For years I've been putting without looking at the ball. It started as a tip from a scratch player. I was complaining that my stroke was really herky jerky. He told me to go play a couple rounds just looking at the hole. It worked great. I went back to looking at the ball and the trouble returned. So I went back to looking at the hole. While doing that on shorter puts I realized I could see both ball and hole. I then experimented looking somewhere on my line ahead of the ball. On 22-15 footers it's about a foot to 18"ahead of the ball. As a result of this my speed improved and putting has become my strength.
Here's the trick to it. Find your line. Square the putter. Trace a line back from the hole to the ball and back out to that foot or so in front of it. All the while, keep that face sqaure, dont wait dont think, just let it go.