Here's another little secret about the failure of GRE to correlate with grad school "performance" as measured by paper output. My greatest exp is postdocs, not grads, but I think it extends. As a mentor my job is to work with individuals, with their strengths and weaknesses

to advantage them in their careers after my lab. I have not had one pair of postdocs that one can say have the same portfolio of strengths/weaknesses. So my job is in large part to get them to first author pubs because that is one of the most fundamental things that advances

them. The path to those first authors differ *tremendously* and are likely in part predictable by what they have shown prior to entering my lab (no, I don't know about any postdoc's SAT/GRE test scores). but if 1st authors are the outcome measure, being in my lab constricts

the range because I prioritize this particular outcome measure for the trainees. This does NOT mean that I believe that they all are equivalent in competing for a particular job type on exit from my lab. or would be equivalently successful in, say, my chair.

anyway, point being, that my view is that since a mentor should be taking whatever comes to them and striving to make that person 'successful', this is going to tend to constrain the variance on any particular success measure such as "finishing the PhD" or "papers".