## Let me buy a brick and get the other on cossimy

Benford’s Law, also known as the rule of first-digits, is a rule that says in data sets borne from real-life (perhaps sales of coffee or payments to a vendor), the number 1 should be the first digit in a series approximately 30% of the time, instead of 11% as would happen had a random number between one and nine been generated.

The rule was first developed by Simon Newcomb, who noticed that in his logarithm books the first pages showed much greater signs of use than those pages at the end. Later the physicist Frank Benford collected some 20,000 observations to test the theory, which he too stumbled upon.

Benford found that the first-digits of a variety of things in nature, like elemental atomic weights, the areas of rivers, and the numbers that appeared on front pages of newspapers, started with a one more often than any other digit.

The reason for that proof is the percentage difference between consecutive single-digit numbers. Say a firm is valued at $1 billion. For the first digit to become a two (or to reach a market cap of $2 billion), the value of the firm will need to increase by 100%. However, once it reaches that $2 billion mark, it only needs to increase by 50% to get to $3 billion. That difference continues to decline as the value increases.