Cangemi Perspectives: How Benford’s Law Uncovers “Hidden Figures” for Auditors

September 6, 2018

Michael P. Cangemi a former CAE, CFO & CEO, is a Senior Fellow and Advisory Board Member of the Rutgers Continuous Auditing and Reporting Lab. The opinions expressed in this article are solely those of the author.


Most data are composed of numbers, and the accumulation of numbers into data sets, which would appear to be a large collection of random digits. Could there be hidden patterns in all these numbers that could be useful to financial professionals and auditors? When I heard my first lecture given by Professor Mark Nigrini PhD, in the 1990s, he expressed that there could be identifiable hidden predictable patterns in numbers, and to me, it seemed to defy logic.


Could it be that when fraudsters make up numbers for or by cheating, they may be overusing certain digits which upsets the underlying predictable patterns of the digits, serving as a red flag to auditors?


As a former CAE who was a CFO at the time– this was thought-provoking, and I was interested in learning more, but as admitted, it first appeared to be academically interesting, but not practically applicable to my business. I was wrong, and I’m very glad I went on to learn more about Benford’s Law.


In the 1930s the physicist, Frank Benford discovered that there were indeed predictable patterns to the digits in numbers. In essence, the hidden patterns in numbers, as basic as the digits 1 and 2 appearing more frequently in the first position than the other digits, does result in a predictable pattern.


In the 2016 movie Hidden Figures, a biographical drama about black female mathematicians who worked at NASA, during the 1961 space race, Katherine Goble used a little-known old math theory, to solve a trajectory math problem for NASA. Similarly, in the 1990s, Mark Nigrini brought to light the use of Benford’s Law in the accounting and auditing professions . Since then pattern recognition analytics has been included as a module in analytics applications like CaseWare IDEA. This has resulted in a greatly expanded use of the reliable analytical tool, with auditors around the world using it for many practical audit applications.


I first heard an example about the application of Benford’s Law at an analytics company’s user conference. The auditors had discovered many possible travel and entertainment (T&E) violations, and they needed a way to identify the vilest potential fraudsters. They ran the Benford’s Law routine, included with their analytics package, to prioritize the exceptions and focus on the worst offenders first. By making excessive expense reimbursement requests below the company limit for requiring receipts, this artificial tampering with real numbers produced a discoverable pattern.


Mark has not only been an advisor to companies like CaseWare, but he has also written a couple of books published by Wiley that I recommend: Benford’s Law; Applications for Forensic Accounting, Auditing and Fraud Detection (2012) and Forensic Analytics: Methods and Techniques (2011). Nigrini also publishes frequently, continuing to suggest new applications of Benford’s Law; a recent example is his article in the May 2018 Journal of Accountancy – “Round Numbers: A Finger Print of Fraud”. All of us in the finance and GRC professions owe a debt of gratitude to Mark Nigrini. I suggest we honor him by learning about and using the great analytics tools emanating from Benford’s Law to add value to our work!


For more information about Benford’s Law and how it’s used in IDEA, click here.


About Michael P. Cangemi

Michael P. Cangemi is a senior fellow at Rutgers University and serves on the Rutgers Continuous Auditing and Reporting Lab Advisory Board. A former CFO and CEO, a prolific writer, active speaker and senior advisor to various companies, Mr. Cangemi now focuses on providing continuous auditing, continuous monitoring and analytics intelligence for GRC, Finance and Business Process Improvements. He also serves on FEI’s Committee on Finance & Technology (CFIT) and their GRC Sub Committee; the EDPACS Editorial Advisory Board; and the Libra Audit Advisory Board focused on auditing blockchain.  His book Managing the Audit Function 3rd Edition was published by Wiley.

Connect:   Michael P. Cangemi