Here i is summed over five physics sub-specialties with Ni being the number of faculty in that area. Unlike the previously considered linear forms, this formula suggests that there is an optimum balance among the various sub-fields of physics which can be found by differentiating the above formula at fixed total faculty size. The department's perceived quality is then optimized if
The theoretical quality of a program is given here in terms of six variables and seven
The question arises whether there are any simpler functions of the research profile
of a department which give an equally good or better fit with fewer parameters.
The fact that the previous fits show that subatomic physics plays a key role
in the high ranked schools and that smaller departments are more likely to be highly
ranked if they have a larger fraction of subatomic physics suggests that there should
be a simplified fit depending only on these quantities.
We have in fact found the following improved formula
eq. 7This formula has six free parameters (five coefficients and one exponent) and depends on three quantities: NNobel, the number of Nobel laureates on, or recently on, the faculty, Nsub, the number of nuclear and particle physicists (including mathematical physics, cosmology, cosmic rays etc but excluding plasma) and Nother = Ntotal-Nsub. The fit shown here, with six free parameters has a mean absolute fractional discrepancy from the actual NRC assigned qualities of 0.09178.