Are there any numbers on publication rates for different areas of mathematics? For example, I would expect that the average in graph theory is higher than the average in analysis.
I'm hesitating to give this answer, but Italy has researched the question "on average how many papers per year does a professor in a given field publish", and they have made this into a selection criterion for promotions. It's a crazy system, but here is their table, for what it's worth. It will tell you that in mathematical analysis or statistics the average output of a full professor (I fascia) is 10 papers in 10 years, while in mathematical logic it is 5 papers in 10 years.
These are among the lowest rates in the table, if you are in the medical profession the average output can be above 10 publications per year. In my own field, condensed matter physics, I might qualify as an Italian professor with less than 3 papers per year.
This "bean counting" procedure was made into a national law, if you can read Italian it will bring tears to your eyes.