1. Shot Model for Basketball from Three Different Positions
Jason Ponder & Kamryn Sakamoto
MA3232
Spring 2010

2. Outline Court Size and Shapes Background of the Shots
Setup for the Problem
Variation of parameters
Graphs
Shot Recommendations

3. Shot Positions
GOAL!!

4. Background of the Problem
Desire to determine possible shooting angles for various shots and determine the release velocity required to reach the basket.
Assumptions: Shot will be to center of basket for the perfect “swish”
There is a margin for error that can be applied for follow-on projects in both the distance front-to-back and left-to-right in the rim.
This would require 3 or more ‘for’ loops and differential equations to produce the full model of a realistic shot taking trajectory and other factors into account.
Additional Parameter: Maximum Height of Shot cannot exceed 50Ft. (reasonable Height of Scoreboard and Speakers in Most Arenas).

5. Variation of Parameters
x: horizontal distance of the shot: Free Throw, Half Court, Full Court. (Ft)
Θ0: Initial Shot Angle: From 1 to 89 degrees (impossible to shoot with a zero or 90 degree angle release). (Degrees)
Maximum Height: Must be considered because arenas often have a score board or speakers at center court which could block a potential shot. (Ft)
V0 : Velocity determined to make the shot at the given release angle possible. (Ft/sec)

6. Peak Shot Height vs. Release Angle
Free Throw Shot Ft.
Peak Shot Height (Ft)
85 Degrees is the Maximum Release Angle
Release Angle (Degrees)

7. Release Velocity vs. Release Angle vs. Peak Shot Height
Free Throw Shot Ft.
Peak Shot Height (Ft)
Release Velocity (Ft/sec)
Release Angle (Degrees)

8. Free Throw Recommendations
Shaq Attack
Jamaal Wilkes
At this distance there are a lot of options.

9. Peak Shot Height vs. Release Angle
Half Court Shot Ft.
Peak Shot Height (Ft)
75 Degrees is the Maximum Release Angle
Release Angle (Degrees)

10. Release Velocity vs. Release Angle vs. Peak Shot Height
Half Court Shot Ft.
Peak Shot Height (Ft)
Release Velocity (Ft/sec)
Release Angle (Degrees)

11. Half Court Recommendations
Mo Williams
Careful what you wish for.
A little luck goes a long way.

12. Peak Shot Height vs. Release Angle
Full Court Shot Ft.
Peak Shot Height (Ft)
58 Degrees is the Maximum Release Angle
Release Angle (Degrees)

13. Release Velocity vs. Release Angle vs. Peak Shot Height
Full Court Shot Ft.
Peak Shot Height (Ft)
Release Velocity (Ft/sec)
Release Angle (Degrees)

14. Full Court Recommendations
Andre Iguodala
The King
Long way away
A Slightly different approach to the long distance shot: Above the goal.
Throw it up… Hope for the best.

16. Release Velocity vs. Release Angle vs. Peak Shot Height
Comparison Chart
Peak Shot Height (Ft)
Release Velocity (Ft/sec)
Release Angle (Degrees)

17. Conclusion
All shots and angles are possible. Just need a little luck and maybe a last second gust of wind.

18. Questions?