April 29, 2013

Human Biodiversity: Seven-Footers

Here's a fun 2011 Sports Illustrated article by Pablo Torre on retired NBA seven-footers:
An actual accounting of 7-footers, domestic or global, does not exist in any reliable form. National surveys by the Center for Disease Control list no head count or percentile at that height. (Only 5% of adult American males are 6'3" or taller.) "In terms of the growth spectrum, 7 feet is simply extreme," explains endocrinologist Shlomo Melmed, dean of the medical faculty at L.A.'s Cedars-Sinai Medical Center. The term 7-footer is itself a kind of outer limit, a far-off threshold beyond which precise measurement seems superfluous. A 6'4" guard isn't a 6-footer, after all. The curve shaped by the CDC's available statistics, however, does allow one to estimate the number of American men between the ages of 20 and 40 who are 7 feet or taller: fewer than 70 in all. Which indicates, by further extrapolation, that while the probability of, say, an American between 6'6" and 6'8" being an NBA player today stands at a mere 0.07%, it's a staggering 17% for someone 7 feet or taller.

There are a lot of issues with this, but it's not a bad first cut at the question. 

The article focuses upon iSteve favorite Mark Eaton. I learned an important lesson from him when we were at UCLA in 1981.

68 comments:

Anonymous said...

And that's why if you're a 7 footer and you don't make it into the NBA, people look at you funny.

DR said...

Height in basketball seems to be at least as much an advantage relative to actual athleticism and skill, as weight is in boxing.

Why is it that weight classes are established in boxing to make matchup fair relative to weight, but no such effort is made in basketball.

It's a team sport and a league game, so it's a little more complicated than boxing. It could be as simple as creating separate leagues for for height ranges. Or you could do something like set an aggregate height cap on the players on the court. Or penalize teams who rely too much on height by giving point, time, fouling or other advantages to their opponents.

The fans certainly want to see dunking, the WNBA proves that. But overall oafish monsters like Shaq probably detract from the game for most fans.

Anonymous said...

But overall oafish monsters like Shaq probably detract from the game for most fans.

Shaq, at his prime, was very popular and at the top of endorsement dollars too. They gave him movies!

sf said...

Does this have anything to do with today's story about a gay seven footer (Jason Collins) in the NBA?

Anonymous said...

Mark Eaton is very interesting he didn't play ball until community college at Cypress. He was a wielder someone talk him into going into Basketball.

Rob said...

I remember Nassim Taleb saying in one of his books that the bell curve model doesn't allow you to predict the percentage of exceptionally tall or short people in a population. He uses this as a way of demonstrating the inadequacy of commonly used statistical models to predict economic catastrophes.

Steve Sailer said...

The article looks like it uses the government's NHANES study of sizes, where the 95th percentile was around 6'3" for both whites and blacks, then projects out from there. Of course, you could have fat tails (or thin tails). Also, NBA players can be measured in their shoes and round up, while NHANES are, essentially, barefoot measurements and the subjects probably aren't trying quite as hard to stand up straight as NBA prospects.

But, in general, there aren't a lot of true seven footers. At Rice, the two 6'11" guys on campus were on the basketball team, and at UCLA the two seven footers on campus (out of 35,000 young people) were on the basketball team, and played 18 years in the NBA between them.

Anonymous said...

The fans certainly want to see dunking, the WNBA proves that. But overall oafish monsters like Shaq probably detract from the game for most fans.

You obviously don't know anything about basketball. Lack of dunking is not what makes the WNBA and women's basketball terrible. Basketball is a team sport. Players like Shaq play with 4 other people.

Dave Pinsen said...

"Height in basketball seems to be at least as much an advantage relative to actual athleticism and skill, as weight is in boxing.

Why is it that weight classes are established in boxing to make matchup fair relative to weight, but no such effort is made in basketball."


Among heavyweights in boxing, there can be huge differences in weight and size between boxers. There was a boxer a few years ago named Lance "Mount" Whitaker. Wikipedia doesn't give his weight, but at 6'8", he must have been well over 300lbs. His size was enough to help him rack up wins over mostly mediocre competition, but according to his Wiki page he lost his last notable fight to a 6'2" Dagestani Avar, Sultan Ibragimov.

