I have a question pretty specific towards my situation but I think its an interesting thing to think about anyways. I am in the process of applying for graduate programs for the fall, and from two professors I got slightly different advice. One said that I should apply to few top schools, few mid range, and few lower "safety" schools. Decent advice, right? Now the other professor told me that considering my GPA and GRE score, I should apply to few mid range schools, and apply more to top schools because luck has a lot to do with being accepted to a program, and he thinks I will probably get into mid range schools (USC, Irvine, etc). To put things in perspective My GPA is just shy of 3.8, my GRE score is 160 and 169, verbal and math respectively, and I dont know my physics GRE score yet. What do you think? Does luck play big enough role in graduate school admission to warrant applying to lots of top schools?