Does it hurt the professor's career in any way if their students drop out? Assume a PhD student gets the professor's funding and publishes an adequate amount of papers. They then decide to quit (maybe with a master's). What benefit is it to the professor for the student to continue working?
Professors seem to be concerned about taking students who might not survive the entire program, but I don't see what the problem is.
For reference, I am particularly interested in the USA within CS.
EDIT: I am in the UK, and therefore my answer is relevant to there. Things may be different in the US, although I'll note that others have stated that student graduation rate is a performance metric there as well
I am a bit hesitant to answer this because I guess the answer might put people off making a decision that is the correct decision for them, but honesty is always best, so the answer is yes, it can hurt a supervisor for their students to leave.
Where I am, the % of students who submit a thesis within time limit is a key metric on which an academic is judged. One reason for this is that government funding for PhD programs requires that submissions within time limit are above a certain threshold. This is also the reason that many universities will not initially register a student for a PhD, but will require the students to undergo a confirmation review after a year - if the student is dismissed at this point, it doesn't count against the department, but after this it does.
An academic will probably not suffer too much from a single student not completing in time (although yes, they will lose the right to say "my graduation rate is perfect" on a promotion case or job application). More than one and questions will definitely be asked, and that PI might start to find it more and more difficult to win the right to recruit students.
However, none of this should affect a student's decision as to whether continuing a PhD is right for them or not, and the damage done to a student staying in a programme when it is not right for them massively out-weighs the damage done to the supervisor if they leave.
That would depend on the reasons that students drop out. Some will do so for health and family reasons. Some leave because they have decided to follow a different path. None of that reflects on the advisor.
But if students (plural) drop out alleging abuse by the advisor, personal or professional, then it certainly should reflect badly, though some get away with bad behavior for a long time.
In addition to the existing answers: inevitably, PhD students tend to require more input from their supervisor in the first half of their programme, and then gradually become increasingly independent towards the end. Conversely, outputs and impact tend to be low in the first half of a programme, and increase towards the end. A student who leaves half-way through may therefore have consumed considerable amounts of the supervisor's intellectual resources (time, energy, ideas) but not yet delivered the anticipated payoffs (papers, impact). This is undoubtedly a negative from the supervisor's perspective.
I think the answer is yes, it will hurt a bit. This is mostly because it is good for a professor to have a record of graduating a high proportion of graduate students they take on, and anyone who leaves without their degree reduces this proportion to some extent.
It is true that the reasons for the student leaving matter, particularly in terms of the evaluation of the professor by their existing department. However, if a professor applies for an external role, one of the things they are going to do is to give information on their experience supervising graduate students, and the proportion of students who make it to successful completion is going to be a rough proxy measure for outside universities to evaluate their success. In an academic job application, it is much better to be able to say "95%+ of my graduate research students have successfully completed their programs" than to only be able to say "20% of my graduate research students have successfully completed their programs, but here are the reasons this wasn't my fault".
In regard to this issue, you should bear in mind that successful graduation of graduate research students is one metric that universities use to evaluate the success of their higher-degree programs. In some countries (e.g., Australia) it is also a metric that directly affects government funding of the university, and so the university has a financial reason to care about this. Since it is important to the universities, there is always some pressure on professors to do a good job in this regard, and a student drop-out will usually have some negative effect even if it occurs for reasons beyond the professor's control.
It should but it doesn't.
High drop-out rates, high past the time limit (normally 3 years in UK/IRL) and not infrequent way-past-time-limit (a PhD put in 5 - 11 years after commencement) seem to have no effect on research council, university or private grant absorption. This is provided the HoD and/or PI are "connected" and shameless enough to maintain a healthy application rate, "timely" (i.e. inside knowledge from colleagues on national or EURAM research boards) applications plus a certain skill at phrasing technological concepts in colloquial language and flattering presentation hosts.
Of course, there are practical and financial reasons to avoid a student who is felt to be unsure in character if not in commitment: additional RA support enlisted to help in that side of the work remain on the university payroll, allocation of expensive instrument time and/or consumable materials plus disappointment at failing industry supporters are all good reasons in themselves for supervisor diffidence. Supervisors don't want wasted effort investment of their own in not fully committed PhDs, as well as a human desire to avoid any association with failure.
When a death of a PhD or particularly a fellow occurs, it's a scramble around the research group to find someone capable and willing to finish off the project committed to. No doubt it puts the PI under a compliment to that fellow/staff-member also.
If you are gauging your professor's caution towards taking on any applicant by attitudes, airs and gestures, please also make allowance for some academics capacity to dramatize.
If a student drops out (or is forced to leave!), and the student's work is in such shape that there is no recovering it for publication, and the next student cannot simply pick up where that student left off, than the mentor has sunk time into wasted effort. This is true regardless of the reason the student left. You do this too often, and it will hinder a career.
If students periodically end up leaving a mentors group, then that mentor may develop a reputation for not being able to get his students through their research programs, and that will not help in future recruitment efforts.
I'd like to add to the main point in Ben's and Ian Sudbery's: yes, for the reasons they both discuss, it can hurt an academic, and especially an academic at the start of their career.
It takes a while for a new academic to be able to say "I have supervised a PhD student to completion" -- a year or more to obtain funding, several months to hire a good candidate, and then 3-5 years (depending on the country; I know you asked about the US but most of my experience is in Europe and the UK) until completion.
And while I'm not sure this is a formal requirement for a promotion/career advancement in the US, certainly some European systems will explicitly require that an academic has supervised a number of PhD students to completion, so I would assume it is an important factor in the US.
Early career researchers (and in general, academics in more postdoc-oriented systems such as the UK) will rarely have PhD students "lined up" one after the other. So if the first or second PhD student of a supervisor drops out of the programme, it might add a couple of years before the academic will be able to claim they supervised a PhD student to completion (which is often needed for career advancement, as well as grants certain advisory/supervisory independence to the academic).
A student dropping out or the professor categorically failing that student will absolutely not hurt the professor, as there is no mechanism for that to happen. Of course, this will give the department something to spread rumors about, but there are no consequences. There are no written policies to punish professors for not ensuring success.
There is only one universal truth: funding.
A PhD student dropping from a program will not have any affect whatsoever on that professor's ability to gain funding, and as a result, there are absolutely no negative consequences. That professor is infinitely more valuable and visible to that department than is the student. The 'last man standing' is the professor, and the student will get flushed down the drain. The professor can then say or do anything to justify why that student wasnt able to perform. God forbid they take any responsibility, because that would inevitably involve a failure on behalf of the entire department. That is not realistic. The student is at fault. period.
Success is rewarded. Failure is externalized.
