Jan 21

# Mathematical Rule Uncovers Several Hundred Thousand Dollar Fraud

An article recently published in the Wall Street Journal details how “the law of first digits”, also known as Benford’s Law, can uncover fraud.

Benford’s Law, named after a 20th century American physicist, states that in nearly all real-world distributions of numbers the frequency of ones, twos, threes, and so on, in the first digit place is predictable and occur in descending frequency. Simply stated, when looking at a batch of data, there should be more 1’s than 2’s, and more 2’s than 3’s, and so on, with 9’s taking up the smallest percentage of first digits (the probability of occurrence is 30.1% for 1’s, and less than 4% for 9’s). Frank Benford showed this to be true for datasets garnered from everything from natural formations to numbers randomly drawn from magazines to randomly chosen street addresses.

As described by the WSJ, an auditor discovered ongoing embezzlement during a routine audit of a call center using Benford’s law.  The auditor looked for an atypical pattern of first digits in crediting logs to test whether call center operators – able to grant bill credits and refunds for small amounts without a supervisor’s approval – were granting improper credits.

In fact, the percentage of 4’s found in the logs of approximately a dozen operators were significantly higher than the rest of the data and the probability of occurrence set out by Bedford. By no coincidence, bill credits of \$50 or more required a manager’s approval. Further investigation confirmed that a small group of operators had been diverting funds to their friends, family, and other co-conspirators over a number of years, totaling several hundred thousand dollars.

Data analytics and rules such as Benford’s law assist forensic accountants and special purpose auditors in performing investigations to help ensure businesses are treated fairly.  A listing of situations that benefit from applications of forensic accounting and auditing techniques is described here.