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I know it has a lot to do with who is graduating and how many students the professor has already, but I just want to get a feel of how this process works. Do professors take in 1-2 students each year until they don't have any more room? and then wait for some to graduate before taking in more?

Someone I want to work with isn't taking new graduate students next year, and I'm wondering whether that means I need to wait one year or more.

Also, It would be nice if someone had an estimate of what the chances a professor isn't taking new graduate students for any given year.

Thinking about PhD for cognitive psychology/science.

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    Sorry but there's no way we could answer this. It would be different at every school, in every department, and for every professor. – Dave Kanter Jun 22 '16 at 18:24
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    @DaveKaye: I somehow feel it might be possible to answer this question by pointing out possible factors that influence how many new candidates are accepted at a time (which, concerning the factors suggested in the question, boils down to a "no, it is not generally based on these factors for all professors"). – O. R. Mapper Jun 22 '16 at 18:47
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    @DaveKaye, don't understand why such a comment as yours always appears here. Almost all the questions in this forum can be discarded with your reasoning! Answer to OP's question with (1) some sort of data for average no of new students per faculty member (if there is such data for specific university/universities/country/research-areas), (2) anecdotal/observational answer, (3) data from personal experience e.g. own group. One can ask OP to specify specific research area, or ask to generalalize question (not to predict chance his/her preferred prof would take him/her). But why such negativity? – John Jun 22 '16 at 18:51
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    @John: It's not negativity; it's sound advice not to try to give a general answer to questions like this. Even after you do all the work of restricting to some particular subpool of the vastness of all academia, the data / anecdotes / personal experiences won't help you figure out whether/when a particular professor will take more students. Asking them explicitly is better than anything we could possibly say. – Pete L. Clark Jun 22 '16 at 20:06
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    @John: I believe that what you suggest -- suitably scoped -- would be an on-topic question on this site. But the OP was rather explicit about her motivation, and an answer to the sort of statistical question you are interested in is not going to help with her situation. I think it's best to give the best answer for the OP here, and then if you want to ask your question separately, we can apply that same sentiment to you. – Pete L. Clark Jun 22 '16 at 21:06
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There is no way to guess how many students an unknown professor is likely to accept, because professors vary wildly in the number of graduate students that they accept each year. Reasons for this variation include, among others:

  • Amount of funding varies, from professors who are totally broke to professors who need lots of warm bodies to feed into their research machine.
  • Personal taste and scholarly style vary, from some professors who love to be in charge of a big lab with lots of things happening, all the way to others who would prefer to have just an occasional disciple or two.
  • Career and life events vary: a professor about to go on sabbatical may not want to take any new students, while one in the fresh excitement of an opening line of research may want many.
  • Program structure varies, from some programs that admit students almost entirely without reference to professors and the students don't even link up with professors for their first year, all the way to others where the individual professor is almost entirely in charge of admission.

The best way to guess how many students a particular professor is likely to be hiring is to look at the web pages of their students and see when they started their programs. Even that, however, only gives you some indicators about the past, and not the likely near future, given all the sources of variability.

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  • "all the way to others who would prefer to have just an occasional disciple or two" It goes farther: many professors never have PhD students. This includes, of course, the overwhelming majority of faculty members at institutions without grad programs. But it also includes faculty at institutions who do. E.g. here is the webpage listing the mathematical descendants of my thesis advisor (a super-eminent mathematician): genealogy.math.ndsu.nodak.edu/id.php?id=11730. More than half of his 56 students have had no students of their own; this includes more than a few tenured lifers. – Pete L. Clark Jun 22 '16 at 20:02
  • By the way: I agree with your answer, but I think one should also say: better than the best way to guess is to ask the faculty member directly. If they say "Not this/next year" then one can ask about what happens after that. When pressed, most faculty will describe the circumstances surrounding their uncertainty. If they insist on being noncommittal, then that's their answer: they're not committing to the student, so the student should not commit to them. – Pete L. Clark Jun 22 '16 at 20:11
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My personal observations:

There are many different styles based upon which professors search for doctoral candidates, how they prefer to get in touch, how picky they are when choosing doctoral candidates1, and, in general, how much effort they tend to spend to personally guide doctoral candidates in different phases of their projects.

Yet, one thing at least I have almost never witnessed is that a suitable doctoral candidate as well as funding for them is readily available, but the professor decides against accepting them for merely organisational reasons (such as "having too many people to guide at the moment"). Reasons for this may be, but are probably not limited to:

  • The funding is time-bound. With funding that is available in specific amounts per specific timespans, you cannot "save" the money for later. If it is not used now, it is gone.
  • Even worse, the opportunity might be gone in the future. If significant amounts of funding are not used, this can create the impression with some administrations that the respective money is not required and thus it will not be granted again in the next year.
  • Another, unrelated, but common reason is professors have to coordinate a lot more than their personal guidance schedule. Chances are that an open position for a doctoral candidate is a part of a larger project. People in other institutes or other universities or organisations are expecting to start working on the project at a fixed date, and the open position (or even several at a time) need to be filled by then in order for the team to fulfil its contractual duties.

1: This does not mean that anyone will be accepted, but professors have different stances as to how "exceptional" their applicants need to be and how much "shaping of their researcher personality" still has to happen.

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