Joel Embiid is an NBA all-star. He relishes banging his 7-foot body against 76ers opponents, and averages 24 points and 11 rebounds per game.
"That's what I live for, being physical," he said after a Jan. 15 win over the Toronto Raptors.
Yet, wary of his injury record, and of the litany of fractures and sprains suffered by former NBA big men such as Yao Ming and Bill Walton, the Sixers continue to restrict Embiid's playing time. The star center has missed some games this year due to back tightness, and sits out for others that are scheduled on consecutive nights, due to a surgically repaired knee. All told, he has appeared in three-quarters of the team's contests, and is on the court for an average of 31 out of 48 minutes in each.
Too cautious? Probably not, experts in orthopedics and biomechanics say. The conventional wisdom — that larger bodies are at greater risk of injury — is correct.
There are exceptions to the rule, and Embiid, 23, a superb physical specimen who once protested, "I'm not made of glass," may well enjoy a long and fruitful career. But he would be wise to play it safe for three main reasons.
Weight. Embiid's weight is listed at 260 pounds — a big load for his muscles, bones, and joints to support.
True, his muscles are larger than those of most smaller people. But taller people run into a core principle of physiology, said Chicago orthopedic surgeon Benjamin Domb.
The strength of a person's muscles is linked to their cross-sectional area — for example, the circle of tissue you would get if you imagine cutting through someone's biceps. The bigger that circle, the stronger the muscle. A person's weight, on the other hand, is roughly proportional to body volume.
"It's the ratio of size to strength," said Domb, a sports medicine specialist. "As we get larger, they don't scale together."
In other words, the increased muscle strength in a taller person does not keep pace with the increase in weight. For someone in supreme physical shape, such as Embiid, it is hard to make a direct comparison, as muscle weighs more than fat, but the rule holds true. The Sixers center is 21 percent taller than the typical 5-foot-9, 187-pound American male in his 20s, but he weighs 39 percent more.
"Somebody like Joel Embiid could probably lift a bigger boulder than you can or I can," said Domb, a 6-7 former basketball player at Princeton University, "but his strength is not necessarily proportional to his size and weight."
This is OK for everyday activity, but it can be an issue with the extreme loads of sports — when joints and bones are repeatedly asked to come to a sudden stop, taxing them to the breaking point.
And there is less margin for error than one might like, said Columbia University applied physics professor Irving P. Herman, author of Physics of the Human Body. If a barefoot person jumps from a height of just 1 meter, or 3.3 feet, landing stiff-legged on one leg, that generates enough force to break the tibia, Herman said.
Normally, people cushion their landings by flexing the muscles and wearing shoes. But jumping in a basketball game is often not normal.
"They are jumping against massive people," Herman said. "And they're at funny angles."
One especially weak link in the body comes as no surprise: the Achilles tendon. When a person is running, the cross section of that narrow band of tissue feels a force roughly seven times body weight — equivalent to half the amount of stress needed to snap the joint, Herman said. Embiid's Achilles is probably bigger than average, but again, he is a lot heavier.
Repeated loads below the breaking point can lead to micro-tears — which, when they heal, are part of the body's normal process of building strength, said Paul DeVita, a professor of kinesiology at East Carolina University. But if the body does not get a chance to heal, that spells trouble.
"If the stresses occur a little more often than the healing, the stress catches up," said DeVita, past president of the American Society of Biomechanics. "Eventually micro-stresses turn into fracture."
Center of gravity. As common sense suggests, a taller person is likely easier to knock over than a shorter person. The key is the center of gravity — the "average" point at which body weight is distributed.
This measurement differs somewhat depending on body type — lower for a pear-shaped person, and likely higher for a weightlifter with large arm and shoulder muscles. But on average, studies have found the center of gravity for a young, physically active man is about 57 percent of his height, and for a woman 55 percent of height.
For Embiid, that point would be 4 feet off the ground. For a typical 5-9 American man, the center of gravity is about 9 inches lower — just 3 feet, 3 inches off the ground.
Again, Embiid is a lot stronger and heavier than that typical guy. But when an opponent bangs into the Sixers center, the laws of physics suggest that he needs to be on guard. And when he does fall, he is starting from a higher position — meaning that generally, he lands with a bigger thud than a shorter person.
Pro tip: As Embiid and his court mates are well aware, they can lower their centers of gravity by crouching, a common tactic for NBA players as they muscle their way into position beneath the hoop.
Torque. Embiid has long limbs, which enable him to wreak havoc on the court, swatting basketballs away from the rim and grabbing rebounds. When drafted by the Sixers in 2014, his wingspan — the distance from outstretched fingertip to opposite fingertip — was measured at a staggering 7 feet, 5 inches.
But when force is applied to one end of his arms or legs, his joints experience a much higher degree of torque than those of normal-size people. It's the same principle that children discover on a playground teeter-totter: the farther out they sit, the greater load they can apply. Embiid's long legs are in effect like long teeter-totters, exerting greater loads on his hips and ankles.
Likewise, his long arms mean more torque on his shoulders — just like it is easier to carry a bag of groceries close to the chest than if you hold it farther out.
Imagine two people who both weigh 200 pounds, but one is taller, said East Carolina's DeVita.
"If they both squat down in the same position, the taller person will probably have more load on the joints," DeVita said.
What do the numbers show? A review of 17 NBA seasons, published in 2010 in the journal Sports Health, did not find a statistically significant relationship between player injury and either height or weight. But Domb, one of the authors, said the evidence was nevertheless suggestive — with the graphs showing spikes in the injury rates for the tallest and heaviest players. The most common orthopedic injuries were lateral ankle sprains and knee inflammation.
In a more recent analysis spanning 2000 through 2014, the number-crunchers at fivethirtyeight.com found clear evidence that taller players spent more time on the bench. Among those drafted in the annual NBA lottery, those measuring 6-9 and above missed 17.9 percent of their games, while those 6-8 and shorter missed just 13.5 percent.
The tallest players — those measuring at least 7 feet, like Embiid — missed 23.5 percent of games. Yet some do just fine. Take 7-foot-1 Wilt Chamberlain, who still holds the all-time record in stamina, at more than 45 minutes per game.