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# Basketball: Optimal aim points for bank shots

Date:
March 15, 2011
Source:
North Carolina State University
Summary:
New research show that, from many areas of the basketball court within 12 feet of the basket, you have a better chance of scoring with a bank shot than with a direct shot. The study also shows the optimal aim points to convert a bank shot from most areas of the court.

After simulating one million shots with a computer, the NC State researchers show that the bank shot can be 20 percent more effective when shooting at many angles up to a distance of about 12 feet from the basket. Bank shots are also more effective from the “wing” areas between the three-point line and the free-throw lane.
Credit: Image courtesy of North Carolina State University

The basketball is in your hands. The score is tied and there are only a few seconds left on the clock. You have the ball about 10 feet away from the basket on the right side of the court, just outside the free-throw lane. It's decision time: Is it best to try a direct shot to win the game on a swish? Or do you use the backboard and bank home the winning basket?

Time's up; the buzzer sounds. Were you a hero or a goat?

New research by engineers at North Carolina State University show that you had a better chance of scoring that particular game-winning bucket with a bank shot than with a direct shot.

After simulating one million shots with a computer, the NC State researchers show that the bank shot can be 20 percent more effective when shooting at many angles up to a distance of about 12 feet from the basket. Bank shots are also more effective from the "wing" areas between the three-point line and the free-throw lane. However, straight-on shots -- those corresponding to the area around the free-throw line -- from further than 12 feet are not as well suited for bank shots.

The researchers also found the optimal points where the simulated made baskets were aimed. The results show the optimal aim points make a "V" shape near the top center of the backboard's "square," which is actually a 24-inch by 18-inch rectangle which surrounds the rim. Away from the free-throw lane, these aim points were higher on the backboard and thus further from the rim. From closer to the free-throw lane, the aim points were lower on the backboard and closer to the rim.

The researchers also discovered that if you imagine a vertical line 3.327 inches behind the backboard and found where it crossed the aim point on the "V" shape on the backboard, you'd find the optimal spot to bank the basketball to score a basket.

"Basketball players can't take a slide rule out on the court, but our study suggests that a few intuitive assumptions about bank shots are true," says Dr. Larry Silverberg, professor of mechanical and aerospace engineering at NC State and the lead author of a paper describing the research. "They can be more effective than direct shots, especially from certain areas of the court -- and we show which areas on the court and where the ball needs to hit the backboard."

The researchers made a few assumptions while conducting the study. They used a men's basketball, which is slightly bigger and heavier than a women's basketball; launched the simulated shots from 6, 7, and 8 feet above the ground; and imparted 3 hertz of backspin -- which means three revolutions per second -- on the shots. The latter variable was shown in previous research to be optimal for successfully converting a free throw.

The research was published in the Journal of Quantitative Analysis in Sports. Lecturer Dr. Chau M. Tran and undergraduate student Taylor M. Adams co-authored the paper with Silverberg.

The Department of Mechanical and Aerospace Engineering is part of NC State's College of Engineering.

Story Source:

The above story is based on materials provided by North Carolina State University. Note: Materials may be edited for content and length.

Journal Reference:

1. Larry M Silverberg, Chau M Tran, Taylor M Adams. Optimal Targets for the Bank Shot in Men's Basketball. Journal of Quantitative Analysis in Sports, 2011; 7 (1) DOI: 10.2202/1559-0410.1299

North Carolina State University. "Basketball: Optimal aim points for bank shots." ScienceDaily. ScienceDaily, 15 March 2011. <www.sciencedaily.com/releases/2011/03/110310151224.htm>.
North Carolina State University. (2011, March 15). Basketball: Optimal aim points for bank shots. ScienceDaily. Retrieved July 23, 2014 from www.sciencedaily.com/releases/2011/03/110310151224.htm
North Carolina State University. "Basketball: Optimal aim points for bank shots." ScienceDaily. www.sciencedaily.com/releases/2011/03/110310151224.htm (accessed July 23, 2014).

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