Benford’s Law is one of those things that has always made me scratch my head.  It just doesn’t make sense!  Here’s what the law boils down to:

A second earth-shattering fact is that there are more numbers in the universe that begin with the digit 1 than 2, or 3, or 4, or 5, or 6, or 7, or 8, or 9.  And more numbers that begin with 2 than 3, or 4, and so on.  This relationship holds for the lengths of rivers, the populations of cities, molecular weights of chemicals, and any number of other categories.  What a blow to any of us who purport to have mastered the basic facts of the world around us!

One of the cool things this law allows us to do is to detect inaccurate corporate accounting!

In fact, Benford’s law has been used in legal cases to detect corporate fraud, because deviations from the law can indicate that a company’s books have been manipulated.

Jialan Wang wanted to find out if corporate accounting deviated from Benford’s law and how that changed over time.

So according to Benford’s law, accounting statements are getting less and less representative of what’s really going on inside of companies.  The major reform that was passed after Enron and other major accounting standards barely made a dent.

Next, I looked at Benford’s law for three industries: finance, information technology, and manufacturing.  The finance industry showed a huge surge in the deviation from Benford’s from 1981-82, coincident with two major deregulatory acts that sparked the beginnings of that other big mortgage debacle, the Savings and Loan Crisis.  The deviation from Benford’s in the finance industry reached a peak in 1988 and then decreased starting in 1993 at the tail end of the S&L fraud wave, not matching its 1988 level until … 2008.