Addendum: In the face of Professor Pi's extraordinary mathematics, I have been forced to reconsider my write-up. I think Ben Franklin said it best when he said that the greatest tragedy in the world is when a beautiful theory is murdered by a gang of brutal facts.

This node has earned me a nice chunk of XP though, and reworked it may yet prove feasible (there is a little bit of historical data that wasn't made completely impotent). So for posterity's sake I'll leave my unedited version here. Besides, what good is a counterpoint without its point?

The genealogy of the granny shot is lost to me, and hours of tedious research have done little to alleviate this situation. It was likely developed by a rather athletic individual before the evolution of basketball into a national passtime.

The granny shot is an underhand throw of a basketball at the hoop. The name was derived from the resemblance of the shooter to a hunched-over old hag. It is often considered that it should only be used by children and special people. However, contrary to popular belief, the granny shot is scientifically the superior way to shoot a free throw. There are several reasons for this:

• Trajectory: A standard NBA-approved basketball has a circumfrence between 29 to 30 inches (for the non-prodigy or calculator-deprived, that is a diameter of 9.40 inches). The hoop itself has a diameter of 18 inches. In other words, one circle is quite a bit bigger than the other. Now, imagine the trajectory of the standard free throw. It starts at the player's hand and goes in a low-curve arc towards the basket. Imagine the hoop from the ball's perspective. It is entering at a very slight angle. Instead of aiming for a circle with a 8.60 inch margin for error, it is aiming for an ellipse with a much narrower margin. A granny shot, however, goes up and down at an arc with a much higher curve. It goes more down than forward, making our basketball-cam see more circle than ellipse. The greater margin consistantly grants greater accuracy on free throws.
Note: The highest margin of error would be from an extremely high arc. However, with the more power applied, accuracy would suffer, undermining the advantage.

• Spin: Much like the English on a pool ball, the spin on a basketball affects how it will enter the basket. The common overhead free throw puts a backspin on the ball; the granny shot puts frontspin on it. Imagine the ball hitting the front of the hoop. With backspin, it hits, bounces back, and misses. With frontspin, however, it goes forward--into the basket! If it hits the backboard, the arc of descent will cause it to drop directly into the basket after impact. The arc and English of the free throw will bounce the ball back to you. No point. You've let down the team.
• Muscle: For anyone who has ever lived a non-sedentary lifestyle, it is common knowledge that the biceps (which flex the arm) are stronger than the triceps (which straighten it). With the normal free throw, the arms are straightened while shooting. It requires more force, which results in less detail and subtlety in those ever-sensitive motor neurons. With the granny shot, you are using your strongest arm muscle. Actually getting the ball to the hoop is not a concern of those pythons. That leaves you to concentrate on more important things, like actually scoring a point.
• Control: Almost every professional basketball player shoots in the classic style. One hand behind the ball, one hand steadying it, over the head. To represent why this is inefficient, try to balance a golfball on your index finger, while using your other index finger to steady it. Then try to balance it while holding it with both fingers. It is much easier to control the ball when both hands are on it. Control means points.
• Sight: A lot of things can go wrong while trying to make a basket. Having the ball in your line of sight can really help your shot. You can see the ball from start to finish. Any minor adjustments can be made, resulting in that precious free throw.
The granny shot should not normally be used in regular play, because people will have their arms up and attempting to block your shot. The jump shot gets over these obstacles--the granny shot is a poor idea in this case.

Now, some people may offer the repartee of “Well if it’s so cool, why isn’t EVERYONE doing it?” Well, basketball is a spectator sport, particularly in the United States. The sportsmen are showmen as well. The granny shot is associated with children and old people. It’s a blow to their pride to use it. However, there have been actual NBA players to use the granny shot. As a matter of fact, former record holder Rick Barry, who retired with a .900 free throw percentage using what NBA.com described as his “odd, outdated underhand style.” There was even a time when he missed only 9 free throws in an entire season. He is ranked 15th top scorer of the NBA and 6th of the ABA. Those are some impressive numbers. It’s all about the physics.

BIBLIOGRAPHY
Rist, Curtis. DISCOVER MAGAZINE “The Physics of Foul Shots: Underhanded Achievement”
NBA.com. NBA Legends http://www.nba.com/history/barry_bio.html?_requestid=7052