For instance if we assume that half the time we need to divide into halves, 1/4 of the time into thirds, 1/8 into quarters and so on, then over 90% of the time you wish to split something into 1/2, 1/3, 1/4, 1/6 or 1/12. All of which are trivial in a duodecimal system. By contrast only 56% of the time do you wish to split into the similarly easy 1/2, 1/5 or 1/10 in decimal. Even if we say that 1/4 and 1/8 are OK in decimal, we still wind up with inconvenient repeating fractions over 3 times as often as duodecimals do.
However, I was impressed by the far-reaching implications of this fact. The regularity of the base 12 times table was particularly compelling. You know how easy the 2's and 5's row is to learn on the times table, right? There's an obvious pattern that's easy to memorize? Lots of numbers are like that in base 12.
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Babyl...
But it seems unlikely as the origin of the Babylonian system cited. The 60 symbols are written in base 10; if it grew out of a culture that counted to twelve on their fingers, I'd expect to see five groups of twelve, not six groups of ten.
I can think of a more natural explanation. When I am counting something on my fingers (in the conventional way), I often want a way to store the tens digit. Perhaps the Babylonians did, too. That the tens digit is drawn as two groups of three is suggestive that whatever method they used stored a trinary and a binary state.
So, when I count off (palms up), I get to ten on the thumb of my right hand. It has a little more dexterity than my other fingers and can store more states. It's pretty straightforward to get to six by leaving it bent/straight and pointing out/up/in. It's natural to do while counting, too. (Bent and pointing in is a little uncomfortable if I want to use the other fingers, but then . . . you don't ever need to actually store 'six').