Friday, December 28, 2012

The stable state PhD equations

Down in the hall we have a nice poster with faces of all faculty, staff members, postdocs, and grad students. It is not updated too frequently, but overall reflects the structure of the department. A great idea, by the way; each time I forget one of these strange English names people have in this country, I just go down and refresh it in my memory.

But seeing this poster made me ponder on the following: how does this distribution of roles in our department match the career plans of said grad students and postdocs? If our university were the only one in the Universe (or if all other universities followed about the same organizational structure), would this system be sustainable? Like in chemistry, you know, when you have a system of reactions, and you know the kinetic constants for each of them, you can calculate the concentrations, and vice versa. What's about the PhD pyramid?

So, we have about N professors, and about N postdocs working for them, and about 3/2*N aspiring grad students. Assuming (again) that one spends 5 years in grad school, then ~7 years as a postdoc, and ~30 years as a professor, what would be the probability of getting a TT position in a world like that?

Well, the formula is simple: it's just a ratio of the frequency at which new candidates are popping out, and a frequency at which old professors retire. So the total probability, from the grad student point of view, would be: p = N_TT/Time_TT/(N_grad/Time_grad) = 11% . Had the Universe be molded after our department, about half of the candidates would be fired at the grad-school-to-postdoc stage, and then about one fifth of the postdocs would make it from the postdochood to the TT. Which surprisingly perfectly matches my estimations for our field in general! It may be a nice coincidence, or a case of convergent evolution. Or maybe some clever people in the administration consciously try to keep the department about in the middle of the spread (which is usually a wise thing to do).

Still, it's kind of funny. 11% doesn't sound like much at all. That's a competitive field, huh?

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