It's on the right track. (alphabetic position - 1) definitely does have something to do with it, as does factors of the length, but most common letter does not - however, thinking about that might lead you to the correct answer.
I would mention that one thing I previously stated would contradict your theory - that in the case of anagrams, the status won't change unless the first letter changes. Thus (ignoring all other elements but the most common letter thing), your theory would suggest ABBCC and ACCBB could possibly have a different outcome; but they could not as the first letter is unchanged. However, ABBCC and CCABB possibly could.
(For the record, all four of those example koans are, in fact, black.)