I'm glad you are enjoying this little puzzle. Like I said, it is really simple, but a good way to use up some time when you are bored (either in class or at work ).
Yes, to clarify, you must use ALL of the letters in the word in your anagrams, and the anagrams MUST be valid words (I would probably just use dictionary.com or something to check for valid words). That's what makes it more challenging...the longer the word you use, the more VALID anagrams you must find to give it a higher score.
EXAMPLE:
if your word is TIN, you can obviously find TIN, TNI, NTI, NIT, INT, and ITN as anagrams, but only TIN and NIT are also words (unless you're a computer programmer, then INT would probably count ). No acronyms allowed. So therefore, there are only 2 VALID anagrams of TIN...and that means the score would be 2/3 or 0.67...hope that makes sense
Besides the 1.75 score that I saw (which I still don't know about ), I have only gotten a score of 1.5 (woon also posted this answer).
Another thing you can do is figure out the highest score for each length of word.
IE. we know that for 2 letters, the highest score can ONLY be 1.0...
what's the highest score you can find for 3, 4 5, 6, etc letters?