Although I'm not an expert on this by any means, I'd stress (like some other people on this thread) that the most important thing is fit. My SOP went through at least 30 drafts and I had several professors tear it to shreds several times. I changed it for each school and I didn't choose top-tier programs because they were top-tier, I chose them because of the faculty that I wanted to work with, faculty that I respected, had read, and was nuanced by their contributions to my field.
I didn't graduate from a top-tier university for my B.A. or my M.A., or have any publications, or have an amazing subject test score, or perfect verbal, but they were good enough, and I showed with my writing sample (which was from my M.A. thesis and highly edited and reworked like my SOP) that I could work my ass off in my M.A. program and that I also saw the direction of my future work in alignment with the particular school's.
The point is that I'm not here to toot my own horn, but I am saying that it is possible to go your dream school or top-tier school without having an ivy-league B.A./M.A pedigree. Maybe I did work harder than one, maybe I didn't, I don't know. I only have this recent experience of mine to offer some insights.