(This is the seventh in a series of stories about the science
behind the Olympics to run daily this week. The full list will
be updated at )
By Sharon Begley
NEW YORK, July 21 (Reuters) – In a multibillion-dollar sport
like basketball, one might expect trainers had figured out every
nuance of aerodynamics, mechanics and all things Newtonian to
increase the rate at which the ball goes through the hoop. Think
again.
Take free throws. For 50 years professional players in the
United States have sunk these shots from the “charity line” – so
called because the points are supposedly such sure things
they’re gifts – at a rate of about 75 percent.
That figure that seems to reflect a fundamental limit on
human performance, like a three-minute mile. But mechanical
engineer Larry Silverberg of North Carolina State University
doubts it. He believes the reason free throw percentages are not
higher is that no one had properly analyzed them to determine
the optimal trajectory.
Using a computer simulation of millions of trajectories
based on shots by the best free-throw shooters, Silverberg and
colleague Chau Tran determined how various factors affect the
chance of success. The magic formula: a launch angle of 52
degrees, 3 revolutions per second of backspin, and aiming for a
spot 7 centimeters (2.8 inches) back from the center of the
basket, toward the back of the rim.
“With backspin, if the ball hits the rim or backboard, the
contact deadens the ball,” said Silverberg. “That means it comes
off slower, stays closer to the basket and is more likely to
fall in.”
Backspin that exceeds 3 revolutions per second is even
better: at 9 rps, Silverberg and Tran calculated, a free throw
that hits the very top of the backboard will drop straight down
for a point. But 9 rps is too difficult for players to achieve.
The target point is even less intuitive. Many players aim
for the center of the basket, assuming “nothing but net” makes
success more likely than hitting the rim, which can produce
unpredictable bounces.
The NCSU scientists’ calculations show that the spot that
maximizes the chance of a field goal is 2.8 inches behind the
center of the 18-inch-across basket. That puts the back of the
ball just over an inch from the back of the rim.
The main reason that target is better than the net’s center
is that shooters aren’t perfect. Aiming for the center of the
basket increases the chance of hitting the front of the rim and
having the shot drop straight down.
“This is the least well-known aspect of free-throw shooting,
so it offers the most opportunity for improvement,” said
Silverberg. “For anyone but the best shooters, the ball has a
better chance of going in if you aim between the backboard and
the center of the hoop, not the center itself.”
FIND THE ANGLE, SINK THE SHOT
Finally, the launch angle, or arc. A launch angle of 52
degrees minimizes velocity compared to shots with more arc or
less arc. Less velocity means less chance of a rebound that
misses the basket. The millions of shots that went into
Silverberg’s simulation showed that 52 degrees produced the
greatest chance of sinking the shot for a 6 foot, 6 inch player.
Since players can’t easily tell the angle at which they’re
launching a free throw, a more useful strategy is to shoot so
the top of the ball’s arc is even with the top of the backboard.
That’s doable with practice, and works no matter a player’s
height.
The NCSU computer simulations also filled a gaping hole in
basketball wisdom: although lay-ups and bank shots off the
backboard are the most common shots in basketball, no one knew
with any certainty the optimum spot on the backboard for making
the ball drop in for two, or three, points.
Simulations showed that the optimal banking points varied
with the location of the shooter, as expected. Completely
unexpected was that these points form what Silverberg calls “a
magical location: a ‘V’ near the top of the shooter’s square,”
the rectangle above the basket that’s painted or taped on the
backboard.
To determine where on the V a bank shot should hit to have
the greatest chance of going in, a shooter imagines a vertical
line behind the backboard. Where it intersects the imaginary V
on the backboard is the sweet spot where a bank shot should hit
to score a basket.
A player can’t do all of this mental imagery in the frenzy
of a game, of course, but by doing it in practice he can get an
intuitive feel for where to aim from different points on the
court. “It’s a training tool,” said Silverberg. From near the
free throw line – that is, in front of the basket – the ideal
bank point is lower; from the sides of the court it’s higher.
Knowing this “can improve your field goal shooting 20
percentage points,” said Silverberg.
(Editing by Michele Gershberg)
