Benfords Law

This spurred up after a discussion at BTL.

Benfords Law and application in the real world

Benford’s law states that in any real-world dataset consisting of data in orders of magnitude, the number 1 will appear as the most significant digit about 33.1% of the time, followed by the number 2 and then the number 3. This results in an exponential decay of the occurrence of natural numbers as the most significant digit. Benford’s law is typically applied to data that is in orders of magnitude and may not hold for datasets with a uniform or normal distribution. However, it has a wide range of applications, including detecting financial fraud, analyzing electricity bills, estimating the size of rivers, and even analyzing COVID-19 case data reported by different states.

For example, during the 2020 presidential election, there was speculation that Joe Biden’s voting data did not follow Benford’s law. However, this was later disproved as the analysis only considered the first digit of the data and ignored the fact that the population distribution in Chicago was normal, meaning that it would not be expected to follow Benford’s law. Similarly, a YouTube channel called Stand Up Maths demonstrated that when the last digit of Donald Trump’s voting data was analyzed, there was a significant error, leading to suspicions of fraud. However, these claims remain unproven.

Benford’s law has also been featured in popular media, such as the television show “Ozark.” For more information on Benford’s law, Wikipedia is a good resource. Additionally, any series that follows a power law or is expanded geometrically will also strongly follow Benford’s law, such as the Fibonacci series.