Yes, it's true the short game does account for a high percentage of the game . Figures vary but it is inevitable that it can save you numerous shots during a round. The chip & run around the green is all too often overlooked. This area no matter what level you are at can be mastered quite easily. People just don't practice it enough. Below I have a picture of a lie board I use to practice purity of strike, but you can use a piece of 2x1 MDF. The objective here is to catch the ball first then the board creating a clean, crisp strike. The lines are to ensure you are square & the line on the ball tells you whether the ball is spinning correctly. Very simple but effective drill. When doing this drill, try to hole the shot as when the ball hits the green it will react like a putt.
Keep your stats & try this simple drill twice a week & you will be surprised how quickly your touch around the green will improve.