Thursday, December 11, 2014

Fighting Fraud with Mathematical Weapons

According to a Wall Street Journal article, forensic accountants recently uncovered a several hundred thousand dollar fraud committed by employees at a national call center simply by “wielding mathematical weapons.” Using data analysis, they were able to identify a number of fraudulent refunds that call center employees were issuing. The find was critical to the company as it helped them discover where they were losing a lot of money.

Benford's Law
The forensic accountants who detected the fraud at the call center used a mathematical test known as Benford’s Law. Contrary to popular belief that there should be an even distribution in the starting digits of numbers, Benford’s Law says that “more numbers start with one than any other digit, followed by those that begin with two, then three, and so on,” and that “ones should account for 30% of leading digits, and each successive number should represent a progressively smaller proportion, with nines coming last, at under 5%.” In the case of the call center, the forensic team noticed an exceptionally large percentage of refund amounts where the starting digit was a four. It also happened to be that employees could issue refunds to customers up to $50 without needing additional supervision. By using Benford’s Law and investigating the transactions where the leading digit was a four, forensic accountants discovered a small number of operators at the call center “who had issued fraudulent refunds to themselves, friends and family totaling several hundred thousand dollars.”

At first you might think that fraudsters could learn about Benford’s Law and then make sure that their fraud doesn’t violate any of the statistical properties that the law says should be present. However, Mark J. Nigrini, accounting professor at West Virginia University, says that “while you are doing your scheme, you don't know what the data look like. It's a little tricky to beat Benford's.” With employee fraud costing companies throughout the country around $300 billion each year, data analysis is becoming more and more common among auditors and forensic teams, and it is becoming much more difficult for people to commit a fraud in such a way that data analysis can’t detect the fraud. As data analysis continues to improve, I think we will see more and more frauds uncovered that in the past could be hidden from a human but now can’t be concealed from the math.

See this link for an article in The Journal of Accountancy that Mark J. Nigrini wrote about Benford’s Law.


  1. What do you think this type of mathematical analysis could tell investigators about the herbalife MLM? Do the SEC and FTC conduct these kinds of forensic audits?