The basic idea is that in order to run your eyesight along the ground straight sideways in a LINE and this line being the SAME line that the putter face aims t address, you learn these two pieces separately.
First, to run a straight line of eyesight along the ground, aim the SKULL / FACE at the ground, then ROTATE the HEAD / SKULL on its axis of rotation. The FACE (as part f skull) aims PERPENDICULARLY to the AXIS OF ROTATION of the skull vertically from the center of the neck out the top of the head. When the perpendicular line of sight gets rotated sideways with a rotation of the head axis, like spinning an apple on a stick, the line of sight like a laser beam on the ground runs a dead straight line sideways. Job 1 done!
The second part is to match this laser line to the aim of the putter face at address before rotating the head. That is done by matching the AXIS OF ROTATION to the top of the heel-toe line of the putter face -- the top edge of the putter face. Since the neck from base of neck to top base of skull is the SAME line as the AXIS OF ROTATION in the skull, matching the THROAT or neck line to the leading edge of the putter face (i.e., not necessarily exactly vertically above the leading edge, just parallel to it even if offset a bit left or right) is the skill. This can also be done by matching the line in the skull across the two eye sockets or the line across the two pupils with the aim direction of the putter face. The aim direction of any putter face is always perpendicular to the heel-toe leading edge, but either matching the throat to the leading edge or matching the pupil line to the aim line of the putter accomplishes job 2!
In actual practice, job 2 comes first, then the head rotates -- it's just more logical to explain them in reverse order.
Okay, how to match the throat line to the leading edge? First, straighten out the neck in relation to good chest posture, vertically in gravity, without a tilted neck. Golfers USUALLY have some neck tilt because they spend countless hours in a "modified K" posture at the back of the driving range, and then they all look like and putt as poorly as Paul Azinger! All great putters have good posture and no tilted necks!
Then if you marked the throat line with your rear hand held to match the throat line, like positioning the palm and fingers aiming up into your chin, you can lower the upper torso and neck and head into position above the putter face, watching the heel-toe line to see that you are matching these up.
Or you can get sensitive to the horizontal alignment of the two pupils (again, no neck or head tilt!) and lower this feature of your world to match or parallel the aim of the putter face. You can also help this a bit by holding one hand (I use the lead hand) like a level salute just below the pupils so my pupils look over top of this level hand. Then as I lower the face into the putt, I match the line of this level-salute hand to the aim line perpendicular off the face of the putter.
Notice that you do not have to match this level-hand salute or pupil line to the EXACT aim line off the putter face for THIS part of the skill, but if in fact you do this, this accomplishes the aiming of the SKULL not the eyes required for job 1. So yes, get the top line of the saluting hand to match exactly the aim line of the putter face, Then job 2 is done!
Once job 2 is done, AND the SKULL aims at the center of the putter face, then the head axis is the same as the heel-toe line of the putter and the head is ready to ROTATE.
A rotation of the head axis spins the axis, and does not move it about at the top end or the bottom end. The top end is the peak of your skull. If the SKULL rotates on the axis properly, the CHIN (as part of the skull) rotates in front of the shoulders and chest at exactly the same distance out, without trending closer or farther away from the chest and shoulder line. So in general it's not that great to set up with the shoulders open to the aim line, as you don't get the benefit of the shoulder line to help steer the head rotation. The rotation like an apple on a stick CAN be done properly with an open stance in the shoulders, but it's a little vaguer whether you're on track accurately.
Another feature of a proper head axis spin is that the top of the head does not change location during the spin. If you stuck your rear index fingertip against the top of your head and then made the head spin, the scalp will NOT "scratch out" from beneath the finger tip. More of this is to imagine sticking the top of your head against a sharp nail extending out of a wall level, and then spinning the head so the nail does not "scratch out" the scalp.
As to your question about neck posture, yes, making the neck / throat match the same horizontal plane as the surface of the green helps the neck turn be a bit more accurate. This ALSO requires that the eyeballs be vertically above the ball when the neck is "flat" to the green, and also makes the "back of the head" also "flat" to the green. The BENEFIT of this is that the spinning of the head sends everything turning in a VERTICAL PLANE like a FERRIS WHEEL. Each eyeball is carried by such a vertical-plane spinning of the head just like two gondolas on a FERRIS WHELL. Basically, the front eyeball rises vertically from its bottom starting, and then the rear eye tracks straight behind and then vertically up just like a following gondola on a FERRIS WHEEL. You can know this and then experience this, and this helps get the head turn more accurate.
