Benford’s Law: Applications
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Kate M. Pospisil, CFE
ACFE Communications Specialist
This blog serves as part two in a three-part series on Benford’s Law. To read part one, click here.
Benford’s Law is one of the most interesting things that so many don’t know about — it feels like a trick, but it’s simply a law that applies for no apparent reason. Benford's Law is a theory that says that in lists of numbers, the first digits of the data set follow a pattern, i.e., random numbers aren’t always as random as you think they are. For more information about Benford’s Law, please see the previous blog in this series, Benford’s Law: What It Is and Why Fraud Examiners Use it.
If you’re sampling data about something, Benford’s Law states that the leading digit follows a specific pattern: It’s more likely that the first digit will be a 1 than a 2, a 2 than 3, a 3 than 4, and onward. There’s a 1 in 3 chance the leading digit will be a 1, and a 1 in 20 chance that the leading digit will be a 9. But why though?
For example, let’s say that your city has a population of 100,000 people and you want to know what kind of percentage increase would be required in order to reach 200,000 people. This would require a 100% increase as the population would have to fully double to achieve a new leading digit. However, if our city was 900,000 instead of 100,000, then it only needs to grow by 11.1% in order to reach 1 as a leading digit with 1,000,000.
Some interesting things that follow Benford’s Law are Tik Tok likes on popular videos, the area of countries across the world, and population counts. Population counts are actually the number two best fit in adherence to Benford’s Law, based on this massive data analysis. According to this data, the number one best fit for Benford’s Law is the number of people visiting a location or event each year. Fascinating! For more information about random things that abide by Benford’s Law, this video breaks it down very well.
Benford’s Law can’t work on everything, of course. Things like ages of a specific group of people, such as NBA players, will generally have a 2 or 3 as the leading digit; heights of adults, which generally have a 6 or 7 as a leading digit in centimeters, or 5 or 6 in inches; or the lottery — don’t shoot the messenger, but winning lottery numbers will not abide by Benford’s Law. Lottery numbers aren’t the size or amount of anything: the numbers are really just symbols. I’m sorry.