The 21st Minute


The Numbers Never Lie

Applying Benford's Law with Data Analytics

An Audit Division That Has Mastered Its Use

Employee fraud costs the U.S. $300 billion a year. Fraudsters are becoming more sophisticated and clever in their schemes, but when it comes to manipulating data, the numbers rarely lie. According to Benford’s Law, named for physicist Frank Benford, irregularities can be spotted by analyzing digits in numerical data.


Benford's Law can only be used for naturally occurring data such as inventory, purchasing, payables, etc. Large data sets yield the most useful results.

Benford analyzed the distribution of the first digit in a natural population of numbers and discovered that the number 1 as the first digit of every number occurs in 30.6% of the cases compared to the number 9 as the first digit in only 4.57% of the analyzed cases. Extensive research by other experts has proven that numbers starting with lower digits occur more frequent than higher digits. Known as the "First-Digit Law," it has helped accountants and auditors detect fraud and uncover deceptive practices.

Decades later, Benford's Law has infiltrated purpose-built data analytics tools and used in forensic accounting investigations. Mark Luciani, National Field Examination Manager for CIT Commercial Services, a leading provider of factoring services, and a unit of CIT Group Inc. (NYSE: CIT), a leading provider of commercial lending and leasing services, and Lee Sullivan, Assistant Field Examination Manager, first became acquainted with Benford’s Law in 2000 while attending data analytics training.

The utilization of IDEA (data analysis software) enables us to discern meaningful relationships within seemingly unrelated data. Recognition of often non-intuitive relationships within our databases can help us anticipate, rather than react to, client needs and spot potential new business opportunities.

Mark Luciani, National Field Examination Manager, CIT Group Inc.

"We utilize Benford’s Law on every exam engagement," said Luciani,. "It provides a quick perspective on the characteristics of the specific database being analyzed. Then, based on our years of industry experience, we can compare and contrast features of the data set we are analyzing against the backdrop of similar data across a wide spectrum of industries and time periods."

CIT Commercial Services, relies on its field examiners to examine and audit clients and prospective clients. The group analyzes financial records of U.S. corporations in various industries, specifically current assets such as accounts receivable and inventory, to evaluate and test internal controls and systems. More than a dozen examiners, mostly collateral auditors, provide information to loan officers and senior credit officers to help mitigate risks inherent in providing secured loans and factoring facilities to clients and potential clients.

Newly Added Benford’s Law Tests Included in IDEA

Last Two Digits Test

Analyzes the frequency of the last two digits. Useful for analyzing inventory counts, election results, or any situation where padding or number invention is suspected.

Second Order Test

Based on the digits of the differences between amounts that have been sorted from smallest to largest (ordered). The first two digits of the differences should follow the digit frequencies of Benford’s Law. Useful for indicating data integrity issues.

Summation Test

Similar to the traditional Benford’s Law test, but instead of calculating the number of occurrences for each first two digits, it sums each amount. Useful for identifying significant amounts that do not follow the expected results of Benford’s Law.

Advanced Settings

Extract "suspicious" data whose digit frequencies do not follow the digit frequencies of Benford’s Law. With Advanced Settings, you can also refine this output to limit the size of the output database.

For the past 14 years, CIT Commercial Services examiners have relied on data analytics tools to help them examine large amounts of data to analyze the characteristics of various client data such as cash, accounts receivable, inventory and liabilities. The examiners frequently apply Benford’s Law to any scenario where data could be deliberately manipulated.

When reviewing financial statements, digital analysis can be applied multiple ways to examine irregularities or abnormalities in transactions. For example, manipulation of checks, cash on hand, accounts, double payments or invoice numbers, and others. It is also effective in analyzing systematically incorrect valuations of inventories, and looking for amounts just below limit and/or approval levels.

"The utilization of IDEA (data analysis software) enables us to discern meaningful relationships within seemingly unrelated data," said Luciani, "Recognition of often non-intuitive relationships within our databases can help us anticipate, rather than react to, client needs and spot potential new business opportunities."

IDEA Version 9 included new Benford’s Law fraud-fighting tests, developed by renowned expert Dr. Mark Nigrini. CIT Commerical Services examiners adopted these new tests to help them uncover material errors and identify unusual patterns in client data, which upon further investigation, sometimes revealed instances of fraud.

"The improvements to IDEA’s digital analytics in V9 allowed us to test digits for deviance," said Luciani. "We often use the Last Two Digits Test when evaluating inventory, payables and accounts receivable data. We perform subsequent and more detailed analyses on subsets derived from Benford’s Law tests."

According to Luciani, Benford’s Law benefits examiners and auditors well beyond the mere technical application of the theory.

"It has caused us to think more deeply and expansively about number theory in general," said Luciani. "Specifically, how we can develop algorithms that can identify patterns in large data sets. It helps us think in terms of Big Data to see patterns within the numbers that we wouldn’t normally find. Benford’s is hard to beat, even for the cleverest fraudster."

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