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in a way i wonder if this is good for yao. Maybe he won't be under so much pressure by china officials that he will be retiring
Agreed... One of my favourite NBA players
in a way i wonder if this is good for yao. Maybe he won't be under so much pressure by china officials that he will be retiring
Class post by EricB. I couldn't say it any better and since he shared my sentiments so precisely, I might as well quote him.
It should be guys like Garnett or Kobe that have this kinda luck.
nice post Indazone. I'm really sorry to hear about Yao. As you can tell, we love and respect the out of Yao. He's a class person and a fantastic baller to boot. And Houston is a good franchise that I cheer for.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.
Second longest, and still just a fraction of an 82 game season.
I was concerned about this team next season but with no Yao ...sad
Too bad for the Rockets and Yao.
another counterexample: Mark Eaton -- 7 foot 4, 290, played 10 good seasons and a couple with knee/back injuries, never a stress fracture or foot problems. He is still the record holder in blocks-per-game and is behind only Kareem in career blocks.
It's disheartening to hear about that. Get well Yao, take the time needed to heal & return at 100%.
I fill sorry for the guy he is such a great ambasador for basketball and for China. But just look what playing in the summers does to players we only have to look at Manu so I fill your pain Rocket fans.
I hope that China will leave him alone and he can heal up and play for the 2011 season if not that would be a sad ending. He kinda reminds me of big Dave....
One question is how long is his contract and what do you all think Houston can or should do?
Sad for Yao, and for the league as a whole. It's a real bummer to see one of the leagues biggest stars (consider the astronomical number of Chinese fans blown away by these reports), and seemingly nicest guys go down like this. The worst part is, even if he were able to defy the odds and return from this injury, one has to wonder around what corner the next one would be lurking.
Best wishes to him, and the Rockets franchise. While some might find it nice to have another contender off the list, I never like to see it in this fashion.
Like Manut Bol, maybe there is just a point where the body is just...too big for the rigors of the sport.
Makes Dikembe Mutombo seem like a freak of nature for his durability, considering he was only running a few inches shorter.
I would strongly be against this, because of it throwing records off. With more international play, the solution would be to make the nba season shorter. Therefore less games played less stress. I just cannot see it being done since less games is less money.
Carrying the expectations of more than a billion Chinese on his shoulders have finally taken their toll.. really feel bad for Yao but only contempt for the Chinese Sports Authorities who never allowed him to fully heal when his body showed signs of breaking down years ago.
Sucks for Yao...
I can't agree with the Spurs fans who think Yao going out means that the Spursdon't have to worry about the Rockets.
1. Without any picks, they went out with cash and got some pretty good picks. Morry as GM has really done a great job for them after leaving the Spurs.
2. They are gonna have to go out and buy a center free agent which is gonna drive the market price up for guys like Amare, Sheed, etc. They'll be desperate and won't care how much they have to spend or trade.
3. The talk on Houston radio is all about how they can drop the salary of T-Mac (22,000,000) and take a medical exception worth about $10,000,000 on Yao.
4. They are going to have to revamp the team under pressure and that is going to shake up the entire player market throughout the league.
such a shame...
TP
Manu
The Lakers
We must hire their medical staff
Those picks are both wing players. Houston didn't have a legit backup for Yao last season, and now without Yao they're one of the weakest front courts in the league. Scola, nice player, not a difference maker. Landry, nice player, not a difference maker. Hayes, a joke.
They're going to have the same MLE to offer that everyone else has. Except Houston's mle belongs to a team that won't be a contender in 09-10.2. They are gonna have to go out and buy a center free agent which is gonna drive the market price up for guys like Amare, Sheed, etc. They'll be desperate and won't care how much they have to spend or trade.
Yao needs to be out a full calendar year before they can even apply for that exception. And even if they do get it, it's not going to be anything close to $10 mil. It's the lesser of 50% of the player's salary, or the average salary. Average salary being equal to the mle.3. The talk on Houston radio is all about how they can drop the salary of T-Mac (22,000,000) and take a medical exception worth about $10,000,000 on Yao.
If Houston wants to shake up the market they're better off mailing in 09-10 and trying to land someone big in the 2010 free agent market.4. They are going to have to revamp the team under pressure and that is going to shake up the entire player market throughout the league.
Wow..people were sure this guy would get at least one ring when he was starting out. It's really sad if this is true. Not only sad, but ironic and infuriating. Ironic because te injured himself in his most outstanding gutsy playoff performance, one that garnered him a load of respect, including mine. And infuriating because wasn't it kobe that ran straight into him and ed up his foot?
Yao is too heavy for his foot
Who knows when Yao got that stress fracture? It could have been well before the playoffs and I think it was seeing as the symptoms Yao has are asymptomatic. He might have aggravated the stress fracture in the playoffs when another guy stepped on his foot (Landry) but he probably already had this break and may have played much of the season with a broken left navicular bone.
Yao's exact problem.
I don't think man was made to be as big a man as he is.
Bill Walton had the same problem and it ended his career unfortunately.
^ it isnt just the weight on the foot, it's the length as well
it sucks to see a genuinely nice guy go out like this.
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