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Benchmark reports should calculate weighted averages, correctly

Most surveys report average figures, such as the average billing rate of outside counsel or the average number of lawyers per billion of revenue. Most reports calculate their averages by adding each participant’s figure and dividing by the number of participants. That crude average means that law department of two lawyers contributes to the average just as much as does a law department of two hundred lawyers.

A more sophisticated calculation produces a “weighted average.” Depending on how you calculate it, the figure for the two-hundred lawyer department should have something like 100 times as much influence on the weighted average as the figure for the two lawyer department. More specifically, one method multiplies the number of lawyers in a department times the metric you want to weight, sums all those products, and divides by the number of lawyers in the survey group.

Another example of a weighted average is a similar calculation weighted by the revenue of the survey participants. Bigger companies by revenue thereby affect the weighted average more than smaller revenue companies (See my post of Nov. 30, 2005: one way to compute a weighted average; Dec. 31, 2006: a second way to calculate a weighted average; Nov. 25, 2006: weight surveys that cover multiple business components by component revenue; and Feb. 20, 2006: a weighted average for litigation cycle time.). Aside from external benchmark surveys, individual law departments should weight their own data from regions, or law firms, or responsible lawyers.

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One response to “Benchmark reports should calculate weighted averages, correctly”

  1. Dan Williams says:

    Weighted average is a useful tool that both benchmark surveys and individual law departments would greatly benefit from employing. Better yet, I wish benchmarks employed a level of stratification to the data, or at least start breaking out the averages in meaningful compartments such as region or law firm size. I know some benchmarks do the latter, but too few are publicly available to provide meaningful use to the public at large.