorporated research by Seth Kindig '14 on team comparisons into their work. Kindig, a mathematics major, basketball coach and self-professed basketball junkie, decided to approach the question by examining the statistics of the whole season, not just the tournament.
Chartier said, "Seth applied variations of Amy and my research to the March Madness games, and beat 90 percent of the brackets." But, he cautioned, even that result is only better at predicting the outcomes of a limited number of games.
Chartier and Langville marveled at what their students accomplished in eight weeks of research. Chartier recalled, "We needed to slow them down a little bit! So much was being created and tested at one time that we needed to get a grip on their results."
In the final weeks of the session, the group changed some of the research questions based on feedback from their faculty supervisors.
"Dr. Chartier asked if we could compare teams in a way that grouped those with similar styles of play," Kindig said. "I did some research and figured out which stats would tell us how a team plays."
From there they looked at how teams with similar styles played against each other, and tried to predict the outcomes of individual matchups. "The heart of the question is, ‘Can we predict which matchups would result in an upset,'" said Kindig. "That's very different from the question of which team would be likely to be upset. I'm now looking at whether I can apply that idea to other sports, like ultimate fighting."
Kindig and Chartier talked with Davidson Assistant Men's Basketball Coach Matt McKillop '06 about their work, and got his agreement to provide in the coming season information about Davidson games to test their theories.
Student researcher Danielle Shepherd, a College of Wooster student, hopes to make a career as an analyst or engineer in the world of NASCAR. She came to Davidson to collaborate on mathematical research with Chartier and Donour Sizemore, director of trackside systems for Michael Waltrip Racing.
Shepherd was tasked with a "computer vision" project of developing a method to sort through thousands of photos in a short period of time to detect which frames include a Waltrip car. Shepherd explained, "During qualifying for a race, the team may only have 30 minutes to look at the set-up of the car and make adjustments. They can't go through 5,000 pictures in that time. It's too much data to process and use without an appropriate tool."
Shepherd approached the problem first by manually marking characteristics in the photos such as the Toyota logo or a type of grill. Then she developed a program that would recognize and tag frames with those characteristics.
More than once, the students' work took a creative turn beyond the Chambers classroom. The researchers traveled to Queens University in Charlotte to participate in a math and science camp for girls, and collaborated with Davidson faculty Mark Foley (economics), Josh Putnam (political science), Joe Gardner (theatre) and Ken Massey of Carson-Newman College for whom the Massey Method is named. For three days Massey acted as a resource for the students, answering questions and entertaining new ideas.
Recognizing that 40 hours of math research per week can become tedious even for the most enthusiastic students, Chartier encouraged his student collaborators to work on a variety of projects outside of the research, and to join his family for weekly dinners and movie nights.