What Makes The Perfect Free Throw?

 

If you wonder why the sudden interest in math and basketball, it is the season at my school.  Students are participating in regionals and state so there is a lot of interest in it.  I see students practicing their free throw shots all the time because that one shot can make the team pull ahead just enough to win the game.  Of course, there are folks out there who explored the idea that there is a perfect form to get a free throw and used mathematics to find it. 

One of the biggest things is that the fate of the attempt for a free throw is already set by the time the ball leaves a players hands. About 20 years ago, a couple of mathematicians created a computer  program which was able to imitate all the different trajectories of basketballs shot. They spoke with all the coaches and assistant coaches at their college to see what question they wanted answered.  The number one question was "What is the best free-throw?"

If you stop to think about it, basketball is made up of a bunch of trajectories because every time a ball is thrown, it follows the path of a parabola and the path is a trajectory.  The trajectory can suddenly change when the ball hits the rim or backboard and the program took this into account.

The mathematicians figured out a way to change trajectories into statistical probabilities.  They even included a trajectory that went through every physical obstacle except for one so they could see what happened.  Due to the question, they studied the free throw shot first since that was what everyone wanted to know. They studied this question for five years and made some conclusions.

First off, they discovered that players with the same consistency usually made the shot with a 75 to 90% accuracy.  Those who reached the 90% accuracy rate had the best trajectories. Since the fate was decided by the time the ball left the players hands, the mathematicians looked at the perfect "launch" conditions.  The shot is effected by factors such as the distance above the floor, the backspin rate, the launch speed, and the launch angle.

They discovered that a 3 hertz rate for the back spin was ideal because the ball takes one second to read the basket, and a 3 hertz rate allows for 3 spins between the player and the basket. If the ball is released at a point 7 feet above the ground, the ball needs to be launched at a 52 degree angle because it can be off one angle either way and still make the basket.  The launch speed is the hardest one to control.  If the ball is too slow it won't make it and if it's too fast, it will go past.  It is important for the shooter to know how their body moves so they can be consistent with their launch speed. They also discovered that the higher a player is from the ground, the better chance they have of making the free throw. 

The last and most surprising condition was the aim point of the free throw.  The best results come from the player aiming for the back rim because it is more forgiving than the front of the rim.  So over all, players need to aim for the back of the rim, launch the ball at around a 52 degree angle as high above the ground as possible, and launch it with a smooth motion. 

So if you have a student who needs a bit of help improving their free throw, tell them all about this and the research that helped them get there.  Let me know what you think, I'd love to hear.  Have a great day.