Sam was the ideal employee at the manufacturing plant. He worked overtime, needed minimal supervision, was congenial, and often did favors for his colleagues. But behind the façade, he and two others pocketed more than $100,000 from a plant fund in a 10-year period. Sam’s crime could have been caught much earlier if a fraud examiner had used both a mathematical theorem called Benford’s Law and a software program found on most personal computers today.

In the April/May 1994 issue of The White Paper, Mark J. Nigrini, Ph.D., presented a novel analytical method of detecting numerical anomalies that could indicate fraudulent activity. Using Benford’s Law, the method involves finding a pattern in the frequency of digits in a list of figures, beginning from the far-left digit in a figure. As he wrote in the article, digital frequencies refer to the proportion of numbers that have a 1, 2, ¦ 9 as a first digit, and the proportion of numbers that have a 0, 1, ¦ 9 as a second, third, and so forth digit.

The Failure of Common Sense

What are the chances that the first digit of a multi-digit number in a list or table will be nine? Many may assume that the odds are one in nine. Intuitively, we may believe that numbers in large lists are composed of random digits, each having an equal chance of appearance. Unfortunately, sometimes common sense fails us.