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Fractals, power laws, bell curves and soaring litigation costs

The term “fractal” describes nature where small parts resemble the whole, such as a bay’s indentations resembling those of a long shore line (Fortune, July 11, 2005 at 99-100). The pattern of invoices arriving at a law department in a month looks like the quarterly pattern and the latter looks like the annual pattern. The hours clocked in a month by a law department’s lawyers look similar in distribution to those logged during a quarter or a year.

The smaller parts often relate to the larger groups according to what’s called a “power law.” (See my post of July 25, 2005 on power laws.) A power-law distribution implies, for example, that the likelihood of a lawsuit that costs $1 million can be predicted from the frequency of lawsuits costing $500,000, and that the same ratio applies to $250,000 cases. Often, each level higher is one fourth less common.

Bell curve thinking (See my post of Oct. 24, 2005 on its usefulness to law department managers.) demotes the impact of major events, because they are far out on the tail and deemed so unlikely. Power-law thinking reminds us that big hits – while certainly less likely than run-of-the-mill legal expenses – remain a real and calculable possibility.

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