I agree with Googer, 100%. I used to compete in a judged event and we had a saying about certain elements of your performance: They won't help you win, but they can sure make you lose. That is, most applications are going to be in a certain range with GPA and GRE. Those won't help you win, but they can sure as heck knock you out of the running. (An above average score like a 1300-1400 isn't going to guarantee anything, but a combined 700 is probably going to get your application thrown out). So, all things being (basically) equal, what I am learning most through this process is that the LOR and the SOP have far more weight than any of the numbers. Of course we're all going to have solid GPA's and GRE's. That should go without saying. So the real competition is in making your research interests align with the profs that are there now, the kind of research the institution is doing, and (the hard part) the kind of research they want to be doing.
The feel I'm getting after some of these recruiting weekends is: We read your file. The research you're doing is the kind of research we are doing. Here are some profs who you could work with and here's where their research is going, etc. etc. No one has mentioned my stellar GRE or gradepoint on any of these meetings. It's all been about research. So, it seems to me it doesn't matter how many applicants there are. It matters how many spots are open and that your fit with the school's line of research is one of the best 5 or 2, respectively. The visits I've been on have told me that these people are genuinely interested in finding students who will fit with the program institutionally, personally AND academically. It's a big commitment when programs bring in PhD students. They realize that more than I realized that. I wish I could have gone on some recruiting weekends before I had to submit my apps! I would have focused even more exclusively on fit. I feel now like the competition is less between you and the other applicants than it is about you and the institution. What I mean is, your application is competing to show just how great you would fit into the program and it's about showing that you're asking good questions with your research. Anyone can be trained in methods, it's the questions you have asked and plan to ask that are what set you apart and show if you will be a good fit. That has nothing to do with the other candidates. Which is really, just a semantics argument, but one I now have a lot of faith in.
Anyway, that's what I've learned in the last month.