You do not HAVE TO set the eyeballs vertically above the ball, as the PERPENDICULAR aiming of the face at the ball is the real requirement, and this works for checking the aim of a driver by aiming the skull at the tee ball, when the eyeballs are NEVER Vertically over the tee ball -- not necessary. But IF the eyeballs are in fact vertically above the ball, AND the skull is aimed at the ball, then the perpendicularity of line of sight and head axis is achieved and the back of the head and throat will also be "flat" to the surface. But eyeballs vertically above the ball withOUT a"flat" neck or back of the head means the line of sight is NOT perpendicular. Perpendicular SKULL aim is the deal. Period. Eyeballs over the ball are not required, but IF that is the case, PERPENDICULAR SKULL AIM is STILL the requirement, so the back of the head MUST be flat then.
Here is Bob Charles in 1963 using the "old school" eyeballs over ball and back of head flat technique to assess where his putter face aims:
Here is Lee Janzen in 1998 starting out with eyeballs over the ball but then messing it all up by aiming his SKULL out past the ball:
Here are some illustrations of the SKULL AIM and how it works with the HEAD SPIN:
When you say "My skull tends to drift left for some odd reason", I interpret that to mean your entire skull skews target ward (for a right-hander). So the TOP of the head is scratching to the left beneath the nail, and relative to the head, the nail stays in place but moves relatively to the right. That will also mean that your chin comes closer to the left shoulder in your flawed head spin.
This PROBABLY all stems from not really aiming the SKULL -- instead, you aim the eyeballs at the putter face and THINK incorrectly that this aims the SKULL. This eyeball aiming always makes a line of sight that is NOT perpendicular out of the skull to the axis of rotation, and that will roll the face and line of sight to the inside of the real putter aim line. If this is on-going, golfers start from this down-angle of the line of sight, and abandon the head spin, and instead "roll the rear eye only like a gondola on a FERRIS WHEEL." If you do that with eyeball aim making a down-angle not perpendicular, the gondola rolling of ONE REAR eye "scratches" the top of the head out to the target direction, left. This move CAN show the straight line of putter aim, but not consistently and accurately, at least as used unskillfully and as compared to the superior aiming and spinning of the SKULL.
Just to be clear, the eyeballs vertically above the ball are not required -- perpendicular SKULL AIM at the ball is required. And if the eyeballs and SKULL are "inside the ball", the SKULL AIM will be on a TILT, like a TILT-A-WHIRL instead of a FERRIS WHELL. That's fine -- either one spins on the axis.
To straighten this problem out, you HAVE TO aim the SKULL, not the eyeballs. The skull aim is dead level out of the bridge of the nose, so imagine an Indian shot an arrow level thru the back of your head out the bridge of your nose, so th arrow point is not about one foot out from your face. AIM the arrow point at the sweetspot of the putter face, not the eyeballs. This usually makes golfers in putting address posture bend the head MORE, but not necessarily all the way to "flay". This SKULL aiming, though is vital. Don't aim the eyeballs -- aim the SKULL. Then the eyeballs match the skull aim. If you simply "look" at the putter face, you are aiming the eyeballs. If you aim your GACE, you are aiming this arrow point. Then the head spin on the axis keeps the chin the same distance out from the shoulders as your spin and the line of sight runs dead straight sideways like a laser beam.
Other people have a top-of-head that moves away from the target in the head spin. This happens when they aim the eyeballs not the skull and the down-angle of a good spin directs the line of sight on a curve to the inside, like a search light sweeping around in a prison yard. If this proceeds along the ground for a while, THEN the golfer notices that the line of sight is NOT headed towards the target but to the inside. I say "notices" but golfers never actually "notice" this. They just redirect the eyeballs back to the target and look where they HOPED they were aimed, without ever finding out. The re-directing move makes the top of the head "scratch out" from the nail to the rear of the nail -- so this is not your problem.
Your problem could also be that EVEN IF you aim the skull properly at address and match the throat line to the leading edge of the putter face or the pupil line to the aim of the putter face, you have a BAD head spin.
To practice the head spin, set up above an elevated string line or straight chalk line so the pupils match the string or chalk line, and the skull aims at the line, and then practice a good head spin so the top of the axis stays in place while turning. This is done by running your eyesight straight along the string. You can also do this over a line on the floor inside. And your can help this out with the level salute hand just beneath the two pupils, aiming the eyeballs level out of the skull over the top of the hand line. Doing this, one KNUCKLE or other piece of skin on the top of the hand must STAY on the string or floor line all the time the head spins the eyesight sideways straight.
So, aim the SKULL better and practice the head spin.
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