I think that if a young player learns and practises chess enough, and has the dedication and talent, this can go a long way towards making them very strong very quickly. I've seen it myself in my local chess club.
Also, younger people learn faster than older people. That might have something to do with it as well.
I'm curious what you think, on average, makes a young rapidly improving player so strong.
you could call such players prodigals, but I mean to include more players than Just Nakamura and Carauna and I really mean any younger (teens- to 20's) that has gained more than 200 (USCF/FIDE) elo/year.
if you've personally achieved that I am really interested in your "breakthrow" do you find yourself MUCH better at tactics, is you Intuition improved and much more accurate or are you finding it much easier to See "visuallize" the peices?
or would you say that mostly the increase is becuase you know think of chess at every waking moment (that your not doing schoolwork)....