If you are a good ball striker and putt well, you might see even better numbers on your card if your short game stats improve. Knowing what to do depends on where you are around the green.
First, if you can putt, always putt. If the grass is too high in front of your golf ball, simply use a club that will lift the ball over it. This is a chip or a “putt with a flying start”. Pick a landing area and fly the ball to that point, allowing the ball to release and roll to the flag. Experiment with a couple of different clubs to figure out the carry/roll ratios.
As you move away from the green, you need more carry. With more carry and a slightly longer swing, comes a faster moving ball. The additional loft will help the ball come to a stop easier on the green. A pitch and run shot with your wedges will create the cushioned landing you need to keep the ball on the green.
As you move away from the green, your shot may go from chip to pitch and run to cut lob depending on how much green you have to work with and how far away you are from the flag. This long swing/fuller shot will hold the green if you have a high trajectory.
Work on your artistry around the green and you will chip away at your score!