The biggest reason amateurs miss putts, say from six feet and in, is excessive head and upper-body movement as they look anxiously to see if the ball has gone in the hole. Usually it hasn't! This extra motion on the through-stroke causes inconsistencies in speed and face position. To repeat an accelerating stroke with the putterhead traveling square down the target line through impact, a quiet body is essential.
Here's a good image: Assuming you make a compact backstroke where your arms and shoulders are locked in and your head is steady, visualize that your follow-through is a mirror image of the backstroke. To feel this, reverse your hand positions on the putter. If you're a righty, pretend you're Phil Mickelson and then make one of his backstrokes. Hold this position for a few seconds, then while pausing, swap your hands back to their normal position. This is the spot you want to be in after you've hit the putt.
Do this exercise a few times, and then putt with your normal grip, remembering the sensation.
Left is right: as you follow through, feel as if you're making a left-hander's backswing. This thought will keep your upper body steady.
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