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I feel bad for Yao, the team and the fans. I don't like to see any player go out with injury. Hope he can make a full recovery and play again.
that sucks for Yao, hope he gets better and plays sometime next season. hes a good player and seems like a good person overall.
i blame bad luck, his massive frame, and the chinese govt. forcing him to play almost every summer for the natl team.
I feel bad for Yao, the team and the fans. I don't like to see any player go out with injury. Hope he can make a full recovery and play again.
Yup...if Yao is out, go for the tank and start fresh.
Yao Ming and the froghopper
2009 MAY 12
tags: basketball analytics, froghopper, scaling, Yao Ming
by gravityandlevity
Just a few days after a tough and inspiring performance against the Lakers, Yao Ming is injured again, with a stress fracture in his foot. Lakers coach Phil Jackson commented on Yao’s fragility by saying “A person in physics once told me if man was 60 feet tall, the first step he’d take, he’d completely crumble … Gravity’s a .”
But is it true? Certainly larger people have heavier bodies, but they also have thicker bones and larger muscles. So why are tall people more prone to injury? This post examines that question using one of the simplest and most powerful ideas in physics: the scaling argument. I will also try to make a prediction for the “injury prone-ness” of a person as a function of their height.
Before I get to Yao Ming, allow me to discuss a simple example using what is arguably the best athlete in the animal kingdom: the froghopper. The froghopper is a little insect, barely half a centimeter long, but it has about a 27″ vertical jump. That’s about 140 times its own body length, so in a certain sense it would be like me jumping 840 vertical feet. Pretty impressive. But if we put the froghopper in an enlarging ray, and blew it up 365 times so that it was the same size as me, would it really be able to jump 840 feet?
The answer is no. That’s because an object’s weight is proportional to its body volume, which is proportional to the cube of its size. So making the froghopper 365 times larger would make it million times heavier. The froghopper’s ability to jump depends on the volume of its muscles, which also increase by times after it gets put through the enlarging ray. So the ability of the froghopper to jump remains the same: it gets a lot stronger, but also proportionally heavier. Therefore, a 6-foot froghopper could jump the same height as a half-centimer froghopper: 27 inches. It just looks much less impressive.
Now let’s think about Yao Ming, who is sort of like a normal person put through an enlarging ray. The propensity for one of Yao’s bones to fracture depends on the stress he puts on them. Stress can be defined as weight divided by cross-sectional area. So if weight depends on volume (size^3) and the cross-sectional area of his poor foot bones depends on size^2, then the stress grows as (volume / area) = (size^3 / size^2), or in other words, the stress increases directly with size. You can think of it this way: by virtue of his great height, Yao’s bones are about 1.7 times thicker than the average person’s, but he weighs about 2.2 times more. Thus, his bones have a harder time than yours do.
So how much more likely is he to get injured than the average man (height 5′8″) ? Well, there are people out there who break bones for a living and have addressed this very question. They found that the frequency of stress fracture in bone grows as the stress it is under to the power 0.06. Putting together their conclusions, along with the observation that Yao gets some kind of stress fracture every year or so, we can estimate how many years it would take for athletes of various heights to come down with a stress fracture:
Of course, this chart is just a general prediction and is not meant to be completely accurate. Some people will be hardier than others, and those people tend to be athletes (no stress fractures yet for a 7′1″ Shaquille O’Neal). But the shape is important. It suggests that if you’re under 6 feet tall (hooray, most of the world!) there is really not much risk of a stress fracture. You can have a 20-year career as an athlete without too much worry. But for those above 7 feet tall, your chance of a fracture is about 10 times greater than for your 6-foot brethren.
So finally, was Phil Jackson right about the collapse of a 60 foot man? Actually, by my estimate, he was quite conservative. As far as I can tell, a 16′3″ man would fracture his tibia the first time he took a step.
There is a sad and interesting footnote to this story. The depressing far-right side of the graph above corresponds to the 8′11″ Robert Wadlow, the tallest man in recorded history who suffered from an overactive pituitary gland. By his late teens he was already incapable of walking without leg braces, and he continued to grow until his death at age 22.
What the Rockets have got to do assuming he can recover from this latest injury is severely limit his playing time and at the same time, they have got to limit his salary so they can go sign another impact center. Looking at this graph, he will be injury prone for his entire career.
+1Yao has been one of my favorite non-Spur players for a few years now. A good guy like this def. deserves better. sorry to hear this, houston and i hope it all works out whichever way your team decides to go. Get better soon Yao!
Well Shawn Bradley was injury prone too but at least he didn't have to play as many minutes as Yao.
This sucks.
Yao is much better than Shawn but they are nearly the same height that's all.
I wouldn't count this team out if I were you guys. They have shown a lot of fight on the court without T-Mac or Yao. When Yao went down against the Lakers everyone expected them to fold, yet they still put up a much better fight than many other teams could have injury free.
tough luck for both Yao and Hoston. HOpe Yao get better soon
It is the curse of Tracy McGrady. Trade his sorry butt and Yao's foot will magically heal.
One thing to put up some fight for a couple goames. Another to sustain that over an 82 game season.
It is such a damn shame. Hope it isn't as bad as they are making it sound.
Just awful news. His body is just too much for those ankles. Does not sound promising. He is young though, so maybe he could be gtg the following year. But a reinjury or new injury is inevitable. Sorry Yao. At least half the world adores you, that's not so bad.
Or over the longest winning streak in NBA history?
Make that second longest (had to check the stats). Regardless it spanned more than a quarter of the season, just for a little perspective...
Tough luck for the Rockets. Hopefully he can play soon.
Yao's a good guy and hard worker. It's really too bad to see him become Rick Smits two! I hope he gets well.
Note to Manu: See what all that international play every summer does to a career!
That sucks for Yao
I hope he can get better soon
Tanking is less of a viable option when the overall roster of good players might still be good enough to make the playoffs as a lower seed if McGrady and Artest come back.
Being mediocre is not where you want to be though because you have no chance of getting the trophy if you are Houston. Yao deserves better.
I think it speaks to what kind of person Yao is that everybody is pulling for him. I hope he can continue his career because he was starting to get really good. Lakers might not be kissing the trophy without him going down. Also + for him refusing to go out with injury that one game.
Bummer for Yao (and the Houston fans). He seems to have his heart in the right place, plays hard and has made pretty good strides learning english ect... Im thinking his bone structure just aint cut out for the NBA haul but I hope Im wrong. Hes a clean player and I do hope he gets better.
dam i hate the out of foreign players but yao is one who isnt a pussy
wish him the best
Yao is a good dude and it is deeply unfortunate this happens to him.
Why doesn't this ever happen to Kobe?
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