Did anyone research the data about scientific productivity? I.e. what is the average number of articles written by author in a year in a specific field? I am referring to average, since this is maybe easiest to calculate, but it would be interesting to see the distribution data too. This of course depends on how many journals we want to scope, but I would be interested to see any data on say most popular fields like physics, mathematics, chemistry, biology, psychology, economics, etc (order is of no importance).
A comprehensive review was conducted in the field of psychology in relation to publication rates and tenure. There is also a "fun" review related to beer consumption and publication in the field of avian evolutionary biology.
doi: 10.1111/j.1467-9280.2007.01889.x Psychological Science April 2007 vol. 18 no. 4 283-286
Though this is not a direct answer to your query, this hopes to lead to more productive / useful answers.
See this Wiki article, on Hirsch index or h-index that is a widely accepted measure of
both the productivity and impact of the published work of a scientist or scholar.
The article also points to other indices on scientific/academic productivity and impact in the field.
The SAO/NASA Astrophysics Data System Abstract Service provides a gateway to the online Astronomy and Physics literature. A new interface of the ADS provides a tool to visualize the author and paper networks; that tells you how productive the author is, quantified with the number of collaborators and papers produced.
For e.g. see this link; a search for the name Narlikar. On top of the resulting page, next to Top 200 results, you can see a drop-down menu, on which you can select various options like Author Network, Paper Network etc to get various visualizations.
You can contact the project personnels here http://adsabs.harvard.edu/ . They do conduct studies on bibliographic data, which is one of the measure of academic productivity.
Here is a link to the articles that cite J. E. Hirsch's article - An index to quantify an individual's scientific research output- on h-index via Google Scholar http://scholar.google.com/scholar?q=link:http%3A%2F%2Fwww.pnas.org%2Fcontent%2F102%2F46%2F16569.abstract
In the subject that I am familiar with, political science, there is a recent study using bibliometric data on patterns of publishing in journals - maybe this could be interesting (and might be similar to already mentioned work in other comments): https://www.cambridge.org/core/journals/ps-political-science-and-politics/article/patterns-of-publishing-in-political-science-journals-an-overview-of-our-profession-using-bibliographic-data-and-a-coauthorship-network/D946105595ED2C314AE2A04138F7A5B6
As the authors state:
We drew on more than 67,000 papers published from 1990 to 2013 in one of today’s 96 core journals. The network consists of more than 40,000 authors located worldwide.
and regarding your question, they find this:
Whereas some are highly productive in terms of publications, the majority of authors published only a single paper, which suggests significant turnover in the community.
You should have a closer look at it (although polsci is not in your list of mentioned disciplines)
Papers on coauthorship networks such as Newman (2004) have the descriptive statistics on publication rates in different fields, e.g. publications per person per year.