ronburgundy
Contributor
It's really hard to find accurate data on the number of PhDs supervised by the average professor. Here's some data (about 200,000 total records) in Math (about 1500 PhDs per year in the US), from http://genealogy.math.ndsu.nodak.edu/extrema.php (Note: math PhDs, not rigorously collected, data incomplete, ancient scholars included, double counts dual advisors, etc)
About 76% of math PhDs never supervise a doctoral student. Many permanently adjunct, leave academia or take jobs at schools that do not offer a PhD. Only 14% advise more than one student (above replacement).
Median Ph.D. students advised: 0
Mean Ph.D. students advised: 1.06
I suspect the numbers are a bit different for other fields, especially lab sciences. However, the general rule seems to indicate large amounts of attrition - most PhDs don't end up teaching PhDs. That does not necessarily mean that we have suddenly started graduating too many PhDs - the mean replacement rate is still pretty close to 1.
Other data:
AMS Report on Recruitment and Hiring
AMS Report on New Doctoral Recipients
Per professor analyses aren't very informative. What matters is the system wide number of Graduates produced in the discipline. Clearly it is way too many in any discipline where there are tons of graduates scrounging for $10 per hour adjunct jobs.
The extent of the adjunct problem (too many with too little pay) varies greatly by discipline. Discipline's with few or already well paid adjuncts wouldn't be impacted by changes like those I mentioned. Where it isn't a problem is where the grad student numbers are close the the full time job prospect numbers. Some disciplines have more non-academic job possibilities (e.g., math and hard sciences), so they can have more grad students without creating a glut of people with no use for their degree other than being an underpaid adjunct. Some disciplines have more of the undergrad population taking their courses, so they admit grad students as a form of teaching assistant, not caring whether their are any jobs for them later. That part of the problem needs to be solved by using other people like advanced undergrads as teaching assistants who are not in it as a stepping stone to a Ph.D. in that field.