You theoretically have a chance with any girl. The ones you are referring to as 'out of your league' are mostly social hoes. By beefenig up their perceived self worth they are able to pick the, materialistic, best men easily.
When you believe something, others around you feel it. They manipulate that to their advantage to put off people like you who they would actually probably like otherwise and attract men that, at that age, don't know any better.
The best way to solve this is by either inflating your own self worth (warning: may cause you to become an *%#!@*@) or deflating hers (my personal choice). She thinks she's perfect, you can see she's not. When she walks into the room 99% of the men are going to say she looks perfect, and it'll confuse the hell out of her when you say different.
The trick here is to balance out the negatives with actual positives. It's fine to compliment girls on the way they look, they love it, but don't say something not true and don't slobber over them. Genuine things like this are noticed more and at worst will get you a good chunk of attention to get to know the real her underneath the balloons of silicone wrapped around her face.
Whether you like them or not after that is debateable. I spent a month with "the sexiest girl in the school" doing this and found out that usually people that feel they have to be somebody they're not have something wrong with the real person they are.
The one in my case was a real *!!%% and I didn't really feel comfortable being with her at all. There are the other types that are 10/10 material and aren't hoes at all, and in those cases you just need to buck up and put yourself forward. The only time you're not in the same league as a girl is when you remove yourself from it purposefully.