A finding from a researcher working at General Electric in the 1930s can help today’s accounts payable professionals ferret out fraud. Benford’s Law is named for Frank Benford, the GE physicist who tested and publicized the theory; it’s sometimes called the first-digit or leading-digit law. It holds that in many, (albeit not all) lists of numbers, about 30 percent will start with the number one, about 18 percent with the number two, and only 5 percent will start with either eight or nine. (While the law is named for Benford, he actually wasn’t the first to note this phenomenon. Simon Newcomb, an astronomer, wrote about it in the 1800s, although his research was largely ignored.)
Of course, this seems completely counter-intuitive. Most of us would guess that in any group of numbers, every digit would show up first about every one out of nine times, or 11 percent of the time. As Benford discovered, that’s not the case. Instead, the probability (P) that the first digit is a specific number, D, can be calculated with the following formula: PD = log10 (1 + 1/D). The probability that a specific digit is first is highest for 1, and declines from there.
Benford’s law can be applied within accounts payable to help track down instances of fraud. Here’s why: when someone tries to submit phony invoices, the tendency is to include an excess of numbers that begin with digits other than one or two. Software programs can be designed to flag transactions if many of the totals start with higher digits.
That’s not to say that Benford’s law will apply to any set of numbers, as this study by Cindy Durtschi at Utah State University and two co-authors point out. For instance, it doesn’t work with numbers that have been assigned, such as zip codes. The law is more likely to work when the numbers studied are the result of a combination of numbers – say, invoice totals that are the product of a quantity of items and their prices.
And, of course, not all sets of invoice totals that fail to follow Benford’s law mean that someone’s been ripping off the company. However, the theory is one more tool an AP manager can use to analyze the accounts.