+1 for various anime, to be sure. I'm not the top expert, but I've seen a lot that, while having significant natural gifts, also place as much weight on training as performance--and if you count mid-contest growth as well as explicit training, then growth is the primary focus.

I'm talking about things like Dragonball (Z), and also sports anime like Hajime no Ippo and Eyeshield 21. I might even describe them as level-up porn.