Take Your Best Shot

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 from NC State engineers shows 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 researchers found 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 farther than 12 feet are not as well suited for bank shots.

Ready, Aim, Shoot

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,” actually a 24-inch by 18-inch rectangle that surrounds the rim. Away from the free-throw lane, these aim points were higher on the backboard and thus farther 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 and the study’s lead author. “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. Previous research showed that 3 hertz backspin was optimal for free throws.

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.