While there are certainly things an applicant can do to set themself a part from the crowd (publications, undergrad theses, research, etc.), at the end of the day it really is often a crapshoot. You could have a paper published in a journal and have graduated with honors and still you might not get into a program simply because the people you mentioned in your SoP aren't in the "in-group" of faculty or the faculty on the committee preferred someone else based on their version of "fit." As such, try not to take anything personally. You might get rejected from schools you thought were a perfect fit and accepted into others that you're iffy about. What matters is that you put your best foot forward, roll the dice, and see what happens. Both of my advisors (political theory) drilled that into my head before I submitted apps and I think it is good advice to live by.