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Random Walk Picture of Basketball Scoring

Author

Listed:
  • Gabel Alan

    (Center for Polymer Studies and Department of Physics, Boston University, Boston)

  • Redner Sidney

    (Center for Polymer Studies and Department of Physics, Boston University, Boston)

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 continuous-time anti-persistent random walk. The time intervals between successive scoring events follow an exponential distribution, with essentially no memory between different scoring intervals. By including the heterogeneity of team strengths, we build a detailed computational random-walk model that accounts for a variety of statistical properties of scoring in basketball games, such as the distribution of the score difference between game opponents, the fraction of game time that one team is in the lead, the number of lead changes in each game, and the season win/loss records of each team.

Suggested Citation

  • Gabel Alan & Redner Sidney, 2012. "Random Walk Picture of Basketball Scoring," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 8(1), pages 1-20, March.
    • Handle: RePEc:bpj:jqsprt:v:8:y:2012:i:1:n:6
    DOI: 10.1515/1559-0410.1416
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    References listed on IDEAS

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    Cited by:

    1. Roy Cerqueti & Raffaele Mattera & Valerio Ficcadenti, 2025. "Kendall correlations and radar charts to include goals for and goals against in soccer rankings," Computational Statistics, Springer, vol. 40(4), pages 1849-1872, April.
    2. Tal Neiman & Yonatan Loewenstein, 2014. "Spatial Generalization in Operant Learning: Lessons from Professional Basketball," Discussion Paper Series dp665, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    3. Martín-González, Juan Manuel & de Saá Guerra, Yves & García-Manso, Juan Manuel & Arriaza, Enrique & Valverde-Estévez, Teresa, 2016. "The Poisson model limits in NBA basketball: Complexity in team sports," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 464(C), pages 182-190.
    4. Paola Zuccolotto & Marco Sandri & Marica Manisera, 2023. "Spatial performance analysis in basketball with CART, random forest and extremely randomized trees," Annals of Operations Research, Springer, vol. 325(1), pages 495-519, June.
    5. Paola Zuccolotto & Marco Sandri & Marica Manisera, 2021. "Spatial Performance Indicators and Graphs in Basketball," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 156(2), pages 725-738, August.
    6. Song, Kai & Gao, Yiran & Shi, Jian, 2020. "Making real-time predictions for NBA basketball games by combining the historical data and bookmaker’s betting line," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    7. Christopher Magee & Amy Wolaver, 2023. "Crowds and the Timing of Goals and Referee Decisions1," Journal of Sports Economics, , vol. 24(6), pages 801-828, August.
    8. Haroldo V Ribeiro & Satyam Mukherjee & Xiao Han T Zeng, 2016. "The Advantage of Playing Home in NBA: Microscopic, Team-Specific and Evolving Features," PLOS ONE, Public Library of Science, vol. 11(3), pages 1-18, March.
    9. Léo Régnier & Maxim Dolgushev & Olivier Bénichou, 2023. "Record ages of non-Markovian scale-invariant random walks," Nature Communications, Nature, vol. 14(1), pages 1-7, December.
    10. Song, Kai & Shi, Jian, 2020. "A gamma process based in-play prediction model for National Basketball Association games," European Journal of Operational Research, Elsevier, vol. 283(2), pages 706-713.
    11. Tal Neiman & Yonatan Loewenstein, 2014. "Spatial Generalization in Operant Learning: Lessons from Professional Basketball," PLOS Computational Biology, Public Library of Science, vol. 10(5), pages 1-8, May.

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