Why Every Banker Should Understand Benford’s Law [Calculator]

Bank Analytics

A good banker can sometimes tell that a number set is wrong just by looking at it. Today, we are going to teach you a trick that all bankers should know in order to help stop fraud, help in credit analysis and will be invaluable in M&A. We have even attached a calculator at the end to help you put it into practice. It doesn’t matter if the banker is a loan officer, a teller or a CEO. The trick is derived from Benford’s Law which is a mathematical postulation that says that in a naturally occurring system, such check amounts, account balances or loan amounts, the frequency of numbers are not evenly distributed. This is helpful as most fraudsters either try to randomize numbers or inject their own biases that fly in the face of a naturally recurring system. As such, astute bankers can often visually spot numerical anomalies and can statistically test data sets for normality adherence.


It Started With An Observation


It was a General Electric physicist, Frank Benford in the 1920’s that noticed that the first set of pages in his logarithm tables (the old way to find the logs of numbers) were more worn than the rest. He had previously assumed that that if the numbers that he looked up were random, then all pages should be equally worn.


To test this theory, Benford put together 20 different data sets from random places to total more than 20,000 observations. He used data from all walks of life including demographic data from NY, scientific findings and even pulled out all numbers in a set of Reader’s Digest magazines. Sure enough, what he found was the numbers were not evenly distributed. The number “1,” as a first digit, appeared in 31% of the cases instead of the 9% as originally assumed (zero can’t be a first digit). “2” appeared 19% of the time, “3” 12% and so on until you get to “9” which appears only 5% of the time as a first digit.


Zero is the most frequent, second number, appearing 12% of the time, while “9” remains the least used digit in natural systems and appears 8.5% of the time as a second digit. Using more data, Benford’s findings have been more refined and are now standardized in this table that is often distributed in risk management fraud classes. The table can be found below:


Benford Bank Table


Why This Works


Bankers can quickly grasp the concept of Benford’s formula by thinking about a checking account balance. If $100 is deposited (one of the most common account opening deposits) and it grows at 4% (interest and new money coming in), then the first digit will continue to be one for some time until the balances reaches $200. As balances grow, compounding happens quicker and it takes less time to reach another digit. Thus, the persistence of the number one will occur with any balance that has a growth rate.


How Bankers Can Use It


Benford’s Law not only works great with bank balances, but amounts on checks, debit and credit cards as well that makes it an ideal formula for catching fraud (it is already built into most third-party bank fraud systems). Loan officers can use it for looking at a set of net income numbers from a business, tax return data, corporate disbursements, accounts payable ledgers, customer refunds or for checking inventory levels for a collateral review.


In fact that it was in 1993 when the State of Arizona took Wayne Nelson to court and the accused was found guilty of defrauding the state out of $2mm. Nelson, who was in the finance department for the State, wrote some 23 bogus checks. Like most criminals, he tried to randomize his check amounts and numbers and got a distribution almost the opposite of what Benford’s Law would predict. This is not uncommon among fraudsters as they tend to also use higher numbers and repeating digits more often that what would show up in a natural system.


For M&A and audit, Benford’s Law is excellent for working on system conversions as the test is helpful detecting errors in duplication. Duplicate numbers usually skew numerical distributions.


Benford’s Law can be helpful in many other areas and is a key skill every banker should know. To help you put the concept into practice, we give you the spreadsheet calculator (HERE) that we use to do quick tests on numerical sets complete with tests, alerts and graphics.