Benford’s law or Newcomb-Benford’s law is a result of environmental monitoring discovered by Simon Newcomb at the end of the 19th century. He noticed that the first pages of his logarithmic books were much more worn out than the last ones. This means that in the data sets he examined, numbers are more likely to start with 1 than with any other digit. The law was generalized, formulated, and published by Frank Albert Benford in his scientific work “The Law of Anomalous Numbers”. This law states that:
Many independent and naturally occurring data sets are prone to start with smaller digits, and this can be applied to any number system (10 – decimal, 2 – binary…).
The probability that a number starts with a digit 
in the calculation system is calculated according to the following formula:
A similar calculation is possible for the second, third, or any other digit of the number, but from the second digit onwards, the probabilities almost even out.
Historically, this law has been used in various areas of life to try to determine the authenticity of data. A few examples:
- In financial crime investigations – The use of the law has identified more than one financial fraudster, and the discrepancy of financial numbers in America with this law is considered one of the main evidence.
- In macroeconomic data sets – Greece, when joining the European Union, may have submitted counterfeit or embellished economic indicators that do not match this law.
- Authenticity of scientific papers
This law is widely used, so there are at least several optimal “R” replacements that will check your data without any major problems. Just remember that this law is only advisory and only indicates possible deviations from it.
Leave a Reply