Is it better to go to a school with one great advisor or a department with many very good potential advisors?

A2A'd by anon. It comes down to this: how much do you doubt your judgement of possible advisers? If you are very confident, then choose the school with the perfect adviser. If you are doubtful, then choose the large school. Unfortunately it's hard for undergrads to be certain in this situation because this issue has many other questions boiled in. I'll try to give a brief overview of what it means to be a "great" adviser, and what factors could potentially influence picking one of these options over the other. (This will be a bit beefy, but I hope helpful.) Consider how you measure whether an adviser is "great." First off, advisers aren't great in the abstract -- they are great for you. Just like there is no algorithm that can losslessly compress every file, there is no adviser who is great for every grad student. There are many ways to evaluate whether an adviser is great. All of them have drawbacks or holes. Methods of evaluation can mostly be divided into two classes. First, there are extrinsic evaluations, i.e., how their guidance helps you to perform on some downstream task: the caliber of job you got with their help how many papers you published under their guidance (or how many high-impact papers, or whatever) etc. And there are intrinsic evaluations, i.e., how their guidance helps you in ways that can't be listed on your resume: how much more you learned more with them than you would have with other people how able you are to identify research directions that are both viable and important. etc. Extrinsic evaluations tend to be noisier. For example, you can hide behind other students to get a good pub record. In contrast, intrinsic evaluations are usually more meaningful to the student, but -- at best -- only correlated with downstream tasks, like publishing. A good rule of thumb is, a great adviser should rate "excellent" in a  set of measurements that includes both extrinsic and intrinsic  evaluations. Which measurements depends on your goals. If you want to be faculty, for example, you should care about publishing and being able to identify research directions that are both viable and important. You might be wondering how to get such evaluations. I would recommend talking to current students before you apply, and asking them for very blunt appraisals of their advisers. Are the students like you? Do they have similar motivations? Are they smart? Do they find the adviser's style to be helpful? Would you? How is the lab set up, with a lot of one-on-one time with the adviser, or do post-docs and students advise other students? Do you prefer one or the other? A great adviser might be the one who is really and truly incentivized to help you succeed.This is a corollary to point 1. They must not only be great for you, they must be great for you. Example. I have a friend who went to an amazing CS school. His adviser had just gotten tenure, and was graduating his "flagship" student. He was incentivized to find that student a job. He was not really incentivized to publish, or to teach this student how to do research. The "flagship" student was also the lab's most senior student. He was incentivized to actually find a job. He was not really incentivized to publish any more or to teach this student how to do research. For the first 3 years, my friend didn't publish anything. He floundered and nearly dropped out. Then, he caught his wind, published, and graduated. He's doing ok now. This was a lost opportunity. If only he'd ended up in a lab where the adviser had structured everyone so that the incentive was to teach the noob. I know many grad students in the former sitation, and they tend to do barely-ok or drop out. I know a few in the latter situation; they've all gone on to top-tier industry labs or good academic positions. ... or ignore that advice if you're already a mature researcher. I know someone else who worked under an extremely famous adviser. This adviser was always busy and had little time for him. He spent most of his time doing (excellent) work by himself. This worked out because: The fact that his adviser's name appeared on the paper meant that it received immediate and thorough attention. He would come to his adviser with good ideas, and his adviser would often give him the small piece needed to make them truly great (or at least greatly marketable) ideas. In each of his "great" papers, he produced a competent draft, and then his adviser left notes that really pushed it over the line into excellence. His adviser's reputation attracted some of the best students in the world. Most of the students went on to professorships at good, and often great, schools. The lab was structured so that junior students were "advised" by senior students. And so on. At the end, he got a powerful letter of recommendation from his adviser and is now a professor at an Ivy. BUT. This adviser turned A students into A+ students and B students into F students. Students who were not already mature researchers ended up trying to work this out, and failing. Remember that there is no point choosing to go to an environment where skills that you don't have are a prerequisite for success. In most cases, whether an adviser is great is informed by what you want to work on.If  you don't know quite what you want to do, you should usually go  to the bigger school. You'll have more room to settle on things that  you care about, since there will be researchers with diverse expertise  who can advise you. Going to the school with one "great" adviser will limit your amount of local expertise you have access to. Critically, even if they let you work outside their core area, you might still be limited by not knowing the ins-and-outs of publishing in the area, it might be harder to get recognition, and so on. On the other hand, if you do know what you want to work on, going to the smaller school could be a better option. You should remember, though, that the vast majority of grad students change their minds about what they want to work on at some point, so this is not without risk. There are also exceptions. I do know some excellent researchers at smaller schools who throw themselves at their students, and wholeheartedly try to prepare them to be scientists. Their students do seem to succeed. But examples like this are few and far between. You can switch schools if you aren't fitting in, but the opportunity cost is high. One of my undergrad advisers was initially at an extremely prominent CS school. It didn't quite work out, and he switched a smaller school with fewer people to work with. He seems to have done well, because now he is a prof at pseudo-Ivy. This comes at a cost though: your 20's are probably going to be your most productive, least encumbered years. Do not simply sacrifice them to switch schools unless you really want to. Advisers change over their academic life.Professors usually have more time earlier in their academic career, so first students often get more attention. The downside is that they won't always know how to "handle" you. Also they might get denied tenure and be forced to leave. Some professors really do sort of check out and leave their students alone after they get tenure. I personally know people like this. Of course, don't discount someone because of their age. Sometimes advisers get better with practice. Most of these nuances won't be apparent at first glance, so you should do your homework. ConclusionsI could list more, but I think this is a good first-order approximation, and the post is already sort of way too long. What I hope you've taken away from this is: An adviser is only great if they're great for you. You should consider your weaknesses and strengths, and select an adviser that fits them well. Perhaps surprisingly, whether an adviser is great for you is not independent of what work you're interested in, whether you basically know how to be a researcher, and what stage of their career they're in. Remember that you're pouring 3-7 years of your life into this. If you choose poorly, you will pay for it later, possibly at the penalty of years. So don't shirk this duty.

A lot of my friends have gone to grad school. Based on their experiences, it looks like a legendary advisor is slightly better than a merely good advisor, while a bad advisor can outright destroy your academic career no matter how smart/hardworking you are. And from the outside it's very difficult to tell how good a professor is as an advisor. Even if they're outstanding in their field they might be a terrible mentor, or might not have a good network. Based on that, I would recommend going to a school with many good potential advisors as opposed to the one potentially amazing advisor.