I just realised that the Molinari, h(m), impact index is really measured in magnitudes...
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
Except if it really were in magnitudes, you'd take the negative logarithm, so higher ranked universities get a lower numbers.
exactly, but the sign is arbitrary, and this way is more confusing and therefore better.
if you really wanted to make it confusing, swap ln for log.
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
Who is the ranking ruler?....probably not a physicst. Rankings are so boring just like politics. Physics works but not for rankings, that's all I have to say!