Amanda J. Bernard, CPA, CFE, CMA
Principal, Maillie LLP
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Benford’s Law is a mathematical theory of leading digits, meant specifically for real-life numerical data sets distributed in a non-uniform way. The theory is based on probability of occurrences. A logical assumption seems to be that each number, 1-9, would appear as the leading digit of a number consistently at 11.1% (or 1/9) of the time. However, Benford’s Law actually states the number 1 will appear as the first digit of a number about 30% of the time, while the larger digits occur in the first position less frequently, with 9 appearing as the first digit less than 5% of the time.
Why does it work? Believe it or not, there is a certain logic behind Benford’s Law. A number that begins with 1 needs to increase by 100% to become a 2, while a number that begins with 5 needs to increase by only 20% to become a 6, and a number that begins with 8 needs to increase by only 12.5% to become a 9, and so on.
The history of Benford’s Law dates back as far as 1881; the phenomenon was then made popular in 1938 by the physicist Frank Benford after he tested it on data sets from 20 different domains, including surface areas of rivers, population sizes, molecular weights, numbers contained in Reader’s Digest, street addresses, and death rates. Today, Benford’s Law is used to detect possible red flags of fraud in financial and other data based on the assumption that people who make up numbers tend to distribute their digits fairly uniformly. The made-up figures simply do not follow the expected Benford’s distribution.
An example of fraud that can be easily detected using Benford’s Law is avoidance of purchase approval policies. One method used to avoid obtaining approval on a purchase transaction is to make sure the cost does not exceed the established threshold requiring approval by splitting larger transactions into multiple smaller ones. For example, if the threshold for approval is $5,000 and the expense data shows a spike in transactions beginning with the number 4, it could indicate someone is avoiding the organization’s purchase approval procedures.
Other data sets where Benford’s Law is especially useful include credit card transactions, customer balances and refunds, vendor disbursements, purchase orders, travel and entertainment expenses, and many more.
Maillie LLP can help you use data analytics, including these Benford’s Law examples, to analyze your financial data for potential red flag indicators of fraud. Contact us today for more information.