As for basketball, beyond a certain height (maybe 6'7"?), it's rare to see high levels of athleticism. And there is room for shorter, but fast and skilled players in the back court. E.g., Allen Iverson (5'10", if memory serves, but Wiki has him at 6') was the NBA's leading scorer in multiple years.

Steve Sailer said...

The NBA has always had a circus side show aspect to it. Wilt Chamberlain, who started out with the Harlem Globetrotters, had a hard time taking the NBA seriously, which is one reason he only won two championships while Bill Russell won nine. Wilt felt that his job was less to win than to come up with wacky reasons for people to talk about the NBA. And, you'll notice, today, Wilt is more famous dead than Bill Russell is alive.

jody said...

"I remember Nassim Taleb saying in one of his books that the bell curve model doesn't allow you to predict the percentage of exceptionally tall or short people in a population."

we know that observed IQ out at the high end does not fit the math that well. there are more real, flesh and blood people with super high IQs than the math predicts there would be. when psychologists go out there and start measuring actual people, high end outliers turn out to be more common than the models would estimate.

it's probably the same for height. i don't believe there are only about 70 guys between ages 20 and 40 in the US who are 7 feet tall. there have to be more than that. i've bumped into a few of them randomly in my time on this planet, not even specifically looking for them. if there really were that few 7 footers, the odds of me randomly bumping into 1 of them would be low. but more than 1? really low.

the rough math in the torre article suggests that 7 footers are about 1 in a million. 70 guys between 20 and 40, maybe another 70 guys between 40 and 60, then a few guys over 60 (people this tall tend to die sooner, so only a few old timers at this height). say 150 guys in total, out of 150 million men in total.

are they really that rare? 1 in a million? i doubt that. it's possible. but seems unlikely in my first wild ass guestimate.

Steve Sailer said...

I'm sure that using a normal probability distribution isn't realistic, but it's hard to say which way it's wrong.

The other thing is that a true 7 footer would likely be called at least 7'1" and probably 7'-2" in the NBA, and that's getting pretty rare. Guys who are really 6'-10" but could be called 7 footers are still very rare in normal life, but not unimaginable.

Steve Sailer said...

People who are frequent fliers probably have more experience running into sports starts than I have had. In my experience, though, a true seven footer is startlingly tall. I walked down Rush Street behind Bill Walton once, and he boggled hundreds of people who walked by.

Dennis Dale said...

Re the Eaton lesson, if Hollywood is any indication people still largely view the demographic world as white/black. I was struck watching The Hunger Games, which is set at least 150 years in the future--the urban crowds are a white majority with about twenty percent black sprinkled throughout (and the only biracial person I saw was Lenny Kravitz in sensitive soul man mode--this noble creature will always be with us, thankfully).
Hollywood would appear so insulated they project out into the future North America's demographic composition of about twenty years ago.
Idiocracy was striking in that the ethnic mix, with lots of what I think of as PIRTs (persons of indeterminate racial type) running around. This must have only served to further unsettle the Right Thinkers who were paying attention.

jody said...

"Height in basketball seems to be at least as much an advantage relative to actual athleticism and skill, as weight is in boxing."

weight is more useful in wrestling than in boxing, but yes height in basketball is similar to weight in boxing, up to a point. there is a limit in boxing and kickboxing, akin to the eddington limit for stars, where each additional pound is more detrimental than helpful. boxing and kickboxing fans sometimes debate where this is, but there is no general consensus. 240 pounds? 260 pounds? 280 pounds? this limit actually has a name but i can't remember it right now. it's why some 350 pound guy will never come in and clobber everybody. at that size he'll be too slow and will get TKO'd by some 250 pound guy.

it has also gone up, as athletes have gotten taller, heavier, and more athletic. the biggest boxer to ever hold a major belt was nikolai valuev, who was 7 feet tall and 300 pounds, and held the WBA belt for a couple years. he was definitely not the best active boxer during his career, and would have been TKO'd easily by either klitschko brother, who he deliberately avoided. but he boxed respectably against a couple other decent opponents in the more normal size range of 6-2 to 6-4 and 220 to 240 pounds.

boxing does not have an upper weight limit but wrestling does. the limit is 285 in NCAA wrestling, 265 in FILA wrestling. i'm not sure when the FILA limit was introduced, sometime in the 1980s. it also used to be 285, which is probably where the NCAA limit originated, but was reduced to 265 in the 2000s.

