David Mildebrath, a mathematician, came to basketball by way of baseball, the most numbers-saturated of sports.
“I didn’t really know much about basketball. Still don’t. I’m a baseball fan. I had to learn something about basketball for purely mathematical reasons,” said Mildebrath, a fourth-year graduate student in computational and applied mathematics (CAAM) at Rice University and a National Defense Science and Engineering Graduate Fellow.
The product of his athletic detour is the article “Optimal Jersey Retirement in the National Basketball Association,” which will be published in an upcoming issue of Transactions of IISE Transactions.
Several sports honor players by retiring their jersey numbers after their active careers. Teams consider varying qualities when deciding which numbers to retire. Mildebrath and his collaborators devised a method for quantifying the preferences of NBA franchises when selecting players to honor with jersey retirement.
“There is a finite number of resources to divvy out. How do we allocate them?” Mildebrath asked.
His co-authors on the project are Andrew J. Schaefer
, the Noah Harding Chair and Professor of CAAM, and Wendy Knight
, who graduated from Rice last year with a B.A. in CAAM and now is working on a master’s degree in industrial engineering at the University of Texas in Austin.
When Mildebrath arrived at Rice in 2016, after earning a B.S. in physics and pure mathematics from the University of Alabama, Schaefer suggested as a research project the most efficient way to retire the numbers on the jerseys of baseball players. When Knight, then an undergraduate in CAAM, joined the team, they switched sports but kept the number retirement idea.
“I know more about the Markov decision process than I do about basketball but that really wasn’t important,” said Mildebrath, who earned his master’s degree in CAAM from Rice in 2018.
Knight more than compensated for Mildebrath’s basketball-knowledge deficiency. As a senior at Rice, she was the shooting guard on the Rice Owls women’s basketball team. She came to Rice on a full basketball scholarship, and the number on her jersey was 10.
“That’s a nice number, mathematically speaking. Binary. But I don’t think there’s much chance it will ever be retired,” she said. “Basically, it’s the Markov decision process – how to make decisions when the outcomes are random and under the control of the person making the decision at the same time.”
A San Antonio native, Knight has been playing basketball since she was a first-grader and a budding fan of the San Antonio Spurs. She played in church leagues and at Reagan High School was part of a team with a record of 122 wins and 20 losses over her four years. In her senior year the team went 28-5, and she was scouted by several university teams. Her decision to come to Rice was based, in part, on the university’s academic reputation.
“I thought about both CAAM and statistics. By the time I took CAAM 378, I had made up my mind,” she said. CAAM 378 is Introduction to Operations Research and Optimization, taught by Schaefer.
“We were dealing with zero to 99,” Knight said. “We wanted to find the optimal number of players whose numbers should be retired before the team runs out of numbers. They could use a little help with making choices that have a little structure in them.”
“Wendy really knew what she was talking about. I did the pencil and paper stuff. She amassed the data and ran the models,” Mildebrath said.
As a result of this and other work, Knight was one of three CAAM majors to receive a 2017 CAAM Chevron Prize, given for outstanding performances in class or notable research contributions.
During the season Knight would spend about 30 hours a week practicing on the basketball court, plus travel to away games. As a junior at Rice, she started in all 35 games for the 2017 Women’s Basketball Invitational champion Owls. She averaged 7.1 points and 4.0 rebounds per game, and for the season totaled 248 points, 140 rebounds, 63 assists and a team-leading 50 steals.
“I love basketball. I’ve had a lot of fun but I look on it as a means to an end. Academics are very important to me. I might end up doing something like sports analytics,” she said.
Mildebrath, too, is leaving basketball behind. His research interests focus on health care, as suggested by the tentative title of another paper he co-authored with Schaefer and submitted for publication: “Optimizing lung transplantation waitlist composition from the transplant program’s perspective.”