Credit: North Carolina State Univ.
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 Univ. 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% 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
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-in by 18-in
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 in
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
“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.