[Content note: scrupulosity and self-esteem triggers, IQ. Potentially not good for growth mindset.]

I.

The average eminent theoretical physicist has an IQ of 150-160. The average NBA player has a height of 6’7. Both of these are a little over three standard deviations above their respective mean. Since z-scores are magic and let us compare unlike domains, we conclude that eminent theoretical physicists are about as smart as pro basketball players are tall.

Any time people talk about intelligence, height is a natural sanity check. It’s another strongly heritable polygenic trait which is nevertheless susceptible to environmental influences, and which varies in a normal distribution across the population – but which has yet to accrete the same kind of cloud of confusion around it that IQ has.

So let’s see what we can learn from the height distribution of every player in the NBA: (source)

The first thing we notice is that nobody shorter than average (ie 5’9) gets in. This is not true eternally and forever – Wikipedia’s List Of Shortest NBA Players names 25 NBA players in history (out of maybe 5000 total) who were below average stature. The all-time record holder is Tyrone “Muggsy” Bogues at 5’3, who was actually pretty good (though not above exploiting his distinction for publicity: his autobiography is called In the Land of Giants ). But Bogues was a spectacular outlier. If we’re going to stick to our resolution to use the histogram we’ve got, the contribution of the left half of the height bell curve is precisely zero.

We can do some very rough Fermi calculations for the next couple standard deviations.

34% of the US male population is 5’9 to 6’0, so about 54 million men. There are 5 NBA players in this band. So about one in every 11 million people of this height is in the NBA.

13.5% of the US male population is 6’0 to 6’3, so about 21 million men. There are 40 NBA players in this band. So about one in every 500,000 people of this height is in the NBA.

2.35% of the US male population is 6’3 to 6’6, so about 4 million men. There are 95 NBA players in this band. So about one in every 40,000 people of this height is in the NBA.

0.15% of the US male population is 6’6 to 6’9, so about 200,000 men. There are 130 NBA players in this band. So about one in every 1,500 people of this height is in the NBA.

0.003% of the US male population is 6’9 to 7’0, so about 5,000 men. There are 160 NBA players in this band. So about one in every 30 people of this height is in the NBA.

0.00002% of the US male population is 7’0 to 7’3, which corresponds to about 45 men. There are 40 NBA players in this band. So about 8 out of 9 people of this height are in the…wait, no, that can’t be right.

Sports Illustrated‘s Dan Diamond does a similar analysis and gets broadly similar results. But he adds several complicating factors. First, at this height people with very rare medical conditions and pituitary tumors start taking over from normal variation, so we lose our ability to derive a census a priori with pure math. Second of all, at this height talent scouts comb the world for suitably tall foreigners and import them, so we can no longer assume we’re drawing from the pool of tall Americans. And third of all, the same way you round up so that you’re 6’0 on OKCupid, NBA players round up so that they’re 7’0 on their official stats.

He concludes that most likely about 17% of seven-foot-tall young men in America are in the NBA. This might still be an overestimate, but is probably in the right ballpark. Forbes Magazine writes that Being Seven Feet Tall Is The Fastest Way To Get Rich In America and quotes a talent scout who says “that he’ll ‘check up on anyone over 7 feet that’s breathing.'” Given that a lot of people this height are unhealthy or uninterested, it might not be much of an exaggeration to say that if you’re 7’3 and have any interest in basketball, you’ve got better than even odds of going pro.

But why stop there? 0.000000001% of men are 7’3 to 7’6. Given the size of the American male population, there shouldn’t be a single person in the US with this height, though in practice a few people with endocrine abnormalities make the cut. There will, however, be a couple of healthy people of this height in the world population. There is one person currently in the NBA above 7’3, and he is a Tanzanian native discovered by talent scouts.

WE’VE GOT TO GO DEEPER TALLER! 0.00000000000001% of the population is 7’6 to 7’9. Statistically, there should not be a single man this tall in the entire world. No NBA players are currently this tall. But Yao Ming, who retired four years ago, was 7’6 exactly. He was the product of a Maoist breeding program specifically aimed at producing tall people to play basketball. You can break a lot of statistical laws if you have breeding programs and flexible ethics. Also if you have pituitary tumors, as the remainder of the List Of Tallest People reminds us. It looks like a little over half of the living people in this height band have played professional basketball at some point.

