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Benford's law

Benford's law, also known as the Newcomb–Benford law, the law of anomalous numbers, or the first-digit law, is an observation that in many real-life sets of numerical data, the leading digit is likely to be small.[1] In sets that obey the law, the number 1 appears as the leading significant digit about 30% of the time, while 9 appears as the leading significant digit less than 5% of the time.

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I remember first hearing about this in the context of detecting tax fraud, years back, and thought that it was fascinating.

Accounting fraud detection

In 1972, Hal Varian suggested that the law could be used to detect possible fraud in lists of socio-economic data submitted in support of public planning decisions. Based on the plausible assumption that people who fabricate figures tend to distribute their digits fairly uniformly, a simple comparison of first-digit frequency distribution from the data with the expected distribution according to Benford's law ought to show up any anomalous results.[33]

Use in criminal trials

In the United States, evidence based on Benford's law has been admitted in criminal cases at the federal, state, and local levels.[34]

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