I was listening to the Numbers episode of Radiolab and came across a very interesting topic: Benford’s Law.

In its simplest form, Benford’s Law says that there is a distinctive pattern on the “population” of numbers. If you gather all the numbers in the world (from numbers found in stock prices, to newspapers, height of buildings, temperatures, cash registers, etc.), approximately 30% of them start with # 1. Let me repeat that, about 30% of numbers in the world start with #1.

But wait there’s more!

About 18% of all numbers in the world begin with #2. About 13% begin with #3. See the pattern?

And here’s the entire gamut:

• #4:  9.7%
• #5:  7.9%
• #6:  6.7%
• #7:  5.8%
• #8:  5.1%
• #9:  4.6%

Visualizing this pattern, we get:

So what’s so significant about Benford’s Law? Surprisingly, the natural distribution of numbers is so universal that it can be applied to any numerical context (i.e. finance reports, random numbers). Any deviation from this pattern denotes that the numbers have been manually modified. In fact, Benford’s Law has been used to detect accounting fraud and other related crimes (see example below).

Lesson: don’t mess with numbers (unless you follow Benford’s Law).