What Benford’s Law actually tells you about an invoice

Benford’s Law is one of the oldest tricks in forensic accounting, and it’s a strange one the first time you hear it: in almost any naturally occurring set of numbers, the leading digit isn’t evenly distributed. The number 1 shows up as the first digit roughly 30% of the time. The number 9 shows up first less than 5% of the time.

Invoice amounts that come from genuine, varied business activity tend to follow this pattern. Amounts that have been manually fabricated — someone typing in a number rather than it arising from an actual transaction — often don’t. People are bad at faking randomness. We gravitate toward round numbers, toward figures just under a threshold, toward digits we simply prefer.

Where it’s useful, and where it isn’t

This is a cumulative test, not a per-invoice one. It needs a reasonable history of amounts from the same supplier before the distribution means anything statistically — on a brand-new supplier, it tells you nothing, and we don’t pretend otherwise. It’s one signal among several, not a verdict on its own.

What it’s good at is exactly the kind of fraud that’s easy for a human to miss: amounts that look perfectly reasonable individually, but that as a pattern, don’t behave like real transactions behave. It’s a hundred-year-old idea doing useful work inside a modern detection pipeline.