It means that you decide for yourself how well you want to play.

" That's up to you " can mean "It's your decision". When people say "That's up to you", it shouldn't be taken literally. It just means that they are giving you the responsibility of making the decision. 

So, in Grey's anatomy, by saying "How well you play, that's up to you.", he or she is probably saying "how well you play is your decision" or "It's your your decision how well you play."

I hope I explained this good and I hope this helps.

hi,i think in this sentence it means u do sth perfectly but totally u say it when u wanna give somebody a responsibility.i hope ive helped u