Benford's Law

Benford's law describes an observed pattern in the frequency of leading digits within many large collections of naturally occurring numerical data, stating that the digit 1 appears as the first digit of a number roughly 30 percent of the time, far more often than would be expected if all digits were equally likely, with the expected frequency decreasing progressively as the leading digit increases up to the digit 9. The pattern was first noted by astronomer Simon Newcomb in an 1881 paper, after he observed that printed logarithm tables in shared reference books were noticeably more worn on the earlier pages, corresponding to numbers beginning with the digit 1. The law was independently rediscovered and documented far more thoroughly by physicist Frank Benford in a 1938 paper testing the pattern across a wide range of unrelated datasets, from river drainage areas to death rates, and it now carries his name. Benford's law has found a significant practical application in forensic accounting and fraud detection, since genuine, naturally accumulated financial figures tend to follow the expected leading-digit distribution while numbers that have been deliberately fabricated by a person typically do not, making departures from the expected pattern a useful signal for flagging data worth closer investigation.