Random Walk Picture of Basketball Scoring
arXiv:1109.2825 · doi:10.1515/1559-0410.1416
Abstract
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 walk. 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 team.
10 pages, 14 figures; version 2: 20 pages, 8 figures, for publication in Journal of Quantitative Analysis in Sports
Cited by in corpus (14)
- Safe Leads and Lead Changes in Competitive Team Sports
- The Advantage of Playing Home in NBA: Microscopic, Team-Specific and Evolving Features
- Luck is Hard to Beat: The Difficulty of Sports Prediction
- In search of peak human athletic potential: A mathematical investigation
- Is coaching experience associated with effective use of timeouts in basketball?
- The game story space of professional sports: Australian Rules Football
- A stochastic approach for quantifying immigrant integration: the Spanish test case
- Identification of skill in an online game: The case of Fantasy Premier League
- Record Ages of Scale Invariant non-Markovian Random Walks
- Environmental structure and competitive scoring advantages in team competitions
- Anti-persistent random walks in time-delayed systems
- Persistent and anti-Persistent Motion in Bounded and Unbounded Space: Resolution of the First-Passage Problem
- Loss of Percolation Transition in the Presence of Simple Tracer-Media Interactions
- Statistical properties for directional alignment and chasing of players in football games