Friday, November 6, 2020

Something That I Never Would Have Thought Possible

What is Newcomb-Benford's Law?

Benford's law, also called the Newcomb–Benford law, the law of anomalous numbers, or the first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data. The law states that in many naturally occurring collections of numbers, the leading digit is likely to be small.[1] For example, in sets that obey the law, the number 1 appears as the leading significant digit about 30% of the time, while 9 appears as the leading significant digit less than 5% of the time. If the digits were distributed uniformly, they would each occur about 11.1% of the time.[2] Benford's law also makes predictions about the distribution of second digits, third digits, digit combinations, and so on.

4/1/2017 Journal of Accountancy shows how to use this to look for fraud. (I suspect that if you look at total monthly sales, and the first digit is distributed in the 11.1% distribution, you may want to dig a bit deeper into the books.) So what?  Here is a collection of data using Newcomb-Benton Law to analyze precinct returns.  While many conform to the rule, others are suspicious.  The red lines are expected frequencies:

When you are making up numbers out of your head, you do not even think of Newcomb-Benton Law, and so you produce results that satisfy your inner Democrat, but do not map well to the real world.