Benford's Law and Securities Fraud.

  If you are a Numbers (The TV show) fan, you might remember this from Season 2.  Charlie used it to help track down a stolen DNA synthesizer in 'The Running Man'.

Your average person has no idea what the law states and what it is used to find but it is also known as the 'first digit law'.

Although this was first discovered in 1881 by an astronomer but it was rediscovered in 1938 by physicist Dr. Frank Benford.  Over a period of eight years, he analyzed a variety of data and discovered an interesting fact.

He discovered that the chance of a certain digit appearing in the first position depends on the number.  For instance, there is a 30% chance of being the first digit while there is a 17.5% chance that 2 appears first and so on.  The higher the number, the lower the probability it will appear first.


It's these probabilities that help investigators determine if a public company is more likely to end up in trouble with the Securities and Exchange Commission (SEC).  If a companies financials have different percentages than those from Benford's law, they are more likely to be caught for accounting irregularities.  It does not matter what the company produces, this seems to hold true.

This was supported when someone went through the companies who had been busted by the SEC.  The statistical deviation between the numbers submitted by those companies and Benford's law was 20 times the average for all firms.  That is significant.

When the companies who were caught restated their earnings, the numbers fell within the boundries for Benford's law.  It has been admitted they cannot catch every company due to the limited budget and employees by the SEC but it appears they catch the ones who are falling apart.

In addition to catching companies who are not using good financial methods, this law has been used to find voter irregularities, Greece's effort to hide debt, alteration of digital photographs and other forensic applications.

If you'd like to give your students a chance to use Bednord's Law, you could check out these three activities.  The first is from Cornell University.  It offers three different activities which utilize this law so they can see how it works in different situations.  The second is from Texas Instruments.  It has students calculate the percentages based on the rates provided. 

This topic came about as I looked for information on how much money is scammed from things like the car wrap and the mystery shopper scams both of which I received via a text.  In the process, I came across this and thought I would share it.

Let me know what you think, I'd love to hear.