Re: Which spot on the basketball court is the best place to shoot from?

Well, there really isn't a best spot the way most people shoot.  Typically
players don't shoot to hit the backboard, but rather on an arc to hit
"nothing but net."  But we can walk thru a quick derivation of what goes
into
analyzing the potential success of a shot.

Obviously, making or missing the basket depends on the accuracy of the
shot,
but the accuracy is affected by errors in aim and effort. An NBA regulation
bask
etball is close to 29.5 inches in circumference which corresponds to a
diameter
of about 9.4 inches.  The hoop is about 18 inches in diameter -- almost but
not
quite 2 ball diameters.  The ball will have a chance to go in it if the center
of m
ass of the ball is inside an imaginary cylinder extending upwards over the
hoop.
  No matter what one does to get the ball into the basket it will have to
enter
this imaginary "target zone."  The ball can be off center left-to-right or
front
-to-back by about 9 inches and still (maybe) go in.

If you want to include the arc of the incoming ball, this cylinder would be
tilte
d toward the incoming ball.  If the ball is coming in too flat, the target
zone
disappears and its unlikely the ball will go in except by "a lucky
shooter's bounce" off the rim.  

So if you are shooting at only the hoop angle (spot on
the court) really doesn't come into the shot success.

Errors in aim are going to propagate with distance.
For example:
I aim at the basket but shoot the ball so that it moves two inches left of my
line of aim for every foot it travels.   If I am 3 feet away the ball will still
likely go in because the center of mass of the ball is only 6 inches off center
in the target zone.   But if I am 10 feet away my shot will drift 20 inches left
and I just put up an embarrassing  air ball.  

Shooting from a closer spot allows the shooter more error in aim.

Harder to figure in the potential success of a shot is the effect of the
speed o
f the incoming ball.  In general, a really fast ball (hard shot)  will
bounce of
f the rim harder than a slow ball (soft shot).  So if you hit the rim, you
are b
etter off hitting it softly because the change in direction of the ball is
going
 to be less and may keep the ball in the target zone.  If you have ever
witnesse
d a missed slam dunk you can see this effect in action.  A missed power
dunk can
 travel upwards of 20 feet!

Shooting a ball softly is difficult.  Basically what the shooter is trying
to do
 is have the peak of the ball's flight path as close to the hoop as
possible and
 the downward flight of the ball still be in the target zone.  If you watch
basketball notice how the "good shooters" seem to shoot the ball in this way.

A softer shot is better most of the time.

But of course, in a real game, how the ball is shot is dictated more by
factors like defenders and motion of the shooter.  

Maybe this answer will help you figure out what is the best shot in a given
situation :)

Sincerely,

Tom "Brick Thrower" Cull