US MMA rules also use the 265 limit, but this is not an international limit. some MMA rules outside the US have no upper limit the same as boxing. technically speaking, US MMA allows for a class over 265, but no commission uses it.

i don't know what precipitated an upper limit in wrestling, but i know the first talks about it where after the 1972 olympic games when american chris taylor, who was 6-5 and 400 pounds, won mostly by simply laying on guys.

the best huge kickboxer ever is semmy schilt, who is 6-11 and 290. he won the K-1 grand prix 4 times, and the organizers kept changing the rules every year to try to disadvantage him so he didn't smash through the tournament and win easily. very big guys were competitive with him, guys in the 6-4 to 6-6 range and 250 pounds, but he usually beat them. kickboxers smaller than that were never competitive against him.

that eddington limit weight in boxing, has it's analogue in basketball, somewhere around 6-6 or 6-7. beyond that height, each additional inch is more detrimental than helpful to coordination and athleticism. this is why some guy who is 7-5 is never going to come in and clobber everybody in the league. guys who are 6-11 will blow him away.

Cail Corishev said...

There have been "normal-size guy" pro basketball leagues with a height maximum, usually set at 6' or 6'4". They've never lasted very long or grown beyond fairly small regions. Height isn't just about dunking; it's about all the other stuff you can do with the ball when you're that close to the rim, not to mention the large hands guys that tall usually have which let them palm the ball and have extra control over it.

The 7'-plus guys may tend to be somewhat gawky, but there are enough nimble 6'9" guys who can handle the ball and shoot just as well as any 6-footer, plus dunk the ball effortlessly.

Futurama did the definitive bit on this. The crew has been captured by giant Amazon cave-women who worship a female computer (Femputer):

FEMPUTER: Hmm. Perhaps men are not as evil as Femputer thinks.
THOG: But they make fun women's basketball!
FEMPUTER: What?! Did you explain how the women's good fundamentals make up for their inability to dunk?
ORNIK: Yes. They still laugh.
FEMPUTER: The men must die!

jody said...

"Why is it that weight classes are established in boxing to make matchup fair relative to weight, but no such effort is made in basketball."

all combat sports have weight classes, and this is to increase participation rate. team sports have positions. this allows for different body types on the same team, all contributing at once. there are no positions in wrestling, boxing, kickboxing, judo, MMA. it's just man against man.

personally i only rate guys in the highest two classes in any combat sport. that is to say i totally discount any guys smaller than 200 pounds or so for purposes of who represents the sport's pinnacle.

weight classes increase participation by protecting small weak men from getting run over by bigger stronger men. the best midget at any particular sport is not really that good at all, and would easily be beat by hundreds of guys in his own sport, and some guys not even in his sport too.

saying the best guy in boxing is actually some 150 pound shrimp would be like saying the best basketball player is some 5-5 midget who was too small for the NBA, but he coulda dominated the 5-8 and under league more thoroughly than lebron james dominates the normal person league...if such a league existed.

well yeah...but he's still 5-5 and would be dominated by guys who can't even make it to the end of the bench in the NBDL. doesn't really matter what kind of handles and crossover he has. he can go play in the philippines league.

jody said...

OT steve but some 17 year old japanese kid just ran 100 meters in 10.01 +0.9

http://www.youtube.com/watch?v=Iy-BuDc1_wo

The Anti-Gnostic said...

I once loaded some appliances into 7 footer Kevin Willis's Mercedes during a job with a retailer over Christmas. Seven feet is an incredible height and quite awe-inspiring in combination with an athlete's musculature, even with Willis who had to work very hard to keep his mass up.

Anonymous said...

Well, the unfair advantage in height is made up for somewhat by the fact that there seems to be an inverse correlation between height and coordination. Give your typical six-foot man the coordination of an average NBA seven-footer and he wouldn't even make the junior high squad as a bench-warmer.

Gene Berman said...

jody:

I believe your 1980 guess for the end of an unlimited collegiate wrestling weight class is pretty accurate. That very year, I went to see the NCAA Div 1 tournament
(held at the Meadowlands in NJ).

The heavyweight winner was a guy--really huge--named Tab Thacker, (whom I happened to watch in several prelim bouts as well as in the finals). And, although I thought his effort and performance creditable, given his enormous mass, I was unprepared for the downright hostility his great size advantage seeed to arouse in the audience. He did "lean" on his opponent quite a bit (after all, it's smart wrestling to make an opponent carry more than his own weight) but I thought his effort (again,--given his immense size) at a few recognizable "moves" and holds worthy of calling what he was doing, "wrestling." But it seemed the weight limit came into existence shortly afterward.

