The Strange Bias of Leading Numbers

In nature and finance, the number 1 appears as the first digit 30 percent of the time. While you might expect every digit to appear equally, small digits like 1, 2, and 3 appear far more frequently than larger ones.

This phenomenon occurs in everything from stock prices and electricity bills to death rates and river lengths. Because many processes grow exponentially, values spend more time passing through the early stages of a range. Auditors actually use this mathematical quirk to catch tax fraud. If a dataset doesn't follow this natural pattern, it is a clear sign that the numbers have been fabricated.