<p>It is not that you are under-qualified, it is truly as you put it that much a game of chance. People assume that if you have great stats you can get into any top school, and that is often not the case. I have a friend who last year got rejected by University of Chicago and Swarthmore, but got into Brown. She was equally qualified for all three, wrote great essays for all three, but only got into the one, because it is often essentially a lottery for top schools. Also you are interested in one of the most selective schools in the country where almost every applicant is qualified.</p>