All advanced statistics try to take something that is incredibly complex and distill it down to a simple result with a simple calculation. It's not that simple.
To really get a "correct" answer, a model needs to be incredibly complex with many variables.
Something like "completion percentage" is more complicated than simply keeping track of whether or not a pass was caught for a gain.
What you are really trying to decide, anyway, is if the QB is an accurate passer. Completion % doesn't really tell you the full story with regard to that.