Passing along an article from Golf Digest - www.golfdigest.com/.../how-a-putter-fitting-changed-everything
The author's experience is very similar to mine. My 20+ foot putts would be tap-ins. But my 4-6 foot putts would also result in a tap-in. I was equally capable of missing the same short putts LH or RH. I took a short game course with my instructor/fitter to tighten up my stroke and then come in for a fitting with Science and Motion (the site is also a Showcase Partner). After the analysis with a face-balanced putter, and selecting a SC for a LH, it was pretty much down to a Phantom-X 7.5. I needed a little toe hang. The loft was adjusted to 2.5 from 3.5 degrees to improve roll on longer putts.
The take-away is one can give away strokes in their short game with a putter that isn't built for their swing. Buying for looks is fun but the equivalent of a Trackman fitting is more likely to cut strokes. And yes, I'm far more comfortable inside of 6 feet.