Puzzle #221: Word Points

If answer is worth 16 points, cat 8, dog 8, Kamloops 19, puzzle 16, smoky 12, soap 8, yes 6, and yoyo 6, what is the rule for how many points a word is worth?

(Hint: The rule has to do with the letters, not the meaning of the word.)

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, August 30, 2017 at noon Pacific Time. I will post the answer shortly after.