# The Math Behind Basketball’s Perfect Pick and Roll

For most New Englanders, the period between December and March is full of anticipation for the holidays (and sometimes a white Christmas) followed by an agonizing post-holiday reality of barren and frigid landscape. Take down the tree, turn on the tube and wait out the weather until spring.

As for your author, this period is like Christmas wrapped in an Easter basket baked inside a turkey painted in autumn colors. That’s because December through March is all about college basketball!

We are five weeks into conference play, and in honor of the most wonderful time of year I am going to try to connect my obsession with basketball and principles of math and science. Bear with me.

The pick and roll is one of the most fundamental offensive plays in basketball, and when properly executed, one of the most effective ways to score. Bleacher Report recently ranked the top 12 Pick and Roll duos and attributed the play’s popularity and prevalence to the fact that it simply works. While I can’t argue with that logic, I can argue with their rankings (Chris Paul and Blake Griffin at number seven? Surely you jest.)

The premise is simple and deadly. A player sets a screen or “pick” on the defender guarding the ball handler, causing the defender to have to get around the big man suddenly in their path. The player who sets the pick can either “roll” to the basket or prepare for a pass from the ball handler. The ball handler, now freed of his defender, can either drive the lane, pass to their “rolling” teammate or pass to the wings. It happens in an instant, is notoriously difficult to defend, and more often than not results in a basket.

The pick and roll uses some principles of geometry and physics. The pick requires the player to stand at an angle and position that effectively blocks off the path of the defender. If he sets the pick too wide, high or low or with his body angled half-sided, the defender may simply slip past him to the ball-handler.

The player also has to plant his feet wide and ensure that when he sets the pick the defender does not move him from his position at all. With a defender moving at a fairly fast velocity chasing down the ball handler, he has to change his momentum and adjust his path to avoid the pick or risk pushing through the screen.

Once the pick is successful, the recipient of the ball, whether it be the ball handler, the screener or another player, has to ensure they use the proper mechanics to shoot the ball and ensure it actually reaches the hoop and goes through the net.

Mechanical engineer Larry Silverberg of North Carolina State University simulated thousands of trajectories using a computer and found that shots from the top of the key, where free throws are attempted, had the highest likelihood of going in with a launch angle of 52 degrees, backspin of three revolutions per second and aiming seven centimeters back from the center of the basket.

And as all this action and movement is going on, kinetic energy is at play between the players hands and the ball they bounce up and down on the court, increasing and reducing the force they use to maneuver the ball and successfully complete passes.

So there you have it, the most basic of basketball’s offensive plays is chock full of math and science! Time for tip-off….