AcceptanceLetter

I just read through a stack of applications, and encountered very few 'bad' LORs.. I totally agree with the "damn them with faint praise" statement. The worst LORs painted the applicants as kind of mediocre. Furthermore, if profs had anything bad to say at all, they would be very sneaky about it, and then sugar-coat their criticisms to no end. e.g. "X had some trouble at first, but after a few iterations finally..." or "Y struggled a bit at .... However, as a person, she is great to be around." That said, I found that professors were more damning in the multiple choice section of evaluations (where they indicate what percentile you were, or whether or not they would strongly recommend / recommend / not recommend you). There were a few profs who wrote glowing recommendation letters, but indicated that their student was say, in the top 25% (as opposed to top 1%, 5%, 10%...). In one case, I heard that the admissions board then called the recommender about the discrepancy between his LOR and the indicated percentile, and extracted the (ugly) truth. So yeah, not all profs will turn you down if they don't think too highly of you.

Unfortunately it varies a lot by year too. I'm currently in a grad program, and just because we had a larger than usual class last year, this year there's a smaller demand for graduate students among the faculty. Alas. Would you be comfortable sharing what school you received the invite from?

Acceptance rate varies widely by school, and somewhat by year. When I was interviewing the first time round (I was successful only on the second try), people gave me the whole "they're spending so much money on you because they think you're really awesome" spiel and it turned out to be a HUGE mistake. I was overconfident, which led to a whole bunch of mistakes that I'm ashamed to admit, like dressing super casually (I freaked out the first morning of interviews because everyone was in office wear, while I was in a casual cardigan), replying to invites late, failing to thank profs after the interview, etc... Turns out there are some schools that only accept a very select few of their interviewees (while there are those accept practically all of them). My advice would be to disregard the acceptance rates, and just do your best!