Metrics that conform to power laws are all around us as they appear to be a fundamental property of many things. The populations of cities, for example, are distributed according to a power law. There are a few extremely large cities, more average-size cities and very many smaller towns. If you’ve ever heard people refer to the “long tail,” this is what they’re referring to: the familiar spread of lots of very small instances of some things, like sales of books or numbers of DVD rentals.
Power-law relationships describe mathematically the frequency of events according to their size or severity, such as how often earthquakes of different Richter-scale magnitudes happen. As an everyday example, the — the most used word in English — occurs about twice as often as of (second place), about three times as often as and (third) and so on. Word frequency in English exhibits a power-law distribution.
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