I don't follow the sport very closely--been to "nationals" only 3times (Meadowlands, Omaha, most recently in Philly)--but live in a small NJ town that's really tuned to its (especially at high school level); a core group--about a dozen--go every year, no matter where.

Cail Corishev said...

Give your typical six-foot man the coordination of an average NBA seven-footer and he wouldn't even make the junior high squad as a bench-warmer.

Yes, height is simply a necessity at that level. When I was in high school, I was a big Larry Bird fan and patterned my game after his. I certainly don't claim to be as talented as he was, but I had a similar story: lots of shooting at a homemade backboard in all weather year-round, and in high school I got to be a very good outside shooter and set my school's record for free-throw percentage. Like Bird, I wasn't "athletic," but could nail basket after basket from the baseline corners and had a pretty good fade-away too.

But I was 5'9" and built like Charles Barkley. Had I been a scrappy guard at 5'9", I might have gotten some interest, but a 5'9" power forward? No way. Had I been 6'4", I probably would have gotten some small college interest, as a friend of mine did who wasn't any better than me, just several inches taller. Had I been 6'9", I probably could have made the pros, maybe even gotten some decent playing time. But at 5'9", none of that was ever a consideration, so I just played for fun and then went on with life.

You have to be tall to play at the higher levels -- and then also talented.

Anonymous said...

DR, you know so much about so many topics, but basketball doesn't appear to be your angle. Shaq was never, by the standards of the center position, an oaf. He was more athletic and had better coordination than all of the guys discussed yesterday - Erick Dampier, Shawn Bradley, the Collins brothers. I can think of plenty of other guys 6'11" or taller who were far clumsier and slower than Shaq: Ilgauskas, Fat Eddy Curry, Eric Montross, Manute Bol. Even Yao Ming, who was relatively coordinated for a 7'5" guy, would lose a race to Shaq every time.

Shaquille was basically just seen as sort of an oaf because (1) he had giant hands and facial features, making him seem like a cartoon character, and (2) he was horrible at shooting free throws, and looked awful trying, so it mad him seem like this oversized fish out of water.

If we had a 3-point shooting contest between Shaq and everyone reading this comment thread (this being a skill that has little to do with height, that's all about fine motor skills, hand-eye coordination, and muscle memory), my money's on Shaq.

Anonymous said...

Robert Parish used to frequent the same supermarket and Chinese restaurant as my ex and I, and it's amazing how imposing 7-footers are. In the winter the owner of the restaurant used to bring Parrish his coat, which was about 6 feet long. His wife at the time was only about 5'5".

Bill Russell is less renowned than Wilt because that's the way he wants it. He remains angry in a way that many Sixties black sports stars were (like Jim Brown). Russell is inherently a class act, though, and as the greatest team sports player in history (2 NCAA championships, Olympic Gold medal and 11 NBA titles in 15 years), he feels no need to explain himself to anyone. He was also the quickest big man I ever saw.

Dahlia said...

Steve,
I googled Bill Walton as I'd never heard of him (I'm not a sports person at all)... he had to have been the inspiration for that Michael J. Fox movie from the '80s, "Teen Wolf".

I recently saw a 6'10" man come into a room where I was and he quickly stalled all conversations as the people facing the door stopped talking and began staring and those with their backs to the door began turning around to see what had grabbed everyone's attention. After about five seconds, conversation resumed as if nothing had happened.

candid_observer said...

My limited set of statistics on the proportion of 7 footers who are NBA players is this.

While out in public places (that is, NOT in a sports arena) I've encountered only 2 people who were so remarkably tall -- in the very near neighborhood of 7 feet -- that I was, even at a great distance, amazed at the freak of nature.

When I got closer, I recognized one as Patrick Ewing and the other as Bill Walton.

Steve Sailer said...

Ewing and Walton seem to get around. I've run into both, too. Just huge. I've also seen Wilt, Dennis Rodman, and Horace Grant.

In contrast, the only baseball star I can recall running into was Steve Garvey, who had a movie star look to him. Judging from the number of basketball players I've seen, I've probably walked right by other baseball stars at the airport without noticing them.

candid_observer said...

