I think the more important question that you need to ask yourself is this-- How are you a game-changer? How have you made a tremendous and measurable impact? It’s not, “I will start if you let me into your prestigious school.” It’s demonstrating that you are NOW making an impact, making a difference, making strides for something greater than self. Then, telling that story in compelling context of “Why Us” for the university that you aspire to?
Very selective universities, such as those in the Ivy League, and Stanford (because you mentioned it) are very adept at sniffing out those who are only looking for name brand, and not fit.