I took my own crack at this, because I think your numbers - intended to show the big separation - still make it seem too easy! Lebron is NOT just a 99.99th percentile player!

There's fewer than 500 players in the NBA. There are hundreds of millions of people in the US (being US-centric initially to try to do the YMCA comparison), so probably a few million that play frequently as amateurs? One in a hundred? Let's call it 3 million out of 300,000,000, to work with relatively round numbers.

So being in the best 1 out of 100 - top 99% - is a z score of 2.3. Being in the best 500 is then much smaller even than THAT! 99.983%, z score of 3.481. The single best one? 99.99997%, z score of 4.991.

So if you define closer by z score, they "good amateur" YMCAer is closer to the worst in the NBA than that person is to Lebron, but I think it's more meaningful to define closer by "how many people stand in between you and them" - and the answer is millions for the amateur.

And I think that shows that work alone only gets you so far compared to talent. If you and a million other amateurs all start putting in ten hour days, the vast majority of you aren't getting to the NBA - it's just not big enough.

That is sort of interesting. Depending on how extremely good Lebron James is at basketball could make Brian's statement false. I think I disagree that number of people is a meaningful metric. The difference between you and I, assuming we're both near average competency, could be millions of people, while the difference between Lebron and Brian could be just hundreds or thousands of people but represent a substantially larger skill gap. Otherwise you're suggesting that the more skilled two players are, the less noteworthy differences in skill are because there's fewer people around them to measure with.

That's true, we could be separated by millions of people but at the same time only, say, a year's worth of two-hours-a-week practice.

But in the absence of a reliable way to measure absolute skill, the z score one does seem about as good as we can get, though it can't truly answer something like "Lebron vs Jordan" - and you also would get different numbers depending on which population you picked. Population of the world, population of the US, population of the basketball-playing world, population of people who play basketball at least once a month? That's gonna change the denominator for the percentiles for the Scalabrines and Lebrons both.

I like this but you might want to up the z score for LeBron. GM is 2500 plus norms. LeBron has 4 rings and 4 MVPs. He would be Magnus level or at least one of the few who hit 2800 (there have only been 13).

NB: I'm a huge LeBron fan and a huge Magnus fan.