Dear Stan,
Are you by any chance left-eye dominant putting right-handed? If so, let me know and that's a different kettle of fish.
Assuming not, then your problem is mostly your gaze direction being too much down your cheeks. That makes you sense that the target is more to the right than it actually is when you look from beside the ball to the target, so the putter-face as aligned from behind the ball looks to you from beside the ball as aiming too much inside or left. You would have the same problem lining up the logo of the ball and then setting up beside the ball and looking from ball to target: from behind the ball, the logo looks pointed correctly straight at the target, but from beside the ball, the logo looks aimed left. The fault is in HOW you turn to look from beside the ball.
From behind the ball, HOW you look is not complicated. You position your dominate eye in line with the ball and the target and face forward. Facing forward is well-known to everyone from millions of times that we do just that as adult humans. From beside the ball, HOW you look from the ball to the target is not straight-forward and some ways of doing this are better and give a more accurate sense of the target's true location than other ways. Most golfers use a way of looking that is NOT accurate, including tour pros. The difference is in the direction of your gaze when you turn the head.
If the gaze is straight out of the face, it is the same as when standing erect in front of a mirror looking directly into your own pupil in the mirror, facing forward. If you were wearing glasses, your line of sight in this gaze would be level or parallel to the floor and would pass thru your lens (dominate eye) thru one and only one spot. This "aim spot" of a straight gaze is about 1 inch inside the bridge of your nose. Most golfers (95%+) set up to putt with the gaze directed a bit down their cheeks, not straight out.
To see why this is not good, hold a stick or shaft up at your pupil while facing forward and have the stick or rod represent your line of sight. Make the rod level to the ground and pointed straight out of your face. Then tilt it downward a bit. With that downward-directed gaze, bend to a ball at address until the gaze points at the ball. This is the normal flawed setup of almost all golfers. From this position of head and eye, now turn the head to direct the line of sight from the ball to the target and watch what happens to the line of sight as the head turns. The line of sight curls hard to the inside, like a search light's beam sweeping around a prison yard. Because the combination of downward gaze and a normal head turn produces this effect, the golfer unconsciously corrects the effect by letting the top of the head wander backwards instead of simply rotating in place as the turn to the target progresses. The end result is that the golfer mis-perceives the target as being more to the outside than it actually is. Then when he looks at the putter-face, the putter-face is aimed at the actual target location, and it "feels" or "seems" to be aimed well inside or left. It all starts from the gaze being directed down the cheeks.
Instead, if the gaze is kept pointed straight out of the face, and then the head is bent to look at the ball, the end position at setup has the gaze at the ball being pointed straight out of the face. Then, when the golfer turns the head to "look" from ball to target, the head turn is like a barrel turning on a stick or axis up from the center of the neck out the top of the head, and this axis just rotates in place, and the top of the head stays in the same location while the line of sight is directed along the ground in a straight line to the target. The target is then perceived where it actually is, so the putter-face does not "feel" or "seem" to be aimed inside or left.
Working with a flatter lie moves your head and eyes back from the ball more. If you keep the same degree of bend in your head to look at the ball as before, then the upshot of moving the eyes back from the earlier location is that it redirects the gaze back up from the cheeks closer to straight out the face. It has nothing to do with the putting arc.
Make a tube with your fist and look thru this tube straight out of the face, then bend to the ball until the ball shows up inside the tube. Then turn towards the target and see if the target actually shows up inside the tube, with the top of your head staying in the same space as the head is rotated. When you setup beside the ball, your gaze has to be straight ahead like this, not angled down, so your sense of the putter-face aim from behind the ball will match your sense of the putter-face aim from beside the ball.
In so many words, the tip that the eyes should be directly above the ball is not right, and neither is the tip that the eyes ought to be slightly inside the ball. Both don't take into account the direction the eyes are pointed out of the face. If the gaze is straight out of the face, it doesn't matter whether the eyes are directly above or slightly inside the ball -- the "look" from ball to target by turning the head will run the line of sight in a straight line to the target and give you a sense of the target's actual location.
Another way to see this is to hold one hand up like a salute level just below both pupils, whil standing erect and facing forward. Then bend the head down towards the ball until the ball "rises" above the salute into view. The hand prevents you from gazing below the salute and so your gaze stays straight out. Now turn the head toward the target and watch how the line of sight runs straight along the ground to the target. Keep the gaze steady and just rotate the head about the axis inside the neck out the top of the head.
The moral of the story is a gaze looking down the cheeks when "looking" to the target from beside the ball is guaranteed to give you a mis-perception of the target's location as if it were outside or to the right of where it actually is. Avoid this with a straight gaze, whether the eyes are directly above the ball or slightly inside.
The flatter lie got your gaze straighter out the face by happenstance, so you don't really need a flatter lie either.
And thanks for asking, by the way. I appreciate it!
--
Cheers!
Geoff Mangum
Putting Theorist and Instructor
The PuttingZone.com
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