Rankings Magnitudes

I just realised that the Molinari, h(m), impact index is really measured in magnitudes...

No, really!
h(m) = h/N0.4

is clearly a magnitude system - with a sign ambiguity of course, but that is just to confuse the physicists.
So we should work in log[ h(m) ] and set a "ranking modulus" as a natural metric for departmental distances in rank space.

We are of course free to choose our normalisation - I think h(m) = 5 looks about right, put OSU at 10 pc

So: Hm = log(h) - 0.4*log(N) - log(5)

so for tenure faculty only PSU has a

Hm = 1.892 - 1.124 - 0.699 = 0.07

and Caltech is at 0.11 and LSU is at -0.17
much better.


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Except if it really were in magnitudes, you'd take the negative logarithm, so higher ranked universities get a lower numbers.

did anyone ever tell you you are evil?

more importantly, why does impact go like the square of the fifth root of the aggregate number of referee publications?
I could understand if it was simply square root... must be some sort of subtle diminishing return for large N