Quantifying levels within departments to compare structure

Can a single metric describe different level structures, for instance of three legal groups of 10 lawyers each, where (a) has a GC, four AGCs, and five junior-level lawyers, (b) has a GC, three AGCs, and six juniors, and (c) has a GC and nine direct reports at the same level?  Yes, if you assign a 1 to the GC, a 2 to each lawyer at the next level down – the GC’s direct reports, and a 3 to each of the lawyers at the junior level.  Calculate the average by multiplying the number of lawyers at each level by 1, 2, or 3 and dividing by 10.

Department (a) averages 2.4; (b) averages 2.5, because it has one more junior lawyer and one less AGC and is therefore less flat; while (c) averages 1.9 – the most flat. 

It seems defensible to me to normalize all law departments in a comparison group to a base of ten, and make this calculation.  There will always be one GC, for these purposes, so a 30 lawyer department would divide each level below the GC by three, and then calculate the average the same way.  Larger departments will be less flat, generally, as the AGCs have more lawyers reporting to them than in smaller departments.

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