A calculation called “entropy” can tell us how concentrated the companies are in an industry. Concentration means how large the share is of revenue for the largest company in the industry, that company and the next larges, the two largest and the third, and so on. Specifically, entropy is measured through information described by the shape of the probability distribution of market shares. A higher entropy index describes a large number of participants and represents a lower concentration and consequently higher competition in the industry.
It would be my hypothesis that law departments in lower entropy industries – those dominated by a few companies – would enjoy better benchmarks than law departments in higher entropy industries – those with many companies and no dominant entity.
According to the Journal of Management In Engineering, Jan. 2005 at 19, several alternative indices of entropy gauge industry concentration, including “ogive, national average, portfolio, McLaughlin, and information theory”. However, the article argues, the entropy measure is superior to other measurements in that “entropy can be decomposed into additive elements which define the contribution of diversification at each level of product aggregation to the total”. Accordingly, entropy has frequently been used to measure the degree of industrial concentration and thus competition within an industry.
Even at the firm level, entropy has been employed as a measurement of firm diversification. Some academics argue that the Herfindahl index is a more meaningful measure of industrial concentration, while an entropy measure is more appropriate for corporate diversification.