We're in total agreement regarding the NBA players 6'2 and under (likely to be more at the athletic extreme than your typical NHLer) and regarding the guys 6'9 and above.
But you mention the 6'3 to 6'8 pool as 3% of the general population, whereas the NHL pulls from heights that are 50% of the general population. It's not quite as obvious to me that the number of developing basketball players is more than 17 times higher than the number of developing hockey players. It might be close, it might be more, it might be less. I'd want to see things tightened up on that point. Keep in mind that 75-80% of NBA players are American so the numbers should be re-weighted based on national origin, just like you would with the Canadian population being half of the NHL.
The I
IHF has a survey of registered players, which gives us a better idea of the population of U-20 amateur hockey players. They find just under a million boys.
This study finds 26 million basketball players in the U.S., and from their proportions it seems that 10 million or less would be U-20 boys. If you add another 20-25% for the international proportion of the NBA, then you can see we're inching towards a number close to but still short of a 17 million.
We'll likely never get to a clear-cut answer on this, but I tried to get some useful data on to estimate many people are in the professional basketball
pipeline as compared to hockey.
I tried to find some kind of listing of total pro teams in each sport, but the numbers are harder to track down than one would think. A lot of leagues operate in a weird semi-pro space where it's hard to draw the line as to who's seriously competitive (who knew there was "pro" hockey in Turkmenistan?).
But broadly speaking, we can easily point to the size of the international organizations for a start: there are 58 IIHF member nations, versus 213 FIBA members. Bear in mind the IIHF membership list includes some questionable entries like Spain and South Africa, and I'm sure there are equivalents in FIBA.
I can't find an exact count on the number of professional leagues out there, but based on Wikipedia links I count 157 pro basketball leagues globally. As far as I can tell (and it really is difficult), there appear to be around 35 pro and semi-pro hockey leagues globally.
Trying to make this sort of estimate at the amateur level is so complicated that the answer would be near useless. But at least on a limited basis we can point to 144 men's hockey programs in the NCAA, compared to something like 400 men's basketball programs. In Canada those numbers are 34 and 48 in the U Sports program.
It gets harder when we throw junior hockey into the mix, because it kind of straddles the line between high school, college, and pro. There are 60 CHL teams, 150 Junior A teams, about 235 Junior B teams, 16 USHL teams, 23 NAHL teams, and an indeterminate number of Junior C teams -- a total of around 500 teams plus however many are in Junior C.
Per Statista, there are a little over 35000 players in boys' hockey in the USA, compared to 540,000 in the USA. I can't find comparable data for Canada and of course it's hopelessly complicated internationally. But those numbers would appear to imply about 1750 hockey teams and about 45,000 basketball teams.
Putting all of that in a box, it would appear that the total pipeline of talent leading to the NHL and NBA breaks down as follows:
-- Roughly 10-15 times as many basketball players engaged in basic recruitment and training on the youth level
-- By the time we get to college/junior age, the proportion shrinks to perhaps 5x as many players still engaged in a "pipeline" environment
-- At the pro level we see that 5x proportion again
-- At the international level (best of the best) it shrinks to more like 4x
What this means is that relative to hockey, basketball's promotional "pyramid" has a very wide base and a disproportionately narrow peak. If pro hockey's development pyramid was shaped like basketball's, there would only be about 10-15 pro hockey leagues in the world. That would leave us with only the NHL, KHL, AHL, ECHL, and the top tier of European leagues. We'd say goodbye to the tier 2 Euro leagues as well as the low minors like the SPHL and the Fed. The A-league in Slovakia or Denmark would be the lowest pro level still in existence.
I'm still mulling over your point of the efficiency of the selection for athleticism for each sport. I take your point that an athletic 6'6 kid would probably be steered towards basketball. And surely, they are a disproportionate number of those 10 million or so boys that play basketball. I'm not sure how to weigh that against the central issue that we're talking about - hard limits on the amount of potential athleticism within each subgroup. If you got every last scrap of athleticism out of 6'7 American boys, is that a lot or a little?
Again I think you're eating the pizza from the wrong end of the slice*.
Say there's this one guy who's 7'9" and athletic enough to play in the NBA. Now say that guy gets hit by a bus. What happens? His team isn't going out and finding an UN-athletic 7'9" guy to replace him. Instead they'll find an athletic 7'4" guy and move along with their season (mournfully).
Now let's say we have a very strange day and all the 7'+ guys get hit by buses simultaneously. There are none left in the talent pool. What happens? The teams replace them with 6'11" athletic guys, the average height drops, and they keep moving along with their season. It's not as though freakish height is a requirement to field a basketball team. It's simply a luxury that NBA teams enjoy when they are pulling from virtually the entire global population as a talent pool.
What I'm getting at here is that the NBA draws from the tallest 3% of the population
because they can. There are, somehow, professionally-athletic guys at that height. It's not that the scouts are
bound to the 3%, and have to ignore anyone shorter. It's that when you have half a million candidates for a roster spot, competitive forces are so intense that something as simple as a natural inch of wingspan makes the difference. If the 6'6" guy is equally skilled, there's nothing a 6'2" guy can do to close the gap. So you take the taller guy.
Now, this same height-driven effect
does happen in hockey -- with goaltenders. At this point, a goalie has to be an absolute phenom to make the NHL at under 6'. Yet there are dozens of sub-6' skaters out there, some of whom aren't especially good players (all due respect but Nathan Gerbe has averaged 12 goals a season for over a decade at 5'4" and still gets contracts). What's the difference? There are only about 60 jobs for goalies. That's the equivalent of 3 teams of skaters. Imagine if there were 3 teams in the NHL, how hard it would be to get those jobs. It would be like making the Olympics for Canada or Russia. At some point, the competitive forces get so intense that the physical gaps become near-definitive. When that happens, the slightly taller (or heavier, or faster, or whatever) guy is going to come out on top. It takes someone truly special, a St. Louis or Fleury, to break through. That's what we see in the NBA, where you get the occasional Muggsy Bogues but it's an extreme rarity.
At the end of the day, the NBA just really is that much more competitive. The competition for
any roster spot in that league is comparable to the competition for goalie spots in the NHL.
* not that there's anything wrong with that