[etruong42]

Ah. But there's the rub. What I find unintuitive about Benford's law is the non-random distribution of the most significant digit regardless of base or unit of measure. You propose that it's the "largeness" of a number that enforces Benford's law. While that may be in some ways true, it does not explain the transparency to base or unit of measure. You ate 2 bagels? I ate 4 half-bagels. You earned $5? I earned ¥600 motherfucker! You ran 10 miles? I ran 3bf3e6800 micrometers, in base-16!

Again, your train of thought is not necessarily wrong, but I still find the wikipedia explanation much more robust and illustrative. I hope this is where we can agree to disagree.

[breck]

The reason why it only applies to the most significant digit is that I can say for certain that quantities of 1_ will appear ~2x as much as quantities in the 2_x family. However, I can't say whether numbers ending in 1 are more common than numbers ending in 6, because although 11 occurs more than any number higher than it, it makes up a minuscule proportion of the numbers ending in 1, and 16 occurs more than 21, 31, etc., so there's no clear way to predict what number will occur most in any digit but the most significant.

Thanks for offering your views. My analogy may be wrong or weak and maybe there is a better one to be found.

[Cushman]

Every base is base 10. There's your answer.