The genesis of the sidesaddle style is that Sam Snead suffered the yips and started using a croquet style for his putting, making the stroke between his legs. A pro named Bob Duden created a croquet-style putter called "The Dude", with the shaft bent to put the putter head out in front of the golfer. Snead says:
"The great Bobby Jones was riding around in a cart one day during a PGA tournament with the Commissioner of Golf. Jones saw Sam putting croquet style and exclaimed to the Commissioner... "That has got to go!". And go it went. The USGA promptly ruled it to be unfair in that (while on the green) you could not stand "astride" or "directly behind" your line of putt, and the shaft had to have at least a 1O% angle in relation to the head. "
Bob Duden's croquet-style putting standing behind the ball with stroke between the legs:
In response to the new rule, Snead adopted the "sidesaddle" stance and continued putting face-forward. In this stance, the feet are to the side of the putter head, the golfer leans forward, the opposite-side hand is on the top of the putter handle, the same-side hand is down the shaft on the back side palm facing forward like tossing a ball, and the neck is angled up with the face forward for targeting at the target, but face looking at the putter head and ball for the stroke.
You can see that neither Duden nor Snead, in the croquet or the sidesaddle technique, is really looking at the hole during the stroke. The golfer is looking at the putter head.
There is a little difficulty with this style in terms of targeting. In the conventional style, the golfers first targets face-forward from behind the ball and then steps into a side-on address position, with a second phase of targeting from side-on. In this second phase, the face is aimed at the ball and then swiveled targetward by the neck so that the horizontal line across both eyes is the main feature of the face being used. Then the face is returned to look at the ball for the stroke. In sidesaddle style, the golfer relies on face-forward targeting positions for both behind-the-ball and side-on targeting. But the side-on position is not really the same as the beside-the-ball, but is offset from the putt line. This position and difference creates a slight problem, in that the behind-the-ball perceptions are based on one perspective and the golfer tends to believe that the side-saddle perspective, because also face-forward, should give the same perceptions of target location. But it doesn't.
A second issue is how the neck moves to target. In sidesaddle style, the neck moves the face from looking down at the ball to looking "up" at the target. The horizontal relationship between the two eyes of the face is not used to guide the neck motion from ball to target. Instead, the head is moved "vertically" in relation to the trunk to move the face from ball to target. This sort of body action is more akin to lining up the logo of the ball while squatting behind it, but from a higher position above the ball. This is not that great of a targeting motion pattern. The golfer will naturally be using a dominant eye only for this -- if he's good -- or might be using both eyes in what is called "cyclopean" targeting -- if he's not trained in the difference. Dominant-eye sighting is for clarifying the direction the face is pointing by ignoring one of the two eyes, since the two have difference positions in the face and hence different "directions" looking out of the face at the same target. "Cyclopean" vision is how both eyes give a sense that we view the world with a single eye in the middle of the forehead. This vision is our "natural" one, since the whole purpose of the cooperative subsystems of the visual system is to generate a functioning sense of the world without the distracting "wiring" and blueprints and weldspot showing all the time. This Cyclopean vision used in a targeting movement of the neck moving the face "up" from ball to target strikes me as great for looking at the ball, or for looking at the target, but not so great for connecting the two in a linear relationship in space. I think the physical relationship of the two pupils in a horizontal relationship used to look from ball to target with a sideways swivel of the face is better for putting in several ways. The conventional motion is guided by the physical fact of the two eyes being in a horizontal line matching the putt line - where to move the face is pretty straight-forward as defined by this line and a square setup but in looking "up" in sidesaddle there is not as clear a guide to where to move "up"; the neck motion keeps the axis of the head (center of neck out top of head) still but rotating in space whereas the looking-up action moves the axis so that the conventional targeting look does not alter the shoulderframe-head relationship; and the conventional style really doesn't care whether your visual system is left-eyed, right-eyed, or cyclopean since all three are in the same horizontal line.
A third problem is hand-eye coordination in the stroke. A truly side-saddle stance has the eyes facing forward but the putter head is not in sight during the stroke. That's why Bob Duden's putter has the shaft bent -- to get the putter head out in the view of a face-forward look.
Dr Tony Piparo and Bob Gammon of Down the Line Golf have incorporated this sidesaddle-behind stance with their putter and the stance they recommend. The stance has the same-side foot a step forward with the putter head placed beside this foot. This also works with the fact that the upper torso is canted targetward a little, so the shoulders are out with that same-side lead foot and the other-side foot is back for balance. This effectively isolates the same-side shoulder behind the ball, gets the ball out front more to help hand-eye coordination in the stroke, and results in a simple one-level biomechanics action for the stroke.
The conventional hand-eye coordination is accomplished with the face looking down at the ball and the stroke proceeding along the horizontal eye line (or as I call it, the "skull line"). The sidesaddle style handles hand-eye coordination with the face either looking down at the putter head or looking "up" at the target, with the stroke motion being "straight away" but offset to the side of the body. It's essentially a one-arm action. The true comparison of the two sorts of motions appears to be between the shoulderframe moving the limbs across the torso on line or parallel with the skull line versus the same-side hand moving the one-level system at a target viewed from an offset perspective without constant body cues like the skull line helping stabilize the sense of direction.
And in my book, the use of the hand to generate the motion is not as great as most people seem to think -- the hand has too many degrees of freedom and too many muscle activation patterns and too many habitual-use patterns outside putting to recommend it. Those who always claim that tossing a ball at a target is easier and more natural than putting a ball at a target may not have really tested whether that is so or not. personally, if my life depended on getting the ball as close to the target as possible, and I could choose whether to toss it face-forward or putt it side-on, I'm pretty sure I would putt the ball.
While it is true that face-forward orientation is the "natural" or habitual orientation for human targeting, and is thus more easily employed accurately by the average golfer, sidesaddle putting does not really have an exclusive claim to this orientation over conventional putting, as its proponents so often claim or imply. And it is not a straight-forward matter that face-forward is the same from beside-the-ball. So sidesaddle targeting is probably not inherently superior to conventional two-phase targeting. I'm pretty sure it helps many amateurs quite a bit, especially if the golfer gets the ball a little out in front of the stance to promote better hand-eye coordination. And Piparo and Gammon may well be onto something really nice if the biomechanics of the motion proves itself - time will ultimately tell.
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