In this clip, we watch in open-mouthed wonder as 7-foot-6-inch leviathan Yao Ming becomes the property of 5-foot-9-inch Nate Robinson. Yao, whose defender had left him to guard the ball, receives a pass and leaves his feet for what should have been an easy one-foot jumper. But Robinson flies in from the weak side, takes a strong two-footed leap, and smacks the shot out of Yao’s hands (and back into his face) just as he shoots. Yao doubles over and brings his hands to his face, covering not only his injury but his deep sense of shame.
Before analyzing the physics of this maneuver, it’s tempting to assume the following things: Robinson, who gives up 21 inches to Yao, seems to be an immeasurably more talented athlete who plays with more energy and shows more heart. He certainly has a superior vertical leap (measure the height of Robinson’s shoes relative to Yao’s leg in this clip). But Robinson is not just 21 inches shorter than Yao. At 180 pounds, he’s 130 pounds lighter than Yao’s 310. Every time Robinson jumps, he’s moving less weight, and less weight takes less energy.
Just how much less energy? Let’s figure out how Yao’s and Robinson’s vertical leaps would compare if each expended the same amount of energy. The energy of a jump—and hence the work that must go into jumping—is proportional to both the jumper’s weight and how high he gets off the ground. Since we know that Yao weighs 58.1 percent more than Robinson does (180 divided by 310 equals 0.581), we can calculate that Yao’s vertical leap should be only 58.1 percent of Robinson’s.
Although updated numbers are hard to come by, Robinson’s vertical was measured to be 42 inches when he was drafted, and Yao’s as around two feet (a note to the viewer: two-foot vertical not on display in this video). Robinson can jump twice as high as Yao, so we can conclude that Yao would have to work twice as hard to reach the same height.
The lesson: Apply the same amount of energy to a smaller body and that body will jump higher every time. That, and Yao should dunk when he’s a foot away from the basket. —Michael Moyer