"Judging from the number of basketball players I've seen, I've probably walked right by other baseball stars at the airport without noticing them."

Yeah, one thing that struck me about Ewing and Walton is that they can't exactly just put on shades and go incognito.

They're like walking billboards for themselves.

Anonymous said...

It's interesting for the tall clubs it is 5'10 for women, but only 6'2 for men. That makes considerably more men eligible than women (assuming average female height is 5'4 and men 5'10 with a similar standard deviation).

pat said...

There is a web site which has pictures of the really tall people. Those who are eight feet tall or more. The consistent feature of those photos is that the tall guys all have canes.

I'm 6'4" and I don't really wish to be any taller. I see Ed China on TV and pity him. He's the 6'7" mechanic on "Wheeler Dealers". He's a brilliant mechanic but he can't drive many of the cars he works on. He can barely get in them.

Auto makers design their products, I'm told, for the 99th man. If you are the 99.99th man you won't fit.

About two years ago I pulled my Achilles Tendon and it refused to heal. My doctor suggested I wear some heel lifts. I ordered several different styles over the Net including a pair of real elevator lifts designed for short guys. They were advertised on the Celebrity Heights web site.

I only wore them outside once. They made me 6'6" or 6'7". It felt great. I towered. Alas they racked my back out. I developed compassion for Robert Downey and George Clooney who have to wear these things every day.

I had a moment like your moment when you saw Mark Eaton live. One fine day a while back I saw Willie Brown and Nate Thurmond walking side by side in front of City Hall in San Francisco. They were both dressed identically (or so it seemed) in elegant if slightly flashy suits. They looked exactly alike except for size. They were well aware of the impression they made.

Albertosaurus


cmcoct said...

If a true 7 footer is startlingly tall, wait 'til you see someone 7'4". I 've seen three up close: Ralph Sampson, just after UNC knocked his Virginia team in the '81 NCAA tourney, and Mike and Jim Lanier, world's tallest twins. Mindblowing.
The decline of 7 footers in the NBA is due, IMHO, to the increased athleticism and jumping ability of today's players. 6'2 college kids are routinely two feet above the rim. To me, that's the real change in basketball - more kids can fly. 40 years ago, the game was almost entirely below the rim. But today, extreme height provides less return on the court than it once did.

The Anti-Gnostic said...

In contrast, the only baseball star I can recall running into was Steve Garvey, who had a movie star look to him. Judging from the number of basketball players I've seen, I've probably walked right by other baseball stars at the airport without noticing them.

And NFL quarterbacks except you see so much of their faces on camera they are instantly recognizable. Roger Staubach, Tom Brady, Eli Manning. I'm told Matt Ryan looks like a club-tennis pro off the field.

Jeff George was a beanpole, and I always wondered how he made it out of the league without somebody deliberately pile-driving him and to hell with the fine--and that's just the assistant coaches. But, he was six-four and had good strength in his upper and lower extremities, apparently.

Anonymous said...

"we know that observed IQ out at the high end does not fit the math that well. there are more real, flesh and blood people with super high IQs than the math predicts there would be. when psychologists go out there and start measuring actual people, high end outliers turn out to be more common than the models would estimate."

might be due to the fact that more people are lost from the extreme left end of the bell curve. Bell curve predicts equality on both sides.
La Griffe's posting career rests on such assumptions.

http://andrewgelman.com/2008/08/03/the_mythical_ga/

Anonymous said...

Anyone who follows college basketball knows there are lots and lots of seven footers who never make the NBA. You gotta be a player to even come close and a lot of these stiffs look quite good against anything other than NBA competition.

On the other hand, it's quite well known that 7 feet tall in the NBA usually means 6'10 or 6'9. Exceptions are 7'2 athletic players like Garnett who insist on being billed at 6'11 for ego reasons.

The Legendary Linda said...



Why is it that weight classes are established in boxing to make matchup fair relative to weight, but no such effort is made in basketball.


Because society looks down on muscular men and thus eliminates any advantage their extra bulk confers. By contrast society worships tall men and wants them rewarded for their height.

josh said...

I am 7 feet tall and I have never played basketball.The horses,thats where my interest lie: I always wanted to be a jockey.

JeremiahJohnbalaya said...

