Benford Law

The identification of illegal action is not obvious when a large amount of data has to be processed without data-processing support. The application of Benford’s Law is a way to scan a large amount of data and to identify a digital fingerprint. The identification of a digital fingerprint may indicate irregular processes. Benford’s Law is a practical approach to auditing and controlling to identify forensic accounting.

Frank Albert Benford, Jr., (29 May 1883 Johnstown, Pennsylvania – December 4, 1948) was an American electrical engineer and physicist best known for rediscovering and generalizing Benford's Law, a statistical statement about the occurrence of digits in lists of data. Benford's law, also called the first-digit law, states that in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way. According to this law, the first digit is 1 almost one third of the time, and larger digits occur as the leading digit with lower and lower frequency, to the point where 9 as a first digit occurs less than one time in twenty. This distribution of first digits arises whenever a set of values has logarithms that are distributed uniformly, as is approximately the case with many measurements of real-world values. If examined data unexpectedly shows differences from the distribution stipulated by Benford’s Law, this may indicate abuse when the faulty actor applies the same behavioural template frequently.

Example: The manager of a restaurant noticed frequently the same digits for the total amount of daily income in USD, for example 10724, 9874, 12304 etc. The day data series analysis showed that the final digit 4 appeared by far too frequently. An audit revealed that the chief of staff had put differences in income quite frequently in his own pockets.

This report (PDF-file, 97 KB) shows an example for the application of Benford’s Law inside the the administration of the canton of Berne, Switzerland.

This Excel-Spreadsheet (XLS-file, 222 KB) provides more detailed data to show the usefulness of Benford’s Law.