@BrianRushton regarding the 100 for 1 I'd be curious what do you consider a research position?

Well, I made a math mistake :p. Many jobs on mathjobs.org gets ~600 applicants each. Now, I know that people apply to dozens of jobs, so it's not an accurate count; perhaps there are 10 times as many phds as research positions. And I guess a research position to me would be one where the primary focus of your evaluations for promotion and tenure is your research capability.

@BrianRushton thanks for the clarification. It makes sense now.

and to think he has an account at mathoverflow...