When it comes to graduate school, it is often more about where your “people” are - i.e the people studying the topic you want to pursue. Last fall, S applied to only 3 PhD programs because those were the only places where there were people studying his particular topic of interest and offering PhD programs (his Master’s advisor wanted 10). Fortunately, he had 2 great offers to choose from. The only Ivy-type even close was Yale, and even their program was not quite it. (Of course, their acceptance is like 3/700, so that further discouraged any attempt to apply there.)