SHORT ANSWER · BENFORD’S LAW
How is Benford’s law used in forensic accounting?
Forensic accountants use Benford’s law to compare how often each first digit appears in a set of amounts with the expected pattern, where 1 leads about 30.1% of the time and 9 about 4.6%. A digit far off the pattern is a reason to look closer, not proof of fraud, and the test only means something on complete, accurate rows.
DEFINITION
What is a benford’s law?
Benford’s law is the pattern that in large sets of naturally occurring numbers, the first digit is 1 about 30.1% of the time and falls steadily to 9 at about 4.6%.
THE EXPECTED SHARES
What share of amounts should start with each digit?
Each digit d is expected to lead log10(1 + 1/d) of the time, which gives the shares below. Choosing a tool? See the best bank statement analysis software.
| First digit | Expected share |
|---|---|
| 1 | 30.1% |
| 2 | 17.6% |
| 3 | 12.5% |
| 4 | 9.7% |
| 5 | 7.9% |
| 6 | 6.7% |
| 7 | 5.8% |
| 8 | 5.1% |
| 9 | 4.6% |
The nine shares add up to 100.0%. An amount of 1,840.00 and one of 0.18 both count as a leading 1.
ZeraBooks builds the workflow around your matters and your template for free. No development charge, whether it’s a forensic department or one person.
WHEN IT WORKS
Which sets of amounts does Benford’s law fit?
It fits large sets of naturally occurring amounts that span several orders of magnitude, such as every payment out of an operating account over a few years. It doesn’t fit small sets, or amounts that are capped or fixed, such as charges held under a spending limit or a set monthly rent. Those break the pattern with no fraud involved.
It also needs every row. A missing month or a misread digit changes the counts before you’ve tested anything, so the statements have to tie first. The test is one step in how do you analyze bank statements for fraud?, next to methods such as what is the bank deposits method?
RUNNING IT
How do you run the test on bank statement rows?
- 1
Prove the rows
Tie every statement to its printed balances and confirm no month is missing. ZeraBooks does this before you download.
- 2
Pick one population
Money out from one account, or all card charges. Mixing populations blurs the result.
- 3
Count the first digits
Take the first non-zero digit of each amount and count how often each one appears.
- 4
Compare and follow up
Set the counts beside the expected shares. Pull the rows behind any digit that stands out and look at them one by one.
Does a failed Benford test prove fraud?
No. It shows the amounts don’t follow the usual pattern, which can have honest reasons. It tells you where to look.
How many amounts do you need?
Enough for the pattern to show; a few dozen rows is too few. Larger sets spread across a wide range of amounts work best.
Does ZeraBooks run Benford’s law?
No. ZeraBooks proves the rows are complete and accurate and delivers them in your workpaper, where the test is run.
Sources and further reading
FREE CUSTOM BUILD
Test the digits on rows that add up.
Every statement proven first.
ZeraBooks ties each statement to its printed balances, so the counts in your Benford test come from the whole set.