From Wikipedia:

Benford’s law, also called the first-digit law, states that in lists of numbers from many real-life sources of data, the leading digit is 1 almost one third of the time, and larger numbers occur as the leading digit with less and less frequency as they grow in magnitude, to the point that 9 is the first digit less than one time in twenty …

The law can be explained by the fact that, if it is indeed true that the first digits have a particular distribution, it must be independent of the measuring units used. For example, this means that if one converts from *e.g.* feet to yards (multiplication by a constant), the distribution must be unchanged — it is scale invariant, and the only distribution that fits this is logarithmic.

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