Not sure where you "absorbed" the notion that eyes beyond the ball are "bad" in some sense, but I can certainly imagine. For example, David Edel recently in Golf Magazine opined that if the eyes are beyond the ball, the golfer will "misperceive" the target. He's ignorant, and doesn't know the first thing about it, but someone at Golf magazine lacks critical intelligence. You can note that Edel in that piece doesn't attempt to say WHY it's bad or causes misperception and also doesn't attempt to explain how the putter face aim is CORRECTLY perceived -- since he is ignorant on both these scores.
There are two potential issues that "eyes beyond ball" MIGHT affect: target perception or where the putter face aims, and stroke. Just defining WHAT THE "EYES BEYOND BALL" MIGHT AFFECT is more than anyone else in golf seems capable of, as generally people expressing the opinion that "eyes beyond the ball" are "bad" or "not the Tour model" or some crap like that don't seem to know why they are even talking about the eyes.
David Edel in particular knows absolutely nothing about how a golfer can and should perceive accurately wherever any putter face aims, as I personally questioned him about this on many occasions and offered to teach him for free, but he concluded that if a golfer had the skill of perceiving where any putter face aims, then no one would buy his Edel putters -- which he sells with the promise that the design he selects for a golfer "bandaids" or "cures" that golfer's flawed perception process. Edel also admits that he does not base his putter designs on any scientific understanding of human perception, and instead relies upon APPARENT / ASSUMED "black box" association or correlation between Design #32 helping a "left-aimer" more than Design #46. Edel stated to me personally that if a golfer learned the skills that I was offering to teach him, that would zero out his sales pitch. Precisely. So he decided he would rather sell golfers his "snake oil" approach by promising his putters point themselves, and golfers can forego learning skills. So he DECLINED to learn how any golfer perceives where any putter face aims. That was in about 2008 or 2009. Typical.
The bottom line is that "eyes beyond ball" don't adversely affect either putter face aim perception OR stroke, provided the golfer has skill for these two.
As to perceiving target, the perception of putter face aim from the address posture beside the ball requires 1) running the eye beam in a straight line sideways along the green, and 2) matching this eye beam line to the 90-degree aim direction off any putter face. The main body-knowledge for performing 1) is to aim the eyeballs straight out of the face / skull 90 degrees from the head / skull's axis of rotation, so that when the head / skull is "turned" (rotated" to "look" or "face" down the line the putter face aims), this 90-degree relationship insures that the eye beam along the ground travels in a straight line sideways. This is GEOMETRY, not vision science. Any reasonable eyesight works as well as any other. AND this 90-degree relationship of the SKILL also works to generate a straight-sideways eye beam EVEN IF the "eyes are beyond the ball" looking back a bit to the feet. The head turn on the axis is still the same. Consequently, performing the SKILL correctly with the right body-knowledge means any golfer looking at any putter face even with "eyes beyond the ball" will NOT "misperceive" where the putter face aims and in fact will still "correctly perceive" the aim.
As to the stroke, the skill is to know that the arms and/or upper torso make the stroke motion, and anything above the base of the neck has NOTHING TO DO with generating the stroke. While it's possible that an unskillful golfer makes a "shoulder stroke" that is influenced by the angle of the neck to the surface (as in a neck-up angle promoting a stroke that is tilted "back" from vertical versus a neck-down angle promoting a stroke that is tilted "away" from vertical), that's not at all true for a SKILLFUL golfer. The skillful golfer deliberately orients the thru-stroke so it moves VERTICAL and STRAIGHT ALONG thru impact, in comparison to the green surface, thus delivering a straight and square impact down the line of aim -- EVEN IF the angle of the neck is other than parallel to the green surface, since the body is sufficiently capable of moving the putter head thru impact correctly at ANY neck angle.
Besides, allowing the up- or down-angle of the neck to guide the stroke into a tilted plane causes BAD strokes as this means that the sole of the putter thru impact will not run flat and flush with the surface, and therefore the putter face loft and toe-up or heel-up impact dynamics will mis-direct the line of the stroke. A skillful golfer would not allow that.
The supposition or "belief" or "claim" that "eyes beyond the ball" are "bad" is just another half-baked urban myth passed along as "accepted" by people in golf lacking the understanding of putting skills as well as the critical intelligence to think for themselves in evaluating what floats in the cesspool of putting instruction.
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