Beyond ranking law departments on a metric: show differences from average or show scaling

Sometimes you want to compare companies on metrics that vary widely. As an example, patent applications granted during a year for a group of companies may vary from five to fifty. The external legal spend of those same companies may vary from $750,000 to $6 million. You can rank each company from high to low on patents and then on spend and find that company A is number 5 on patents and number 8 on spending. Thus, company A is somewhat “better” on patents than spending because it was higher on the ranking.

But ranking eliminates most of the data that could more finely discriminate the companies from each other. That company A ranked number 1 on patents merely says it is two positions ahead of company C ranked number 3. You’ve lost the actual difference between them. In fact, perhaps company A had three times as many patent applications granted than company C. Being fixed intervals, ranks lose information.

A method to preserve the granularity of data is to calculate how each company’s figure varies from the average figure for the group. Company A then might be 500% of the average while company C might be 150% (or approximately like that). At least that listing gives some idea of the size of the gaps between companies.

A third method used by data analysts is called “scaling”. When you scale numbers you translate each of them into its standard deviation from the average of the set. Thus a firm that was one positive standard deviation on patents granted is similarly situated by this transformation to a company that is one positive standard deviation on external legal spend. And, companies can be compared within a set of metrics with precision.

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