Available at: https://digitalcommons.calpoly.edu/theses/3282
Date of Award
6-2026
Degree Name
MS in Statistics
Department/Program
Statistics
College
College of Science and Mathematics
Advisor
Kevin Ross
Advisor Department
Statistics
Advisor College
College of Science and Mathematics
Abstract
This paper develops a continuous-time, continuous-state framework for studying “hot hand” performance within NBA games. Rather than defining performance in terms of discrete shot outcomes or short streaks of makes and misses, it tracks a player’s contribution using John Hollinger’s Game Score continuously throughout the game. The Game Score metric aggregates multiple on-court contributions through weighted in-game statistics, evolving as play progresses. This approach allows for the construction of a single metric that indexes a player’s performance over the course of the game. To evaluate whether observed within- game surges reflect genuine “heat” rather than random variation, a simulation-based null model is constructed. We assume that these games resemble a compound Poisson process where event rates and contributions vary over the course of a game. Under the assumption of no hot hand, performance increments are sampled independently from each player’s empirical season distribution, while event times are generated uniformly throughout the game. Simulated null trajectories are then used to construct trend-based heat envelopes for expected performance behavior, quantifying heat by frequency, duration, and area. This framework enables comparison of the frequency, intensity, and persistence of hot performance episodes across players and games. By moving beyond binary shot outcomes and instead modeling performance as a holistic, continuous process, this paper offers a more comprehensive approach to identifying and analyzing the hot hand phenomenon.