# Using a brownian motion to calculate the importance of points in basketball

De Lorenzo, M and Grundy, I 2016, 'Using a brownian motion to calculate the importance of points in basketball', in Ray Stefani and Adrian Schembri (ed.) Proceedings of the 13th Australasian Conference on Mathematics and Computers in Sport, Melbourne, Australia, 11-13 July 2016, pp. 134-139.

 Document type: Conference Paper Conference Papers

Title Using a brownian motion to calculate the importance of points in basketball De Lorenzo, M Grundy, I 2016 13th Australasian Conference on Mathematics and Computers in Sport Melbourne, Australia 11-13 July 2016 Proceedings of the 13th Australasian Conference on Mathematics and Computers in Sport Ray Stefani and Adrian Schembri ANZIAM MathSport Melbourne, Australia 134 139 6 Particular moments during a game of basketball can affect a team's probability of winning. Often, a player's performance can be subjectively scrutinised for their ability to perform during these critical moments. However, identifying the moments that are most critical to a team's chances of winning can be difficult. In this paper, we attempt to quantify the importance of points during a basketball game using a Brownian motion. Closely related to a random walk, and originally used to model the random motion of particles suspended in fluid, Brownian motion has been found in past research to provide a reasonable estimate of the win probability of a team during a basketball game, given the time remaining and the difference in score. By adjusting these probabilities and using an existing definition of point importance from tennis, it is possible to calculate the importance of particular points during a game of NBA basketball. Results from games across six seasons of NBA basketball suggest that the point importance can be reasonably quantified by using the Brownian motion. Furthermore, the point importance can be broken down into the importance of scoring the next one, two or three points. An exploration of these three components indicate that the three-point shot always has a greater importance than either a one-point shot or a two-point shot. We believe that the knowledge of point importance in basketball could be an effective tool in evaluating player performance. Applied Statistics Point importance basketball Brownian motion probability 9780646957418
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