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How Benford Was Discovered
- Frank Benford noticed the front pages of a logarithm table were more worn than the back pages, sparking a curiosity about digit distribution.
- He compiled tens of thousands of numbers and found many real-world datasets begin with 1 far more often than 9.
The Unbalanced Digit Pattern
- Benford's Law predicts first-digit frequencies: about 30% ones, 17.6% twos, down to 4.6% nines.
- This skew means ones occur roughly six times more than nines across many natural datasets.
Why Digits Favor Lower Numbers
- A useful intuition: numbers spend more time in lower leading-digit ranges because proportional growth to the next digit is larger for small digits.
- Thus growing from 1 to 2 takes 100% growth, but 8 to 9 needs only 12.5%, so numbers linger as 1s longer.