Some will give you these extreme examples about hitting every green and having 'X' amount of putts or missing every green and having 'Y' amount of putts and the stat doesn't matter. IMO those extremes don't happen and we live in the real world where people hit greens 30-40% of the time and then get lucky every once in a while with a chip or two. Based on what you've said, if you average 2 putts or less, you will shoot lower scores. Turn a couple 3-putts into a 2-putt and turn a couple of 2-putts into a 1-putt and you just shaved 4 strokes.