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The Problem of Shot Selection in Basketball

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  • Brian Skinner

Abstract

In basketball, every time the offense produces a shot opportunity the player with the ball must decide whether the shot is worth taking. In this article, I explore the question of when a team should shoot and when they should pass up the shot by considering a simple theoretical model of the shot selection process, in which the quality of shot opportunities generated by the offense is assumed to fall randomly within a uniform distribution. Within this model I derive an answer to the question “how likely must the shot be to go in before the player should take it?” and I show that this lower cutoff for shot quality depends crucially on the number of shot opportunities remaining (say, before the shot clock expires), with larger demanding that only higher-quality shots should be taken. The function is also derived in the presence of a finite turnover rate and used to predict the shooting rate of an optimal-shooting team as a function of time. The theoretical prediction for the optimal shooting rate is compared to data from the National Basketball Association (NBA). The comparison highlights some limitations of the theoretical model, while also suggesting that NBA teams may be overly reluctant to shoot the ball early in the shot clock.

Suggested Citation

  • Brian Skinner, 2012. "The Problem of Shot Selection in Basketball," PLOS ONE, Public Library of Science, vol. 7(1), pages 1-8, January.
  • Handle: RePEc:plo:pone00:0030776
    DOI: 10.1371/journal.pone.0030776
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    References listed on IDEAS

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    1. Skinner Brian, 2010. "The Price of Anarchy in Basketball," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 6(1), pages 1-18, January.
    2. Kubatko Justin & Oliver Dean & Pelton Kevin & Rosenbaum Dan T, 2007. "A Starting Point for Analyzing Basketball Statistics," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 3(3), pages 1-24, July.
    3. Jordi Duch & Joshua S Waitzman & Luís A Nunes Amaral, 2010. "Quantifying the Performance of Individual Players in a Team Activity," PLOS ONE, Public Library of Science, vol. 5(6), pages 1-7, June.
    4. Filippo Radicchi, 2011. "Who Is the Best Player Ever? A Complex Network Analysis of the History of Professional Tennis," PLOS ONE, Public Library of Science, vol. 6(2), pages 1-7, February.
    5. Arkes Jeremy, 2010. "Revisiting the Hot Hand Theory with Free Throw Data in a Multivariate Framework," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 6(1), pages 1-12, January.
    6. Skinner Brian, 2011. "Scoring Strategies for the Underdog: A General, Quantitative Method for Determining Optimal Sports Strategies," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 7(4), pages 1-18, October.
    7. C. Sire & S. Redner, 2009. "Understanding baseball team standings and streaks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 67(3), pages 473-481, February.
    8. Tal Neiman & Yonatan Loewenstein, 2011. "Reinforcement learning in professional basketball players," Nature Communications, Nature, vol. 2(1), pages 1-8, September.
    9. Gur Yaari & Shmuel Eisenmann, 2011. "The Hot (Invisible?) Hand: Can Time Sequence Patterns of Success/Failure in Sports Be Modeled as Repeated Random Independent Trials?," PLOS ONE, Public Library of Science, vol. 6(10), pages 1-10, October.
    10. Tal Neiman & Yonatan Loewenstein, 2011. "Reinforcement learning in professional basketball players," Discussion Paper Series dp593, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
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    Cited by:

    1. Jiao Jieying & Hu Guanyu & Yan Jun, 2021. "A Bayesian marked spatial point processes model for basketball shot chart," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 17(2), pages 77-90, June.
    2. Leonardo Lamas & José Vitor Senatore & Gilbert Fellingham, 2020. "Two steps for scoring a point: Creating and converting opportunities in invasion team sports," PLOS ONE, Public Library of Science, vol. 15(10), pages 1-16, October.
    3. 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.
    4. Jorge Serna & Verónica Muñoz-Arroyave & Jaume March-Llanes & M. Teresa Anguera & Queralt Prat & Aaron Rillo-Albert & David Falcón & Pere Lavega-Burgués, 2021. "Effect of Ball Screen and One-on-One on the Level of Opposition and Effectiveness of Shots in the ACB," IJERPH, MDPI, vol. 18(5), pages 1-16, March.
    5. 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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