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| Dunking: Mid Flight |
Though it is technically football season, this is pretty interesting. It points out that physicists and scientists are part of the rest of the world, and pay attention to sporting events: like football and basketball.
Hint: It's probably not a good idea to bet against them in an office pool!
We present evidence, based on play-by-play data from all 6087 games from the 2006/07--2009/10 seasons of the National Basketball Association (NBA), that basketball scoring is well described by a weakly-biased continuous-time random walk1. The time between successive scoring events follows an exponential distribution, with little memory between different scoring intervals. Using this random-walk picture that is augmented by features idiosyncratic to basketball, we account for a wide variety of statistical properties of scoring, such as the distribution of the score difference between opponents and the fraction of game time that one team is in the lead. By further including the heterogeneity of team strengths, we build a computational model that accounts for essentially all statistical features of game scoring data and season win/loss records of each team2.
1. Wolfram Mathworld: Random Walk
2. Physics arXiv: Random Walk Picture of Basketball Scoring, Alan Gabel and S. Redner, Center for Polymer Studies and Department of Physics, Boston University
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