As we have seen, the presence of Nobel prize winners on a physics faculty gives a significant boost to the NRC quality rating. Taking this factor into account allows us to fit the perceived quality to within 9.6% via eq. 5 with seven free parameters or to within 9.2% via eq. 7 with six free parameters. However, although these fits allow us to understand the high rating of the top physics departments, they still systematically underestimate the NRC perceived quality of the next tier (ranks 25 through 40).

    In an attempt to remedy this situation we have identified 122 National Academy of Science members in 30 physics departments using the 1990 physics membership list of the NAS. We have found two simplified formulae using this information that allow a significantly better fit to the second tier schools and that bring the mean absolute deviation from the actual NRC rating of the entire sample of 129 departments to below 9%.     These are:    

Qt = a0 + asubNsub + aotherNother + aNobelNNobel + aNASNNAS 
                                                eq. 8
    In this formula, subatomic stands for particle and nuclear physics and associated specialties but excludes plasma physics. The best fit of the form of eq. 8 is shown in fig. 9 below. The corresponding mean absolute discrepancy is d=0.08494.

   



a01.04365
asub.26563
aother.20499
aNobel.28840
aNAS.31849


This fit suggests that, from the point of view of rank, the optimum ratio of subatomic to other faculty is (.26/.20)2.



             The second fit, which is almost as good, replaces the "subatomic" parameter of eq. 8 by the more restrictive particle physics.    

Qt = a0 + aparticleNparticle + aotherNother + aNobelNNobel + aNASNNAS 
                                                eq. 9
The corresponding mean absolute discrepancy is d=0.08628.

   



a01.13212
apart.19637
aother.23834
aNobel.24906
aNAS.37307


This fit suggests that the optimum ratio of particle physicists to other is (.196/.238)2. This is not inconsistent with the previous fit.




             The fact that the fit using subatomic physics is somewhat better than that referring only to particle physics shows that there is some trade-off value between nuclear and particle physics. A few departments have attained respectable rank by concentrating in nuclear rather than particle physics.

    All of the fits that we have found with mean absolute discrepancies below 20% have a significant intercept value a0. This corresponds to a residual perceived quality for a physics department with zero faculty members. Presumably, in such a physics department, the students learn by reading texts and discussing the concepts with each other. Nevertheless, all the good fits to the NRC data imply a great value to a physics department in having faculty members.

    The fits of eqs. 8 and 9 imply that, for fixed total faculty size, there is an optimum balance that maximizes perceived quality given by

Nsub/Nother = asub2/aother2

and

Nparticle/Nother = aparticle2/aother2

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