Author(s)

Yu Su

Affiliation(s)

Beijjing City International School, Beijing 100000, China.

Corresponding Author

Yu Su

ABSTRACT

This study presents an advanced computational framework for analyzing the physics of basketball rebounding. Building upon a foundational model that uses classical mechanics and Monte Carlo simulations to predict rebound distributions, this research extends its predictive power by systematically relaxing key simplifying assumptions. The study investigates three critical, interconnected domains: the spatial dynamics of rebounds originating from asymmetric court positions, the role of ball rotation (backspin) in altering collision outcomes, and the distinct rebound characteristics of bank shots. By simulating thousands of shot trajectories, we generate high-fidelity, two-dimensional rebound "heat maps" that validate long-standing coaching heuristics about weak-side rebounds from corner shots. Furthermore, the analysis quantifies the energy dissipation effect of backspin, providing a physical basis for the concept of a "soft shooter's touch." Finally, a novel experiment on the bank shot demonstrates that the backboard, as a collision surface, produces significantly more predictable and favorable rebound patterns compared to shots off the rim. The findings are synthesized into a multi-factorial strategic framework, translating complex physical principles into actionable on-court tactics for optimizing rebounding strategy.

KEYWORDS

Computational physics; Basketball analytics; Rebound dynamics; Monte Carlo simulation; Bank shot; Backspin

CITE THIS PAPER

Yu Su. A multi-factorial computational analysis of basketball rebound dynamics: interplay of shot geometry, ball rotation, and collision surfaces. World Journal of Mathematics and Physics. 2025, 3(1): 34-42. DOI: https://doi.org/10.61784/wjmp3015.

REFERENCES

[1] Miller S, Bartlett R. The biomechanics of the basketball jump shot: A review. Sports Biomechanics, 2018, 17(3): 320-340.

[2] Reddick M. The angle of reflection. Angle of Reflection Blog, 2015.

[3] World of Pool and Billiards. How to bank in pool. World of Pool and Billiards, 2023.

[4] How to Bank in Pool - World of Pool and Billiards, accessed September 23, 2025. https://www.worldofpoolandbilliards.com/post/how-to-bank-in-pool

[5] Bank Shots And Kick Shots: Mastering Angles On The Pool Table - Home Games Room, accessed September 23, 2025. https://www.homegamesroom.co.uk/blogs/pool-table-basics/bank-shots-and-kick-shots-mastering-angles-on-the-pool-table

[6] The anatomy of the bank shot in men's basketball - Mendeley, accessed September 23, 2025. https://www.mendeley.com/catalogue/a18b9f24-8cae-3b2d-bcdf-8392f1d73f76/

[7] The coefficient of restitution of pressurized balls: a mechanistic model - ResearchGate, accessed September 23, 2025. https://www.researchgate.net/publication/281791329_The_coefficient_of_restitution_of_pressurized_balls_a_mechanistic_model

[8] Wilke C O. Fundamentals of Data Visualization: A Primer on Making Informative and Compelling Figures. O’Reilly Media, 2019.

[9] Basketball: Will You Bank the Shot? | Science Project, accessed September 23, 2025. https://www.sciencebuddies.org/science-fair-projects/project-ideas/Sports_p024/sports-science/basketball-bank-shot

[10] National Basketball Association. Official rules of the National Basketball Association. NBA Properties, Inc., 2024.

[11] Tufte E R. The Visual Display of Quantitative Information. Graphics Press, 2001.

[12] Okubo H, Hubbard M. Dynamics of the basketball shot with backspin. Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology, 2010, 224(3): 149-161.

[13] Silverberg L M, Tran C, Adams K M. Optimal targets for the bank shot in men’s basketball. Journal of Quantitative Analysis in Sports, 2011, 7(3).

[14] Cross R. The coefficient of restitution for collisions of happy balls, sad balls, and tennis balls. American Journal of Physics, 2002, 70(5): 482-489.

[15] FIBA. Official basketball rules 2024: Basketball equipment. International Basketball Federation, 2024.

[16] Brody H. Tennis Science for Tennis Players. University of Pennsylvania Press, 1987.

[17] Georgallas A, Landry G. The coefficient of restitution of pressurized balls: a mechanistic model. Canadian Journal of Physics, 2016, 94(1): 42-46.

[18] Science Buddies. Basketball: The geometry of banking a basket. Science Buddies, 2013.

[19] Marlow W C. The Physics of Pocket Billiards. Marlow Publications, 1995.

[20] Silverberg L. Time for March Madness: The physics of the basketball bank shot. Science 2.0, 2011, March 15.

[21] Strickland E. As quoted in “How to bank in pool.” World of Pool and Billiards, 2023.

[22] Optimal Targets for the Bank Shot in Mena€^TMs Basketball - ResearchGate, accessed September 23, 2025. https://www.researchgate.net/publication/227378877_Optimal_Targets_for_the_Bank_Shot_in_Menas_Basketball

[23] Coefficient of Restitution - Stanford Advanced Materials, accessed September 23, 2025. https://www.samaterials.com/content/coefficient-of-restitution.html

[24] Coefficient of Restitution – Basketball Bounce Simulation - Dencity App, accessed September 23, 2025. https://dencityapp.in/experiment/coefficient-of-restitution/

[25] Surface Collisions and the Coefficient of Restitution - Mechanics Map, accessed September 23, 2025. https://mechanicsmap.psu.edu/websites/11_impulse_momentum_particle/11-3_surface_collisions/surface_collisions.html

[26] The-anatomy-of-the-bank-shot-in-mens-basketball.pdf - ResearchGate, accessed September 23, 2025. https://www.researchgate.net/profile/Larry-Silverberg/publication/270258336_The_anatomy_of_the_bank_shot_in_men's_basketball/links/5a70718aa6fdcc33daa8bab1/The-anatomy-of-the-bank-shot-in-mens-basketball.pdf

[27] In Time For March Madness, The Physics Of The Basketball Bank Shot | Science 2.0, accessed September 23, 2025. http://www.science20.com/news_articles/time_march_madness_physics_basketball_bank_shot-77077

[28] Coefficient of Restitution | Formula & Equation - Lesson - Study.com, accessed September 23, 2025. https://study.com/learn/lesson/coefficient-restitution-overview-equation.html

[29] Coefficient of restitution - Wikipedia, accessed September 23, 2025. https://en.wikipedia.org/wiki/Coefficient_of_restitution

[30] Basketball: The Geometry of Banking a Basket | Science Project, accessed September 23, 2025. https://www.sciencebuddies.org/science-fair-projects/project-ideas/Sports_p064/sports-science/basketball-the-geometry-of-banking-a-basket

[31] Beginner's Guide to Bank Shots - Emerald Spas & Billiards | Premium Hot Tubs in Grand Rapids, MI, accessed September 23, 2025. https://emeraldgr.com/beginners-guide-bank-shots/

[32] emeraldgr.com, accessed September 23, 2025. https://emeraldgr.com/beginners-guide-bank-shots/#:~:text=Angle%20In%2C%20Angle%20Out,get%20the%20hang%20of%20banking.

[33] At what angle a cut shot is more difficult than a bank shot? : r/billiards - Reddit, accessed September 23, 2025. https://www.reddit.com/r/billiards/comments/1b4hczy/at_what_angle_a_cut_shot_is_more_difficult_than_a/

[34] Angle of Incidence - Angle of Reflection - WordPress.com, accessed September 23, 2025. https://angleofreflection.wordpress.com/tag/angle-of-incidence/