In honest financial records, the number 1 appears as the leading digit 30% of the time.

The Worn Pages of Logarithm Tables

In 1881, astronomer and mathematician Simon Newcomb made a peculiar physical observation while working with books of logarithm tables. In the era before electronic calculators, scientists, engineers, and accountants relied on published bound volumes of numerical tables to perform complex multiplications and divisions. Newcomb noticed that the first several pages of these reference books—the sections containing tables for numbers beginning with the digit 1—were visibly dirtier, frayed, and heavily worn compared to the crisp, barely handled pages near the back corresponding to numbers starting with 8 or 9.

Newcomb realized that this wear pattern was not an accident of human preference but a reflection of the problems people were calculating. Nature and commerce seemed to produce values starting with smaller digits far more frequently than values starting with larger ones. He published a brief note describing the probability distribution of leading digits, but the finding went largely ignored for more than half a century.

In 1938, physicist Frank Benford rediscovered the phenomenon independently after observing the same physical wear on his own logarithm books. Unlike Newcomb, Benford embarked on an extensive empirical campaign to test the idea across real-world datasets. He collected more than 20,000 numerical observations from wildly disparate sources: the surface areas of 335 rivers, the populations of thousands of cities, physical constants, molecular weights, baseball statistics, and numbers harvested from front-page newspaper articles. Across all these domains, the same asymmetric distribution held true, establishing what is now known as Benford's law.