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I recently saw this infogram circling around various social networks:

enter image description here

It appeared in this Tweet with the following claim:

Got a PhD? Your chance of becoming a Professor is 0.45%. Good luck.

Being a bit sceptical of the claim and of shiny info-grams in general, I traced the image back through this blog to this report by the Royal Society (see page 14), featuring various reputable academics in the introduction. The report cites a number of other reports from UK organisations as its source (I did not dig deeper). The infogram seemingly pertains to graduates of PhDs in the UK in STEM fields.

I find the figures literally incredible. I cannot believe them. Fewer than 1-in-200 PhD graduates become professors? This would imply, for example, that STEM professors in the UK would need to graduate 200 PhD students just to "repopulate" themselves.

I would like to compare these estimates with figures sourced elsewhere. And so my question is:

Are any other studies or sources of data for estimating the number of PhD graduates who end up with professorships? (... preferably within the STEM areas and not restricted to the UK)


There is a related question specifically for the maths field and referring to tenure-track positions but none of the answers really address this question: What percentage of phds in math actually get a tenure track academic job?

EDIT: Pointer to a follow-up question asked by @gerrit: How many PhD students does a typical STEM professor graduate during their entire career?

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You're right: the 0.45% figure is literally incredible. I did some "Fermi problem" type calculations and came up with the idea that in mathematics about 20% of PhDs get tenure at a research institution (also Gerald Edgar mentioned this figure on mathoverflow.net) and that maybe 30-40% get tenure at some institution: this is in the US. In other STEM fields there are more industrial jobs, but I would be shocked if the average figure for STEM PhDs in the US were below 10%. (I don't include this as an answer because you want more formalized analysis, not guesswork...) –  Pete L. Clark Feb 26 at 6:57
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A major question here is what "Professor" is supposed to mean --- academic titles in the UK work differently than in the US. Being a full professor in the UK is similar to having an endowed chair in the US, which very few US scientists ever reach. –  Mark Meckes Feb 26 at 8:03
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Furthermore, I believe (though I'm not certain) that many (maybe most?) full-time, researching, career academics in the UK never hold any position with the word "professor" in the title. This is totally different from the US, where all tenure-track positions (and some non-tenure-track positions) are called some flavor of "professor". –  Mark Meckes Feb 26 at 8:06
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Indeed it is not at all unusual in the UK to go through one's entire academic career without ever attaining the title 'professor'. I'm not sure professorships in the UK are as rare as endowed chairs in the US, though. In my department (in Scotland) 1/3 of the permanent staff are currently professors. –  Tara B Feb 26 at 11:12
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If a professor works for 30 years (say ages 40-70) and the situation is steady-state, a 1:200 ratio would require a professor to graduate 6-7 PhD students per year. That seems like a lot. –  gerrit Feb 26 at 19:06
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4 Answers

up vote 10 down vote accepted
+50

Just looked up some numbers for Germany:

  • In 2013, 8700 PhDs were finished in maths/natural sciences.

  • average age at finishing (all fields): 32.5 a

  • average age at becoming professor (maths/natural sciences): 40.5 a

  • predicted number of retiring professors in 2021 = in 8 years = when last year's fresh PhDs reach the average age of becoming professor
    (maths/natural sciences): ca. 190

190 : 8700 ≈ 1 : 46 or 2.2 %

Some of the tables show only overall numbers, and no details for maths. But I think that this result is influenced by the fact that the majority of chemistry and biology students go on for a PhD (though I guess that a non-negligible fraction leaves for industry [slightly] before finishing the PhD - which after all may not be that different from doing a PhD in order to get a better entrance position in industry).

Sources: Statistisches Bundesamt

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So this ignores the fact that the number of overall tenured positions available will probably grow in the next 8 years? –  Federico Poloni Mar 3 at 21:02
    
Interesting sources (I don't read German but this looks more like what I'm asking for, thanks!) but I don't yet follow your math. Assuming that the number of tenured positions remains the same and the rates of PhDs and retirements remain the same, and that it's a closed system (i.e., no foreign professors), we have 8700 PhDs produced in one year and ⌊190/8⌋ = 23 professorial spaces likewise in one year. So that would make it 23 : 8700, no? Not sure why you took PhDs for 1 year and professors for 8 (even if graduates take 8 years, there'll be 8 sets of graduates in that time). –  badroit Mar 4 at 14:34
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@badroit: no. I see now that my formulation was ambiguous and tried to clear it up. In 2021 (= in 8 years), 190 maths + natural sciences profs are expected to retire. –  cbeleites Mar 4 at 15:17
    
@FedericoPoloni: this ignores any predictions whether new professorships will be started (which is something I wouldn't dare to predict 8 years into the future, not even for Germany). But it does include the fact that in 2021 more professors will retire than do right now (at the moment it is ca. 150/a) - which is much easier to predict as long as the retirement age doesn't change too much. –  cbeleites Mar 4 at 16:21
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@cbeleites, understood, thanks for the clarification! –  badroit Mar 4 at 17:40
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It's a shiny info-gram, but I think there is a lot wrong with it:

  • It transports the (common) misconception that the 53% leaving to industry after their PhD are sort of failed professors. At least in CS, and probably a lot of other STEM fields as well, many PhD students start with the full intention of leaving academia sometime. Hence, the better question the diagram should be asking is How many of those that want to become professors actually do?. Basically, I could come up with similar low percentages for every field. Let's say less than 1% of all working population of a city works in supermarkets. Does that mean that supermarket jobs are horribly hard to break into? No, because most people do not have the career goal of working in a supermarket in the first place.
  • Similarly for the 17% non-university research. In CS, good industry labs (like the ones at IBM or Microsoft) are preferable options for many researchers, so they would not take a professorship even if offered.
  • As already stated by commenters above, the title professor means different things in different places. In Austria, for instance, many high school teachers are officially "professors" (tenured even), despite not having a PhD or ever doing research. In Great Britain, very few people are professors (most are lecturers or senior lecturers). In Madrid I know an academic research lab (not affiliated with a university) that calls their staff members research professors. Job titles are almost never clear-cut.

