Could it be that the mechanical nature of the pot is what's throwing the values out of kilter? As I mentioned before, I have seen the readings (from analogRead) change just by applying pressure against the stop positions. So with the initial readings, which is what you are seeing in the program's output, the mechanical movement has not yet completed and it remains out of a settled state?
In other words, perhaps this is similar to switch bounce. It might give a more accurate reading after a short period of time has elapsed once there is an initial change that warrants further sampling. I could do that.
Still, you would think that the spacing of values would be more uniform than going from 0 at the low end to just 14 in the second position. It's a bit puzzling.
93 * 11 = 1023