There are people taller than 7’9, but a lot of them have trouble standing without support, which somewhat decreases basketball ability.

On the plus side, you can do all sorts of awesome things, like take a picture standing next to the world’s shortest man, or…okay, pretty much just that.

II.

This offers us an opportunity to compare our intuitions about intellect to our intuitions about basketball. I recommend taking that opportunity. Basketball isn’t mysterious, it isn’t politicized, and it isn’t tied up with our notions of self-worth. As a result, our intuitions about basketball are crystal clear.

If somebody said “Height plays no role in your success as a basketball player,” we’d look at them funny. Literally nobody shorter than average is currently in the NBA. Your odds at average height are only one in ten million. But if you’re 7’0, you can pretty much walk right in.

But if somebody said “Well, success in basketball is clearly dependent on height, that means there’s no point in practicing, after all you’re not going to grow any taller,” we’d look at them funny too. I don’t know much about sports, but I predict a short guy who’s been playing for years can defeat an untrained giant every time. And of course if two giants go up against each other, experience will be decisive.

If someone found a 5’8 kid who really liked playing hoops in his backyard and was pretty good at it, and they told him “You’re a moron, you can never succeed at basketball because of your height, give up,” that person would be a jerk. The kid is enjoying himself, there’s no point in insulting him about it, and if his goal is just to end up as a college athlete or a minor leaguer, then with hard work he could certainly make it. Even if he didn’t, he might be able to apply what he’d learned to a related area like coaching or reporting.

But if that same kid wanted to go deeply into debt to attend a basketball training camp, and he’ll count it a failure if he achieves anything less than NBA superstardom, you should probably warn him that his hopes aren’t very realistic and that maybe he should lower his standards or pick a sport more suited to his body type or try another line of work entirely.

If somebody who was 6’6 complained that they’d never be able to beat the 7’0 players on the other side, we would tell them to brighten up. After all, Michael Jordan was “only” 6’6, and he’s maybe the greatest basketball player of all time, even though he often had to face off against people taller than himself.

But if a team made entirely of 6’6 players faced off against a team entirely of 7’0 players, and both of them were really motivated and practiced really hard and had great coaches, I know who I would bet on.

Most important, people all over the world innocently enjoy playing basketball, and they are right to do so. Everyone knows that taller players have an advantage, no one’s denying it. But at the levels most people play at, moderate height differences are surmountable by differences in training and technique, and large height differences are so rare as to not come up very often. Yes, the pro leagues are a different story. Yet somehow the 5’8 kid who scores a three-pointer still manages to feel good about himself. And we can be very impressed by Kobe Bryant and LeBron James, praise them for their determination and technique and competitive spirit, all while acknowledging that it’s not a coincidence that the one is 6’6 and the other 6’9 and neither of these is a normal-person height.

All of this is crystal clear when we’re talking about basketball. But as soon as we switch back to talking about intelligence, we’re shouting at each other: “YOU SAY RAMANUJAN WAS REALLY HARD-WORKING, BUT I THINK HE HAD HIGH IQ, SO THERE!” Or “WELL IF SUCCESS COMES FROM INNATE TALENT, I GUESS I’LL JUST NEVER STUDY AGAIN.”

Luke Muehlhauser liked to call his philosophy of religion “common sense atheism”, meaning that he wanted to treat the question of God with the same “common” reasoning that he used for every other question. If we don’t see a tiger in front yard, we don’t say “Since it’s impossible to prove a negative, I can at best be agnostic about the existence of a tiger”, we say “I guess there’s probably not a tiger.”

Likewise, if we can just apply the same common reasoning we use for normal everyday activities like basketball to the question of intelligence, we might find it’s not so complicated and scary after all.

Which is not to say that it’s not important. After all, the other analogy between intelligence and basketball talent is that they’re both skills we need to cultivate at the highest levels if we want to save the world when it is threatened by dangerous future technology we can barely comprehend.