That being said, I do think that there is a problem. If we assume a reasonably stable system (number of professors in a discipline stays more or less constant), then every tenured professor is in average allowed to see one of her/his students through to also become a tenured professor. Given that many tenured professors (at least here in Europe) maintain groups of 15+ PhD students at a time, I is pretty obvious even without digging into the data too much that the job market for professors is insanely competitive (which, incidentally, captures my personal experience hunting for tenure-track positions pretty well).

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I have seen this graph in Physics Today, and would like to come to the defence of the authors: all your caveats were pointed out in full in the caption accompanying the graph. –  gerrit Feb 26 at 18:56
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Correction: It was Physics World, not Physics Today. –  gerrit Feb 26 at 19:27
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Coming from a field and country (chemistry/Germany) where the normal thing to do if you want a job in industry is to do a PhD (of course also if you want to stay in academia, but essentially here > 90 % of the graduating students go on with a PhD) I very much agree with the first point. Note also that this inflates the denominator of the fraction, making the fraction smaller compared to other fields where a PhD essentially means that you aim at a professorship. (The diagram would show this if it started with undergrad students: the main stream would just go all the way BSc -> MSc -> PhD) –  cbeleites Mar 3 at 19:01
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An article in Physics World has more information, and appears to be the source of the figure in question (I'm not entirely sure if it is the original source, as the article draws it data from elsewhere). The article is available to subscribers, and the full citation is:

  • Harris, Margaret. "The academic pyramid." Physics World 25, no. 10 (2012): 54-57.

It appears to be presently mirrored here, and my information is drawn from the mirror. It answers some questions on data sources that were lost when the image got its own life without proper context. Data are for STEM fields, and are relevant for the United Kingdom. The figure caption reads:

Transition points in typical academic scientific careers following a PhD. Based on data from the Higher Education Funding Council for England, the Research Base Funders Forum and the Higher Education Statistics Agency’s annual “Destinations of leavers from higher education” survey.

Furthermore, the article states:

Statistics suggest that the vast majority of people who complete science PhDs will never obtain a permanent academic post. This is vividly illustrated in a diagram published in 2010 by the Royal Society as part of a report on the future of scientific careers in the UK (figure 1). Drawing on data from various UK sources, the diagram follows a “typical academic career” through a series of post- PhD transition points, when large numbers of people leave the university environment for careers in, say, government or industrial research. These data show that less than 0.5% of science PhD students will ever become full professors, while just 3.5% will obtain lower-ranking permanent positions as research staff at universities.

For physicists, that 3.5% figure is probably a little low. Slightly older data collected by the Institute of Physics and the US National Science Foundation suggest that the fraction of physics PhD students who obtain permanent academic jobs has historically hovered between 10 and 20%.

(...) But many more do want to stay in academia:

Indeed, according to an August 2012 survey carried out by the American Institute of Physics (AIP), nearly half (46%) of new physics PhD stu- dents at US institutions want to work in a university. The next most popular career plan among those surveyed, attracting 18% of responses, was “unsure”.

For more information, the article points to the UK group Vitae, UK science advocacy group Science is Vital, and the US NSF Statistics page.

So, for physics, it appears between ¼–½ of PhD students who want to get permanent academic positions, ultimately succeed in doing so. That's a quite different figure than 0.5% (but still problematic, as the article discusses in some detail).

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The statistic in your second quote is for new PhD students, though. Other statistics I have seen (I think for mathematics, but possibly for all subjects, in the UK) show that the proportion of PhD students intending to pursue an academic career drops off considerably later in the PhD. –  Tara B Feb 28 at 14:12
    
@TaraB That may be because they realise the poor opportunities. One could argue that the observation at the start is more appropriate, as it's more independent of probability of succeeding. –  gerrit Feb 28 at 15:24
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Under stable situation, this probably can always be approximated by dividing the number of professor positions by the number of the PhD student positions, and normally makes numbers below 10 %. Same way you can calculate your chances of getting any other reputable, sufficiently well paid position below professor.

Apart lots of hard work, making to professors also requires a great deal of success. Counting on this is same as counting on getting a gold medal in Olympics: somebody does, but if this is the only your reason to participate, be ready for disappointments.

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In the US, only a minority of "tenured professors" work in departments which grant PhDs: I would guess probably 1/3. Is it similar in Europe? (I would guess not so much.) I mention this as a possible explanation for why my percentages (which are US-centric, because that's what I know and have data for) are different from yours. –  Pete L. Clark Feb 26 at 14:49
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Then multiply the number of professors positions by the factor you assume before calculating the proportion. In Europe, "professor" is normally a very highly ranked position in a university or the like. –  Audrius Meškauskas Feb 26 at 16:16
    
Audrius: Okay, good. That brings our calculations/estimates in line then. –  Pete L. Clark Feb 26 at 17:13
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