Partner Series

Kobe Bryant and Ray Allen have spoiled us all season, but especially now in the NBA Finals. Their ability to attract defenders, often the best on the court, stop on a dime, rise up with at least one opponent's hand in their face and send the basketball on a perfect trajectory through the hoop has become not only commonplace but expected. If we were to stop and think of the number of variables involved in the perfect jump shot, we might appreciate just how rare this skill has become.

Now, Dutch researchers have done the homework for us, and their results reveal some of the visual clues to the science of shooting hoops .

Imagine yourself on the court, basketball in hand, staring at the basket. In our three-dimensional world, there are three axes that locate the hoop:

  • X-axis is our relative distance to the basket.
  • Y-axis is the basket's location in a right to left orientation.
  • Z-axis is the hoop's vertical position. Since basketball hoops are at a fixed height, we don't have to worry about that variable.

Other research has shown that players take care of the y-axis by aligning the midline of their bodies with the basket rather early in the shooting process. That leaves the x-axis or computing the distance to the basket. That is where Rita Ferraz de Oliveira, Raoul Oudejans and Peter Beek, all faculty at MOVE, the human movement research institute of VU University Amsterdam, focused their research. The results were published in the Journal of Experimental Psychology.

They first defined the x-axis as a vector with two variables, the magnitude (the distance between you and the basket) and the angle of elevation (the relative height of the basket compared to where you are standing.) As you move closer to the basket, the magnitude decreases while the angle increases. Does your brain rely solely on those two variables and then do some crazy calculation in less than a second to tell you the right aim and amount of force to put on the ball?

The challenge to narrowing down exactly what information is used is the amazing amount of visual data during a basketball game. Players and fans are moving; angles and distances are constantly changing.

To narrow down the variables to just test magnitude and angle of elevation, the researchers designed three different lighting scenarios for the volunteer players to test their shooting. First, in an empty gym they offered full lighting to see the standard backboard and hoop. Next, they put a single small illuminated dot on the front of the rim and darkened the gym so that only the dot was visible. This effectively eliminated all other variables except for the pure magnitude and angle of elevation. Finally, as a control, all lights were put out and shooters were shooting "blind" in the dark. Oh, by the way, unknown to the shooters, the basket was moved either closer or further away. The players would have their back to the basket, then turn around and shoot with one fluid motion giving them minimal time to adjust their shot.

In the first experiment, shooters did just as well in the "one-dot" environment as the fully lighted court. This agreed with the idea that figuring out the x-axis was the key to good aim. Next, to determine which variable, magnitude or angle, is more important, the researchers had players keep their heads very still and tested them first using both eyes, then with one eye covered. They thought that by not allowing convergence, the ability of our two eyes to form a triangle with the target, would test how much our brain used magnitude versus angle of elevation. As expected, the results were the same for either one eye or two eyes, eliminating any advantage that convergence provides and lessening the importance of raw distance measurement as a factor. Finally, the angle of elevation needed to be tested. Assuming that players had learned to calibrate distance knowing that the height of the basket never changes, the last experiment did just that by changing the height of the basket without telling the shooters.

Sure enough, when the basket was raised, shooters undershot the hoop, thinking it was closer from the higher angle of elevation. When the basket was lowered, they overshot the rim because their brain computed the distance incorrectly given the lower angle.

This is similar to studies of baseball outfielders who use the angle of the rise of the ball to determine where to run to catch it. The bottom line for Kobe and Ray are that they apparently use the angle of elevation as the deciding factor in aiming their shots. Having solved that mystery, now we can just get back to enjoying the game.

Dan Peterson writes about sports science at Sports Are 80 Percent Mental.