Frank Benford was a physicist in General Electric’s research laboratory almost a century ago. During that era, data sets were typed or written out by hand. One day, as he was looking through pages and pages filled with numbers, he noticed a fascinating pattern that was consistent across all his voluminous ledgers of work.
First, some background. The “leading digit” of any number is the first digit on the left other than zero. For instance, in the number 8675309, the leading digit is 8, and in the number 42, it’s 4. The numbers 1 through 9 are the nine possible leading digits because 0 is excluded.
People reasonably assume that if you have a page filled with numbers, all of the nine possible leading digits should occur equally, with each one showing up about 11% of the time. However, Benford noticed that in every large list of numbers, the number 1 is by far the most common leading digit.
What Benford discovered – and what has since been confirmed to be correct – is that about 30% of all the numbers in any large data set will have 1 as the leading digit. The number 2 will be the leading digit about 17% of the time, the number 3 about 12% of the time and so forth, with each successive number being less common until you get to 9: by far the least common leading digit, appearing less than 5% of the time.
In 1938, Benford published the Law of Anomalous Numbers, which we now call Benford’s Law. It’s a distribution pattern of leading digits that you expect to see in every large data set of numbers that haven’t been manipulated by a human. That’s why Benford’s Law is such an exceptional tool in rooting out fraud.
Today, forensic accountants scan in the tax returns, financial statements and other transactional data of a business – basically pages with lots of numbers on them – and a computer checks to see whether the leading digits of all those numbers are consistent with the pattern of Benford’s Law. If these “naturally occurring” numbers haven’t been manipulated or fabricated, they will normally fit the pattern. If they don’t, then it’s reasonable to suspect that something fishy may be going on and a deeper investigation is warranted.
In their recent paper “Abiding by the Law? Using Benford’s Law to Examine the Accuracy of Nonprofit Financial Reports,” academic researchers Heng Qu, Richard Steinberg and Ronelle Burger published their findings regarding the first application of Benford’s Law to the tax returns and financial statements of an enormous sampling of charities to see whether any trends were apparent.
The good news is that the financial statements of the nonprofit field as a whole conform to Benford’s Law. In other words, as a group, the numbers of the whole universe of charities do not raise any suspicion. The bad news comes when you look at specific subsets of the data.
“We find close conformity with Benford’s Law for the whole sample, but at the individual organization level, 34% of organizations do not conform,” the researchers wrote.
What immediately jumps out when looking at the research is that charitable work benefits from the involvement of paid professionals. Charities with a paid, professional staff have financial statements that are far more likely to conform to Benford’s Law than those that operate only with volunteers.
“Organizations with paid directors/officers are significantly more conformant by all tests,” the researchers concluded. Further, volunteer-run organizations that pay professional accountants to audit their statements are also far more likely to conform to Benford’s Law. Thus, it behooves charities that deal with significant amounts of money to hire a professional staff person or pay an outside accountant to ensure that funds are being properly handled and protected.
The other significant conclusion to draw is that charities need to be held accountable by an entity that knows how to evaluate their work.
The researchers wrote, “Organizations that receive government grants and those receiving indirect support [such as grants from a community foundation] are significantly more conformant by all tests than those that do not receive these funds.”
Everyone performs better when they are accountable to someone for their performance. Charities that receive support from government agencies and grant-making foundations – and are therefore held accountable by them – are far less likely to have nonconforming financial statements that might raise suspicion.
This column by Bret Bicoy originally appeared in the Peninsula Pulse on March 5, 2021.