Benford's Law: A Powerful Tool for Uncovering Fraudulent Financial Transactions

Usually when you tell people that you’re a forensic accountant, you’re met with the same predictable and equally awful response: “So, you count dead peoples’ money?” Well, not exactly. It’s generally followed by something like, “You must be really good at math.” Again, not exactly. Truth be told, forensic accountants rely on calculators and computers.

Generally speaking, think of a forensic accountant as a financial investigator. Most work with attorneys, insurance adjusters, or law enforcement agencies to analyze complex financial matters with the aim of presenting their findings—hopefully in a simplified format—in a litigation setting.

Even among forensic accountants, there is a wide range of specialties, including fraud investigations, economic damages, divorce, valuation, and bankruptcy, to name a few. In the context of fraud, however, there’s an assortment of very effective tools that are used. One favorite is Benford’s Law. To really appreciate it, though, you first must understand its history.

In the late 19th century, Canadian-born mathematician and astronomer Simon Newcomb was leafing through logarithmic tables at his local library when he noticed the early pages were far more worn than later pages. This apparently piqued his interest, and upon further examination, he postulated that in any given data set, early numbers were more prevalent than others. He investigated and found that in most “natural” number sets, the number 1 appears as the first digit more often than higher numbers. Newcomb went on to publish his findings in 1881.

Then, in 1938, U.S. physicist Frank Benford independently came up with roughly the same conclusion, building on it in the process. He noted that the number 1 appears more than number 2, which appears more than number 3 and so on. He then reported that the number 1 appears as the first digit roughly 30 percent of the time, number 2 appears about 18 percent, number 3 about 12 percent, and so on until you get to number 9, which appears at roughly 5 percent. This can be applied to second digits, too, but we’ll keep it simple.

While this works for census data or lengths of rivers, the practical application of this is that accounting data such as sales, receivables, and payables generally follow the same pattern. Take a typical small business, a doctor’s office, for example. It’s a bare-bones operation where the owner is stretched way too thin and the longtime, trusted staff collects co-pays for services in the form of cash, check, or credit charge. Now, the doctor’s office is an auditor’s worst nightmare because it breaks the cardinal rule of separation of duties, which essentially means that no single person should receive payments, write checks, make deposits, reconcile bank statements, and record transactions.

Despite this rule, the doctor allows one person to collect and record payments in the business’s accounting software and even write checks on occasion. Or, worse yet, the same person may log in to the computer under the owner’s ID and enter transactions as if they were the doctor—but that’s an article for another day.

Even though the employee may be the most trustworthy person on the planet, circumstances and opportunity may dictate to what degree that is true. Fraud can start off innocently enough with the employee rationalizing a small “loan” to pay for the kids’ medical bills that they intend to repay quickly. One thing leads to another, and after the trusted employee has been at it for five years, the owner discovers the fraud. Now what?

This is where Benford’s Law can help. One of the analytical tools forensic accountants use is data-mining software, which can take extremely large sets of data and extract patterns. A lot of commercially available data-mining software incorporates Benford’s Law into the programming, which makes it very easy to spot irregularities in those patterns.

If you were to input the doctor’s check register, Benford’s Law would indicate that transactions with the first digit of 1 occur roughly 30 percent of the time, etc. However, if the culprit were paying a fictional vendor, he likely would make up amounts, probably starting small and ramping up over time. These amounts most likely would not be truly random, so the first digit distribution may be skewed toward the higher end with 8s and 9s occurring more frequently while the smaller digits end up underrepresented. The picture begins to take shape, and something doesn’t look right.

The trained eye would be able to spot these irregularities, which point to the transactions that need to be examined. You can pare down the large data set and focus on transactions beginning with the number 9 making it much easier to find, for example, a $9,500 check to a fictional vendor. Suddenly, it becomes a lot easier to find that needle in the haystack. Couple Benford’s Law with digital audit trails, timecards, timelines, genograms, signature analysis, and other tools and that is when patterns start to show up.

Benford’s Law as a forensic accounting tool is truly a blend of the old and the new. The technology keeps advancing allowing us to cast a wider net with greater speed and precision. It is a complement to the best efforts of fraud investigators and attorneys alike and can be a powerful tool. So keep that in mind the next time you’re looking for a needle in the proverbial haystack.