Definition
Benford's law describes the expected frequency of leading digits in many real-world data sets that span several orders of magnitude. The probability of leading digit d is the base-10 logarithm of (1 + 1/d). That gives 30.1 percent for 1, 17.6 percent for 2, and about 4.6 percent for 9. Frank Benford published the pattern in 1938, and it has since been applied to accounting data.
Why it matters in an audit or review
A digit test is a screening tool. A departure from the expected pattern does not show fraud. It suggests a population to look at, such as invoices set just under an approval limit. The test is weak for data with assigned numbers, narrow ranges or few items.
Example
Illustrative: 2,000 vendor invoices. Digit 1 is expected in 2,000 x 0.301 = 602 invoices. Observed: 410. The shortfall of 192 is large, so the team reviews the digit 4 and 5 clusters just under a $5,000 approval limit.
Common mistakes
- Running the test on check numbers or other assigned numbers.
- Treating a deviation as proof of fraud rather than a lead.
Sources
- Benford, F., The Law of Anomalous Numbers, Proceedings of the American Philosophical Society, 1938
- Nigrini, M., Benford's Law: Applications for Forensic Accounting, Auditing, and Fraud Detection (Wiley, 2012)
- AICPA, AU-C Section 520, Analytical Procedures
Definitions paraphrase AICPA and FASB guidance; read the standard itself before relying on a requirement. Example figures are illustrative. This page is guidance, not professional advice. Report an error