Benford’s Law becomes more clear

You remember Benford’s Law?  Wolfram sums it up:

Benford's law states that in listings, tables of statistics, etc., the digit 1 tends to occur with probability ~30%, much greater than the expected 11.1% (i.e., one digit out of 9).

I think Wolfram meant to add that the law applies to the leading digits of the figures you’re using. In any case, the law applies when you have a large sample of “real” data, as opposed to computer-generated random numbers, and so it’s useful to forensic accountants trying to detect fraud (or so I hear). 

BenfordsLaw_800

It may seem counterintuitive (shouldn’t all digits occur with equal probability?) – but the last few minutes (start at 7:53) of this Numberphile video helped me get a grip on what’s going on: