Benford’s Law

Benford’s Law

I have been in accounting for forty years and I just recently learned about Benford’s Law.  This law states that the first digit of number is much more likely to be a low number rather than a high number.  In fact if a set of data was to conform exactly to the law it would break out like this:

Mike E 1


Of course the first digit cannot be zero.  This can be very useful in reviewing expense accounts or any set of data that you feel is not correct.  Indeed, there are many instances where this law does not apply, but it is remarkably accurate when the data can truly be any numbers.  One test I saw was the population of all the countries in the world.  Here is how that came out:

Mike E 2


It is amazing that it is so close to the prediction from Benford’s law.   You can go to to see many more lists and how they conform to the law.  Remember the data must be random and not a data set where number are assigned sequentially, influenced by human thought, have built in minimums and maximums, etc.

I decided to test the law with a data set from my company.  Below is my date for all the checks written by my company from January 1 – April 15, 2017.

Mike E 3

Again look at how the checks starting with a 1 or 2 are much more than checks starting was an 8 or 9. Given the limitations, there are still a great number of instances where this will work.  If you think any set of data is not correct, you can use it to help detect fraud.

Written by Michael Ericksen

WAC Solution Partners- Midwest


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