DukeofDuke said:
Yeah I know that, but still the difficulty of getting into a school will be somewhat proportional to its rank, if only because perceived rank is how the majority of students will apply.
There isn't a clear rank, or at least the rank isn't what you think it is. In astrophysics, there are some state schools that are harder to get into than Harvard or MIT, and there is a *reason* why they are harder to get into, because for example in observational astronomy, MIT isn't a particularly strong school compared to University of Hawaii. If you like to do radio astronomy, University of Virginia beats Harvard. Loop quantum gravity, Louisiana State University. If you want to do high performance computing, then University of Texas at Austin or UIUC are good schools.
You aren't going to figure what schools are good or not based on general reputation. You need to go into the literature to figure out for yourself what the rankings are in the area that you are interested in. And this is impressive for the admissions people, because if you know that University of Tennessee at Knoxville is good at supernova research, that means that you have some familiar with the literature.
I just don't want to waste hundreds of dollars on application fees- so I want to know what "tier" or range of schools I should practically look at.
The good/bad news is that graduate schools just don't work that way. There is a *huge* amount of randomness in the admissions process and that's a good thing.
One other thing about graduate schools is that the quality of program is affected by the graduate students rather than the other way around. At the undergraduate level, people will admit thousands of students, and one bad student isn't going to sink the school. At the graduate level, the biggest schools will only graduate about 15 people a year, and there are tons of schools that will graduate only one person a year.
What that means is that if a big name school admits a few people that aren't that good, they are toast. Conversely, if you have a no name school that admits one or two people that are really good, then they can very quickly become a big name.
Getting a Ph.D. is really, really, really tough, and you need the right balance between arrogance and humility to survive. Just the right amount of arrogance is important, because if you always say to yourself, I'm a lousy student in a lousy school, then you are not likely to survive.
One thing that you should say to yourself where ever you get admitted, is that school X is a first tier school because they admitted me, and I'm going to do whatever I can to make school X a first tier school. You are likely to be one of only a handful of people that graduate each year, so at the graduate level, your actions influence the reputation of the school, more than the reputation of the school influences your actions.
This matters a lot because it can influence the tone of your personal statement. If your personal statement comes across saying that X is a subpar school and I'm only applying because I couldn't find anyone better, that's not going to go over well. If your personal statement comes across as "I know that school X is or wants to be number #1 in field Y, and this is what I can offer to make school X, number #1 in that field" you are more likely to get admitted.