I talked her out of that but it got me thinking in general about her intensity and what, if anything, I want to do about that as a parent. I don't think it's good for her to be so emotionally invested in this kind of thing -- I want her to accept failures and setbacks more gracefully. (She was crying or on the verge of tears for about ten minutes, until we went outside. She was fine for the last stretch.) I also want her to try though, to not shut down and quit. Not sure what is best for me to do in terms of helping her achieve that balance. (I'm using this basketball game as an example, but she's like this a lot.)
It's hard to be involved in a competitive sport without being emotionally invested in it--the same drive that makes you want to win will make you upset if you don't. On the moment, she wasn't able to accept the failure gracefully, but you helped her calm down and she was fine again, so she's showing good resilience, and you're teaching her how to regain her equilibrium. Even professional athletes will sometimes momentarily be in tears after a big loss. Losing ain't no fun--but it's also not the end of the world, and that's the balance you want her to have, and she does seem to realize that. Praising her effort is really all you need to do to get her to keep trying--if she's already a high achiever, you don't need to push her to make more
effort, because then she can wind up never feeling satisfied with herself.
I agree with jespah that some non competitive activities might be good. Learning to play a musical instrument, for instance, would rely on her own determination, and her need to practice, for her to be able to see improvement and move on to a more difficult level, but she really wouldn't be competing with anyone else. Learning how to master something, like a musical instrument, teaches a lot about how to deal with frustration and how to develop patience with one's own limitations, because improvement is gradual and incremental, and it's a very different sort of challenge than something like her academic schoolwork or even a team sport.
It does sound like you're already encouraging her without pressuring her. Failure, in some area or another, is pretty inevitable, and it sounds like you're teaching her how to deal with it, and she's also learning through her own experiences. You think all the losers at the Oscars really accept their failures so gracefully? As adults we simply learn to mask our disappoint better. Losing at something, or not achieving your goal, hurts. particular if you've given it your best effort, and only the process of maturing helps us to manage that hurt better by getting it in the proper perspective--after we may have a good cry about it.