Actually pretty far off. It's never even really highlighted that she's female, this is like a Buffy/Alex Rider thing where you take some strange and exciting and mix it with teenage life and teenage problems to give it some weight. They just happened to pick a girl.Father Time said:
And she does try hard and believe that she can do anything, but generally not in the way that you're thinking of. She's one of those super over achievers you get at school who get top marks in all their exams, can study well, is good at sports and involved in absolutely everything in official school life. The one who organises the end of school dance (the dance that people actually like). And there's even a jokey in-universe reason for it. Her Dad's a rocket scientist and her Mum's a brain surgeon and their family is always played as comically gifted.
So it's not like she's some average kid thinking 'If I believe in myself I can do this!', she's the person who believes in herself that she can do things because she's always found herself to be good at nearly everything, including working hard.
And the writers actually recognise it too, which is good. It's one of the only shows that when they have an episode dealing with the hero's flaws, I actually recognised the hero as having those flaws. (Normally in shows it's like they decide to be a little bit racist for one episode and get over it, or are bossy for one episode and then get over it). When she finds things she's not actually good at, she gets really frustrated over that and a little bit jealous of the people who can. She does care about the people around here, but she's so used to do everything well that playing second fiddle doesn't come easily to her.
EDIT: Also, she often doesn't end up on those episodes getting good at the things she can't do. It was something she wasn't good at, but more often than not if she works hard, she can become okay at it instead of instantly mastering it when she learns her lesson