The game of basketball was not designed around people like Shaq (or Wilt). The game got uglier with Shaq because if his defenders didn't shove him out of the lane all day long, he could have scored at will (again, I assume the same was true of Wilt). I could never blame Shaq for that; the refs allowed guys to basically just continuously foul him.

Similarly, I think the reason that Shaq was so bad at free throws was his freakish size and strength. If he used the correct wrist-flick-follow-through technique, the ball is going to shatter the backboard. So, he had to use the goofy form that he did. (caveat: I have no idea how much better he could have been with more practice, or if he did practice)

Anonymous said...

But I was 5'9" and built like Charles Barkley. Had I been a scrappy guard at 5'9", I might have gotten some interest, but a 5'9" power forward?

5'9" is too short to be a power forward on the high school JV team.

6'1"/6'2" is really the general minimum lower bound for height in the NBA. The shortest guys on the team, the point guards, are often around that height, with some not infrequently taller. A few very exceptional guys are shorter than that and make it to the NBA, very quick, fast, and skilled types like Iverson, Mugsy Bogues (who was 5'3") and Nate Robinson.

The point guards often look very small on TV but they would actually be considered fairly tall in real life. John Stockton and Steve Nash are 6'1"/6'2".

Anonymous said...

A lot of people over 7' are probably pituitary giants i.e. they have a pituitary disorder that makes them tall but hampers their health and athletic ability. People above 6'6" may also be pituitary giants.

DR said...

"DR, you know so much about so many topics, but basketball doesn't appear to be your angle."

Thanks man, I'll admit it. Not the biggest sports fan in the world... Just had an outlandish idea.

The Legendary Linda said...

The bell curve allows you to predict the number of biologically normal extreme height deviants. Biologically normal seven footers are astonishingly rare, but tall genetic mutants with pituitary issues are a separate population on a different bell curve.

Anonymous said...

A couple inches in height can make a huge difference in the NBA. For example you can be a very solid point guard at 6'2", but if you were just 6'4" with roughly the same skills, you could be a dominant point guard. And that's the case with the other positions as well.

Gene Berman said...

Steve:

Other than on TV, I saw Wilt Chamberlain once--when he was in 9th grade. Three of us followed him surreptitiously for a couple blocks, thinking that it was two kids--one on the other's shoulders, in an overcoat.
It was after a high school football game in which our school had played Overbrook (a Philly school). One of our group, more into following HS sports, finally said, "that's Wilt the Stilt"--the first I'd heard the nickname.

Around 1980 of so, a friend (from the same small NJ town) and I were waiting in a line in LA to catch a "red-eye" flight to Philly. My friend said to me "That guy looks awfully familiar," indicating the back of the head of a black guy a couple places forward of us in line. I looked and, without a moment's hesitation, said, "It's Floyd Patterson," to which he replied, "Yeah--that's who I thought it was." And it was. Just how we were both able to recognize him from the back (neither of us had ever seen him "in the flesh") is still mysterious to me.

Anonymous said...

it's about all the other stuff you can do with the ball when you're that close to the rim, not to mention the large hands guys that tall usually have which let them palm the ball and have extra control over it.

A sports goods manufacturer as a promotion had one of their basketballs having an imprint of Shaquille O'Neal's hand on it. You can easily see why he can receive the ball one handed whereas most WNBA players have to use two hands.

Camlost said...

I once played a city league basketball game against former Houston Rocket ballplayer Chuck Nevitt - all 7'6" of him.

He was incredibly awkward looking. I'm a hair under 6 foot and I swear that the bottom of his hips were at my shoulder level. We had a 6-6, 275 lb former semi-pro football player that just bulldozed him right to the top of the key to keep him away from the rim. With his weak legs he couldn't push back.



Camlost said...

I also hung out with 6-11 former NBAer Dale Davis at a strip club for a few hours once upon a time.

Cool dude. Married to a white woman, of course. (and who can blame him)

DPG said...

Another candidate for gay (former) NBA player: Adonal Foyle. Adopted from Caribbean, attended Colgate, writes poetry, philanthropist, political activist. No mention of a wife from a quick google search, even though he's in his late 30s.

DR said...

I remember Nassim Taleb saying in one of his books that the bell curve model doesn't allow you to predict the percentage of exceptionally tall or short people in a population.

The normal distribution of characteristics, like height or IQ, derives from the fact that they are the cumulative expression of a large number of genes.

