Benford's Law

Benford's Law states that in many naturally occurring datasets, the leading digit is not uniformly distributed — the digit 1 appears as the first digit about 30% of the time, while 9 appears less than 5%. This counterintuitive pattern holds across city populations, financial data, physical constants, and election results. The law emerges because many real-world quantities grow multiplicatively, and logarithmic distributions concentrate more values at smaller leading digits. As a detection tool, Benford's Law is powerful: datasets that should follow the distribution but don't may indicate fabrication, manipulation, or error. It's a forensic lens for data integrity.

When evaluating any large, naturally occurring dataset — financial records, user metrics, operational data — check whether the leading digits follow Benford's expected distribution. Deviations don't prove fraud but raise a flag worth investigating. The law applies best to datasets that span multiple orders of magnitude and are not artificially constrained. It's a first-pass anomaly detector, not a definitive test.

Benford's Law predicts that leading digits in natural datasets follow a logarithmic distribution. Deviations signal potential fabrication or error. It's a low-cost forensic tool for data integrity — a first-pass anomaly detector.