Your point is absolutely 100% crystal clear; I just think it's wrong.
Just to go back a bit, your first post in this thread said "there is nothing to explain" in the difference between the number of top US pool players vs. top European pool players, because the population difference already accounts for it: European pro pool is better than American pro pool because there are more Europeans than American.s That's what I think is wrong, not all the other examples with golf scores and US states.
I think it's a coincidence that the populations of Europe vs. USA roughly match the number of top-rated players, because it doesn't hold for almost any other comparison I can think of: Africa, Taiwan, India, the UK, etc. I think what you're doing is taking a scatterplot where r = 0 and picking out just two of the points to fit a model where r = 1.0.
No I'm not. You think I'm trying to make population a variable that somehow explains something. I'm imagining you think I should be disappointed that Taiwan has so many good pool players and Africa has so few, that they somehow are violations of a model I am proposing.
This is not true.
It has nothing to do with a model. Population is not a variable. It is just the freakin denominator!
California will have about 18,000 new cases of Lung Cancer this year
Kentucky will have about 4,000 new cases of Lung Cancer this year
But the CDC is WAY more interested in KY than CA for this issue. Why? Because when you divide by population, you get 97 cases per 100K people in KY and 47 cases for 100K people in CA. These latter numbers are the ones everybody reports and pays attention to.
It is comparing these latter numbers that gets people looking for variables that might explain a difference. In this case it is likely relevant that Kentucky is dependent on tobacco for its economy, and a far higher proportion of its population smokes compared to California.
If you compare California to Colorado, the incidence is the same, about 47 new cases per 100,000 people. And there is nothing to explain.
If all someone had access to was the absolute numbers for CA and CO, they would see CA has 7 times as many cases of lung cancer. Fortunately everybody knows how misleading absolute numbers are, and you won't find people using them.
When we are looking at the number of players that play above a certain speed, whether it is 600-speed or 750-speed, we have the exact same issue.
The population is just the denominator; that's all. Models and predictions and explanations and variables come later.