Benford’s Law – first stated in 1938 by the physicist Frank Benford – is extremely useful for detecting anomalies in tabulated data.
According to Benford’s Law, the leading significant digit in many naturally occurring collections of numbers – especially numbers which consist of several digits – will almost certainly be small.
With that in mind, a set of numbers is said to satisfy Benford’s Law if the leading digit d (d ∈ {1,…,9}) occurs with probability (P), which makes it likely that:
1 will be the significant digit 30.1% of the time,
2 will be the significant digit 17.6% of the time and, at the farthest end of the scale,
9 will be the significant digit only 4.6% of the time.
This implies that the significant digits
1, 2 or 3 will occur 60% of the time, with
1 or 2 appearing almost 50% of the time.
In accounting, Benford’s Law can be applied to a wide variety of large data sets including:
- Accounts payable data.
- General ledger estimations.
- Duplicate payments.
- Computer system conversion (e.g. old to a new system; accounts receivable files).
- Processing inefficiencies due to high quantity/low dollar transactions.
- New combinations of selling prices.
- Customer refunds or write-offs.
Once the frequencies are graphed alongside the frequencies suggested by Benford’s Law, you should more easily be able to spot groups of data which occur below the thresholds. In some cases, this may suggest an avoidance of sign-off or higher scrutiny, or it could even indicate accounting and expenses fraud.
Benford’s Law can also have econometric applications. If Benford’s Law had been used when Greece applied to join the Eurozone, it would have been immediately apparent that the data they submitted was incorrect. Unfortunately, because Benford’s Law was only invoked many years after the country joined, the damage had already been done (see Müller, Hans Christian: Greece Was Lying About Its Budget Numbers. Forbes. 12 September 2011).
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