Is basketball scoring just a random walk?

Oct. 18, 2017 from 3:30 to 4:20 p.m. — Physics/Astronomy Auditorium, room A102

Sid Redner

Professor, Santa Fe Institute

Watch a recording of this seminar on YouTube.


Watching basketball is nearly the same as watching repeating coin tossings! By analyzing recently available data from recent NBA basketball seasons, basketball scoring during a game is well described by a continuous-time anti-persistent random walk, with essentially no temporal correlations between successive scoring events. We show how to calibrate this model to account for many statistical season-long metrics of NBA basketball. As further illustrations of this random-walk picture, we show that the distribution of times when the last lead change occurs and the distribution of times when the score difference is maximal are both given by the celebrated arcsine law—a beautiful and surprising property of random walks. We also use the random-walk picture to construct the criterion for when a lead of a specified size is “safe” as a function of the time remaining in the game. The obvious application to game-time betting is left as an exercise for the interested.


Sid Redner received an A.B. in Physics from UC Berkeley in 1972 and a Ph.D. in Physics from MIT in 1977. After a postdoctoral year at the University of Toronto, he joined the physics faculty at Boston University in 1978. Sid served as Acting Chair in two separate terms and also Department Chair. He was a Visiting Scientist at Schlumberger-Doll Research in 1984, the Ulam Scholar at LANL in 2004, and a visitor professor at Universite Paul Sabatier in Toulouse, Universite Pierre et Marie Curie and Institut Henri Poincare, both in Paris. In 2014, he left BU for his current position as a resident faculty member at the Santa Fe Institute.

Sid’s research interests lie in non-equilibrium statistical physics. He has worked on the structure of complex networks, physics-based models of social dynamics, phase phase-ordering kinetics, as well as diffusion and first-passage processes and their applications. He has published more than 260 articles in major journals, as well as two books: the monograph “A Guide to First-Passage Processes” (Cambridge Univ. Press, 2001) and the graduate text, jointly with P. L. Krapivsky and E. Ben-Naim, “A Kinetic View of Statistical Physics” (Cambridge Univ. Press, 2010). He is also an Associate Editor for the Journal of Statistical Physics, and a Divisional Associate Editor for Physical Review Letters.