From the time I took up the game until I found an optometrist who was willing and able to experiment with glass lenses I always addressed my putts with the face closed to the line. Of course, to me the face appeared to be square, but evidence showed that in fact it was not. Consequently, I had to push or cut my putts slightly in order to get them into the hole. I was a poor short distance putter. No amount of experimenting with equipment or with putting techniques or with attempted compensations solved my problem.
I had heard of a young optomitrist in a nearby town who could do remarkaable things with lenses, so I walked into his office with my putter and showed him how closed the face was to the intended line. He performed a number of measurements and tests and he devised two special lenses using unorthodox prisms which he mocked up on the spot. The trial glasses seemed to fix me up, so I ordered a pair for real. The lenses were very large and quite thick but my severely near sighted and severely astigmatic eyes worked just fine on the putting green from then on, and my fear of 4 footers became no more pronounced than anyone else.
The moral of the story: If you can't easily and confidently line your putter square, then you can't hole putts with consistency.