**Benford’s Law Again: an example where we KNOW they were lying!**

**Introduction**

I have written about Benford’s Law both here on this blog and elsewhere: Benford Synthetic Data, Benford Gotcha and ST Rich List. In addition, I do presentations on the Law in my live training classes in which I demonstrate the basic law, how it works, examples of how to create a Benford analysis and more. This page demonstrates the Law from a new angle: suppose we KNOW that someone has acted fraudulently, will the Law prove it?

**Bernie Madoff**

As I was preparing my latest training curse materials I thought about presenting a case of known fraud and realised that there is probably data available from the fraudster of all fradsters, Bernie Madoff. It didn’t take me long to find such data either: *Madoff Fund Fairfield Sentry* whose data can be found here: http://nakedshorts.typepad.com/files/madoff_fairfieldsentry3x.pdf

In that file you will see this table:

This table shows the monthly returns of the Fairfield Sentry fund managed by Madoff and his co conspirators from December 1990 to October 2008..

**Power Query**

I used Power Query to unpivot the data in that table to make it much easier to derive the appropriate data from. The resulting table is 216 rows deep so here is just a sample of the data:

Using the LEFT(), MID() and CONCATENATE functions, it was easy to derive the following tables:

For reference, here are the Benford standards that we have to apply:

We see all of these results in chart form for digit 1, digit 2 and combined digits 1 and 2:

**Conclusions**

Given the discrepancies, can we conclude that Benford would have caught Madoff before Madoff confessed: the answer is yes! The Mdoff data diverge significatly from the Madoff data and whilst there may be other tests to carry out, there is certainly enough evidence from Benford to have called in the SEC and whoever else should have known about all of this.

Download my Excel file that contains the data and analysis you have just read about: fairfield_madoff_analysis_blog

Duncan Williamson

9^{th} July 2018

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