Thanks. I´ve been wanting to say that forever. I think it´s pretty obvious that the objective criteria many people are posting here (GPA , GRE and so forth) don´t go a long way towards explaining admission success. That´s good in a way, because GREs are a pretty bad indicator of academic ability, and GPAs are not easily comparable. Other professor´s opinions are probably more highly valued; for example, think of the many many ambitious and hard-working students with low to mediocre intellectual creativity (or even interest), some of which are interested in academia primarily for the career (and the title). An Adcom cannot possibly sort these people out by GPAs and GREs (they are probably even disproportionately good at those), but other professors can (and do). Of course, this does not imply that people that got rejected even though they had good objective stats are always part of this group. But, relationships with professors certainly matter (and their importance sometimes gets diminished in this board, because they are unobservable from our perspective). In terms of research interests, I ´m pretty sure that it pays to be rather specific (and demonstrate proficiency); not necessarily regarding your interest in the future, but at least about some research that you have done before. There is no better way to judge the research somebody will do than by the research he or she has already done (which is, by the way, why the writing sample, another "unobserved" component" of the application that is often neglected here, is probably pretty important).