Sadly @locodog has wasted your time. He selfishly cross-posted in another section... http://forum.arduino.cc/index.php?topic=222458.0 ...where he earlier announced "SOLVED".
I nearly jumped into this with a foolish answer when the thread was new.
The reality is very simple - how many degrees does the pot turn and how many digital steps do you want to detect over that range of movement. If you use 8 bits the degree range is divided by 256. If you use 10 bits the same degree range is divided by 1024 - i.e. it has a finer resolution.
Tricking with resistors to defeat this is a bit like attempting to build a magnet motor.
Try your pot using the 10-bit ADC, which gives a number between 0 and 1023.
Look at what numbers you actually get.
Dividing the answer by 4 might not be the best answer.