A simple way to think about it is that for each of the genes that affects height every human carries the tall or short allele version of that gene (extending this to diploid dominant/recessive genes is trivial). For any given gene which allele an individual carries is basically a coin flip (possibly a biased, coin flip since alleles don't all have 50/50 frequency, but this wrinkle is trivial to the model). So height is drawn from the cumulative sum of a bunch of random binomial variables (possibly with varying magnitudes, but again that doesn't affect the model too much).

The normal distribution is the limit of the binomial distribution as N goes to infinity. So for large Ns, binomial distribution behave essentially identical to normal distributions, particularly around the center of the distribution.

As you get into the tails the continuous nature of the normal approximation breaks down. Draws from the very extreme of the binomial distribution only have a small number of Ns in the binomial sum that are or are not activated. At the extreme normal distributions extend out to infinity, whereas binomial distributions always have a maximum value (at most all coin flips can land on heads or tails).

To bring it back to the question of whether seven footers are outside the realm of the normal distribution of height it depends on how large N is. I.e. how many total different gene-alleles contribute to height in some significant way.

Since seven feet are close to the tallest normal people that exist, we'll assume that they represent a 1 in a 10 million draw from the height distribution. That would ballpark about 150 seven footers among the billion and a a half well-fed males in the world. That would make seven foot a 5.2 standard deviation (sigma) draw.

Standard deviation of a binomial distribution with 50/50 draws is sqrt(N)/2. Statistics rule of thumb is that the normal approximation breaks down at the point in the tail when the activated (or non-activated) coin flips falls below 30.

To fall below this cutoff the number of genes that affect height, N would follow:

0.5 * N - sigma * sqrt(N)/2 < 30
N < 117

So ballpark estimate is that if 117 genes or more affect height in roughly equal measure with roughly 50/50 allele frequency then seven footers are still well within the safe normal distribution approximation.

If the allele frequency is more lopsided then that the lower bound increases. For example for 0.2/0.8 allele frequency then N < 343. But it's still within the same order or magnitude.

Overall though as far as I'm aware already several hundred genes have already been identified that influence height, with potentially thousands more. That would indicate that seven footers are still well within the range for which the normal distribution is a good approximation of height.

Anonymous said...

A little off topic but take a look at this collection of thieves: www.milkeninstitute.org/events

What a collection of sob's from the ruling class. If you want an idea to the end of America look no further than the speaker lineup.

played early today said...

Seems to me the most salient thing one could say about the NBA and height is how frequently heights are overlisted. Take Jason Kidd, for example. Routinely listed as
6'4", but I stood right next to him in a Berkeley smoke shop and if he was 6'2" he just made it. Players listed as 6'9" are almost always about 6'7" 1/2, a good example being Charles Oakley. I remember when Chris Webber, listed as 6'10", was new with the Warriors. For some reason Spencer Haywood was visiting the locker room, and he said on radio, "I thought he'd be bigger." Barkley always said that while he's listed as 6'6", he's really only 6'4" 3/4.

eah said...

Now I'm wondering if there were/are any gay seven footers...just thinking out loud.

Anonymous said...

Most '7 footers' in the NBA are nothing of the sort. I am six five and taller than most of the NBA players I have met.

MC said...

The NBA is the sports league that looks most different when viewed in person compared to TV. On TV they all just look kinda tall. In person, in the lower rows, you realize you're in Brobdingnag.

Dave said...

we know that observed IQ out at the high end does not fit the math that well. there are more real, flesh and blood people with super high IQs than the math predicts there would be. when psychologists go out there and start measuring actual people, high end outliers turn out to be more common than the models would estimate.

Actually for the last several decades, IQ has been FORCED to fit the bell curve. Since the bell curve predicts only one in 2000 Americans should have an IQ of 150, only one in 2000 Americans are ASSIGNED an IQ of 150. Because intelligence is an abstract trait, not something concrete like height and weight, it's very hard to observe it's true distribution.

Anonymous said...

"Why is it that weight classes are established in boxing to make matchup fair relative to weight, but no such effort is made in basketball."

Betting.

E. Rekshun said...

In the late '80s I literally bumped right into Manute Bol as he exited a building and I entered. The Bullets were in town to play the Celtics. Bol was listed at 7-7. He did on 2010 at the age of 47.

