Reminds me of Benford's Law [1], which stipulates that in many lists of numbers from real-world data, the leading digit is 1 30% of the time, and larger digits occur as the leading digit with lower and lower frequency (logarithmically). This has been used to detect made-up numbers in accounting which later turned out to be fraudulent behaviour.

1: http://www.rexswain.com/benford.html