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# The “industry” of a company and a way to create an index of diversification with entropy measurements

Mostly for lack of a better way to classify companies, benchmark surveys ask respondents to choose from a list of “industries.”  We see those lists all the time: manufacturing, technology, pharmaceutical, and so on.  In the messy real world, we all realize, companies are not so neatly boxed and defined.  Indeed, almost any company of much size does business in what could be considered more than one industry.

One way to measure diversification and therefore more accurately study the effects of industry on legal staffing and spending would be to make use of an entropy calculation.  The entropy of a company where P is the proportion of firm sales in SIC code i for a firm with N different four-digit SIC business units,

Total entropy = ∑ Piln(1/Pi) with N over the sigma symbol and i=1 underneath.

That formula is a weighted average of the segments’ sales share, the weight for each segment being the logarithm of the inverse of its share. The measure thus takes into consideration two elements of diversification: (1) the number of segments in which a company operates; and (2) the relative importance of each segment in the total sales of the company.

A hypothetical company, called EntropyCo, has two-thirds of its revenue coming from one four-digit SIC code business unit and the other third from a different SIC code business unit.  The total entropy formula would then be .66 times the logarithm of 1/.66 plus .33 times the logarithm of 1/.33.  That equals .278.  A comparable company that earned three quarters of its revenue from one business unit and one quarter from the other would have an entropy figure of .2557, which is lower, as it is less diversified than EntropyCo.

With the tool of entropy, if participants in a benchmark survey were to break down their revenue by more than one industry, the benchmark metrics could be more finely calibrated.

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Take the GC Metrics 2013  survey; https://novisurvey.net/n/GCMetrics2013.aspx.  The no-cost survey asks for 2012 number of lawyers, paralegals, and other staff; inside and external legal spend; and revenue.  You will receive the Winter Release with more than 1,100 law departments.

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