E. Rekshun said...

Brittney Griner, recently drafted #1 by the WNBA's Phoenix Mercury is listed at 6-8. She also once sucka punched an opposing player in a college game, breaking he nose of White female Jordan Barncastle.

E. Rekshun said...

@played early: "Seems to me the most salient thing one could say about the NBA and height is how frequently heights are overlisted."

Yes, I suspect this occurs in other sports as well. Over Mike Tyson's boxing career, I'm sure I saw his listed height grow from 5-9 to 6-0.

Former Heisman winner and CFL/NFL QB Doug Flutie also seems to have ranged between 5-9 and 5-11.

Truth said...

" I can think of plenty of other guys 6'11" or taller who were far clumsier and slower than Shaq: Ilgauskas, Fat Eddy Curry, Eric Montross, Manute Bol. Even Yao Ming, who was relatively coordinated for a 7'5" guy, would lose a race to Shaq every time."

I was playing pickup ball one time in Studio City when Shaq, Dennis Scott and some NBA benchwarmer showed up. I would have to say that Shaq may be the most incredible athlete, pound-for-pound that God ever invented. The guy was obviously playing half speed and he was leading the fast break, with his left hand and making behind the back passes, he could literally handle, shoot and pass like the 6'1 guys.

After a while people were telling him to post up and he drove a guy who was about 6'3 240 off the court with his ass and dunked on him like he was Gary Coleman.

Anonymous said...

About 6 years ago, I was in Berlin in the summer, and I was walking down a small side street without very many pedestrians. I turned my head and looked a bit down the other side of the street and saw a gigantic Chinese dude, walking down the street holding hands with a very tall Chinese woman. I just thought to myself, "hmm, that's odd", and went on my way. Later that evening I was back in my hotel, flipping through the TV channels. One of the channels they had was the Chinese State TV channel, and they had a report on Yao Ming's recent wedding. I then realized that I must've seen Yao Ming, apparently on his honeymoon, earlier that day on the street.

Whiskey said...

"all combat sports have weight classes"

Sometimes they are suspended in wresting. Like in this match between the 400lb+ Big Show and 155lb Floyd Mayweather.

razorblade said...

A few points relevant to the discussion but not related to each other.

My dad played basketball in the town league against Chuck Nevitt, and since he was the tallest guy on his team at 6-5, he always had to guard him. I used to laugh my ass off watching him try to defend this guy a foot taller than him, since it gave him a taste of how I felt trying to guard him in a pickup game.

RE: weight classes in boxing, but no height classes in basketball.
1) different positions obviate the need for height classes
2) without weight classes there would be no non-heavyweight fighters, because a trained boxer who weighs 230 and has a 78" reach will beat the living hell out of a guy who weighs 145 and has a 67" reach no matter how much more skilled the little guy may be

Anonymous said...

I think the estimate of 70 seven-foot-plus American males between 20 and 40 has to be low. In this list of top NBA prospects (so, presumably around 18-20 years old), eight are at least 7 ft. There's no way every seven-footer in that age range is on that list, but that would be the implication.

http://www.nbadraft.net/ranking/bigboard

At a guess, the real number is a magnitude higher.

Cennbeorc

DYork said...

Barkley always said that while he's listed as 6'6", he's really only 6'4" 3/4.

His mugshot shows 6'8"

http://www.celebheights.com/s/Charles-Barkley-2722.html

Walton seems to claim he's 6'11" but really more like 7'1".

For some 7 foot marks the "freak factor" so while lil' fellers exaggerate their height sometimes, gigantic guys can be embarrassed and diminish it.

Mike Hunt Rice said...

@Gene Berman

Brendan Byrne Arena (The Meadowlands) didn't open until 1984. You meant 1984.

Mike Hunt Rice said...

@jody

The NCAA put in the 275 limit in 1986. It was raised to 285 in 1998.

Mike Hunt Rice said...

LOL and I meant that Brendan Byrne Arena opened in 1981, with Bruce Springsteen and the E Street Band.

ben tillman said...

My dad played basketball in the town league against Chuck Nevitt, and since he was the tallest guy on his team at 6-5, he always had to guard him. I used to laugh my ass off watching him try to defend this guy a foot taller than him, since it gave him a taste of how I felt trying to guard him in a pickup game.


I'm glad someone mentioned Nevitt. He was billed as 7'5", or one inch taller than Tom Burleson (who was actually 7'2").