← The collection

Probability Information & Signals

Benford’s Law.

Leading digits in scale-spanning measurements are often far from uniform.

Interactive experimentintuitiveField note ·

Which first digit is most common?

Leading digits in scale-spanning measurements are often far from uniform.

PLAY & COMPARE

First digit1

19

PLAY THE IDEAMake a choice

Guess the next leading digit

You picked digit 1. Draw one from the theoretical Benford distribution.

Choose a move to see what happens.

First-digit share

Chosen digit share: 30.1%
Digit: 1

This is a theoretical leading-digit distribution for suitable scale-spanning quantities.

This is not a fraud detector by itself; assigned numbers, narrow ranges and many other data sets do not follow this law.

THE IDEA

Which first digit is most common?

In many scale-invariant collections, smaller first digits occupy a larger fraction of logarithmic space.

Inside this model

The theoretical first-digit probability is log10(1+1/d). The chart shows digits one through nine and highlights the chosen digit.

Out in the world

A practical use

Use first-digit patterns as one screening clue when auditing suitable numeric data.

WHERE IT BREAKS

A useful lens. Not a universal law.

This is not a fraud detector by itself; assigned numbers, narrow ranges and many other data sets do not follow this law.

Associated thinkers

DiscussedFrank Benford ↗Supporting reference ↗

Further reading

Explore the original research or the teaching reference behind this experiment.

Frank Benford — The Law of Anomalous Numbers ↗