In tax returns, river lengths and stock prices, the leading digit is a 1 about 30% of the time and a 9 barely 5%. This lopsided quirk, Benford's Law, is now used to catch fraud.
Numberphile's Steve Mould shows why, across huge natural datasets, small leading digits dominate and the pattern follows a logarithmic curve.
The probability a number starts with digit d is log10(1 + 1/d). Noticed by Simon Newcomb in 1881, rediscovered by Frank Benford in 1938, and still not fully explained.
The Numberphile follow-up tests the law on real YouTube view counts, and shows where it holds and where bounded data makes it break down.
Fabricated numbers rarely obey the curve. Forensic accountants and tax agencies run Benford tests on ledgers to flag invented invoices and padded expenses.
After 2020, viral posts claimed vote counts 'failed' Benford and proved fraud. Computer scientist Jennifer Golbeck explains why that reasoning is simply wrong.
Radiolab actually crunches the precinct numbers and digs into why vote totals have no reason to follow Benford in the first place.