Optimal jersey retirement in the National Basketball Association

Abstract

One of the highest honors an individual player in the National Basketball Association (NBA) can receive is to have their jersey number retired by a franchise. Players selected for jersey retirement are often chosen carefully, in part because each franchise has only a finite number of jerseys available for retirement. In this work, we present a method to optimize the selection of players to honor with jersey retirement. We first present a Markov Decision Process (MDP) to model the jersey retirement decisions of a given franchise. We then embed this MDP into a nonlinear regression model, which we solve approximately using a modified support vector machine. Our results indicate that most NBA franchises behave approximately in accordance with our optimality criteria. We also use our model to suggest optimal retirement decisions for several NBA franchises.

Keywords:

• Entertainment services
• integer programming
• dynamic programming

Acknowledgments

The authors would like to thank Tayo Ajayi, Razanne Oueini, and Maxine Tao for valuable conversations and input.

Additional information

Funding

D. Mildebrath was supported through the United States Department of Defense National Defense Science and Engineering Graduate (NDSEG) fellowship.

Notes on contributors

David Mildebrath

David Mildebrath is a Ph.D. student in the Department of Computational and Applied Mathematics at Rice University. He received an M.A. in computational and applied mathematics in 2018, and a B.S. in physics and pure mathematics from the University of Alabama in 2016. His research interests include mathematical modeling and stochastic programming.

Wendy Knight

Wendy Knight is an MSc student in the Department of Mechanical Engineering at the University of Texas at Austin. She received a B.A. in mathematics and computational and applied mathematics from Rice University in 2018.

Andrew Schaefer

Dr. Andrew Schaefer is a Noah G. Harding Chair and Professor of Computational and Applied Mathematics at Rice University. Prior to joining the faculty at Rice, he was a professor in the Department of Industrial Engineering at the University of Pittsburgh. He received his Ph.D. in industrial and systems engineering from the Georgia Institute of Technology in 2000, an M.A. in computational and applied mathematics from Rice University in 1994, and a B.A. in computational and applied mathematics and mathematical economic analysis from Rice University in 1994. His research interests include stochastic integer programming, optimization in organ allocation, optimal cancer therapies, and healthcare systems.