Tuesday, June 21, 2011

More magic numbers


I was alerted to some interesting work by a recent report in the IoP's Physics World magazine. Researchers have finally worked out that there is, in fact, a correlation between group size and quality of research.
The paper (available on arxiv and published in Scientometrics, which is apparently the research of... research) took information from a survey of UK universities (and a few French) and determined the "quality vs quantity" of the research output (the "quality" metric is described in more detail in the paper, but it is essentially the same metric used to determine how much federal funding the researcher gets). This was parameterized (fit mathematically) via a complex system model and something unusual popped out: the model predicted so-called "magic numbers" - at which a research group gets the best return on investment, so to speak. Above this magic number, or critical mass (if you prefer), the group begins to fragment, as is demonstrated in Figure 2 of the paper:

A table of all of the different scientific research areas and the model's predicted "magic number" for that subject is shown below:

Pure mathematics has the lowest magic number (less than 2, a traditionally "every man for himself" kind of field), and one sub-branch of computer science the largest (almost 25, with "business and management" a close second at 24).
Everyone knows anecdotally that, though a trend doesn't necessarily indicate ubiquity, it is true that at a certain point, when a group gets too large, not everyone in the group will be carrying weight and the quality of the research done (per person) goes down. It's fascinating to see this generalization plotted and put to a statistical analysis. As one of the study's authors remarked, he would consider using these results in putting together a research department from scratch.
And, of course, I'd say our group (my last paper had 15 coauthors) is just the right size.


Kenna, R., & Berche, B. (2010). Critical mass and the dependency of research quality on group size Scientometrics, 86 (2), 527-540 DOI: 10.1007/s11192-010-0282-9


  1. Very interesting!

    So the magic number for composers is one, right?

  2. Well, of course!
    While research, presumably objective in nature, can (and should) require input from multiple parties to ensure that it is thorough and impartial, music and the arts can exist subjectively, the experience of one person being shared with - but not tempered by - others. It stands to reason that artists work alone :-)


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