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How to spot dodgy figures

Have you ever been presented with a suspicious looking set of figures, such as a potential customer’s accounts or a disgruntled employee’s expenses claim form, but been unable to prove anything?

A little-known mathematical principle known as Benford’s Law may help.

According to this Law, the first digit in most numbers is more likely to be a 1 than a 2, and 2 more likely than 3 and so on. The leading digit will be 1 about 30% of the time, and 9 only about 5% of the time. It has been found to be true of most real-life data sets, such as electricity bills, house numbers , stock prices, populations, etc. It also applies to business accounts  and, in the USA, evidence based on this Law is now admissible in court hearings.

Here is the actual distribution of numbers:

The logic for Benford’s Law is actually quite simple, if not easy to explain (by me, anyway). If you want to know more about the science behind it, have a look at the Wikipedia page.

How can you use Benford’s Law?
The crucial thing is that most fraudsters or others looking to falsify financial documents do not know about Benford’s law. When they make up numbers to go on their loan applications etc., they assume that using random numbers will look most convincing and realistic. This is a mistake.

The next time you come across a dodgy-looking list of numbers, try testing it with this easy Excel tool.

Please post a comment to let me know what results you get from this, and if you can think of other useful applications for Benford’s Law.

4 Responses to “How to spot dodgy figures”

  1. Bob Doney says:

    So you have a disgruntled employee, who is disgruntled because you keep sending him on audit assignments in Central London which he travels to on the train – same journey every day. Whereas his colleagues get local jobs they can get to by car. He duly submits his expenses sheet. You in turn are extremely disgruntled that his expenses are always the highest in the firm, so you run them through the Benford test. When you see the result, you fire him on the spot for gross misconduct, and are even more disgruntled when you receive the writ for unfair dismissal from Dodgit, Grabbit and Runn – his employment lawyers.

  2. Andrew Gray says:

    Thanks for your post Bob. Yes, that would be unwise! That’s a good example of where Benfords law won’t work- where the numbers repeat because the type of expenditure (train journeys) is the same every day.

  3. Andrew Gray says:

    By the way, reasearchers used Benford’s law to assess economic data for all 27 EU nations. One country showed a distinct deviation – Greece. You can access the data yourself I gather from Eurostat.

  4. Andy Huint says:

    Extremely interesting Andy, I think Google use something like this to spot ‘keyword stuffing’ on websites

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