Stroke Path Straight or Arc? -- BOTH!
by Geoff Mangum
The long-running and never-ending debate over whether the stroke path should be straight-back-straight-through or inside-square-inside detracts from the true fundamental of "a square face moving square thru impact". A closer examination of the mathematics and geometry of the putting stroke reveals that a straight shoulder stroke, because of its rising back and thru and the tilt of the plane of motion, is BOTH straight and arcing inside-square-inside. The trick is keeping the shoulder sockets rocking in the same plane throughout the stroke. [corrected 1-28-03.]
The bottom line in putting is not really "get the ball in the hole" - it's "get the ball in the hole consistently with the fewest strokes." The PATH of the stroke needs to promote consistency.
STROKE PATH, PUTTER FACE, AND A STRAIGHT ROLL
There are essentially three sorts of stroke paths: cut stroke, inside-to-square, and straight. The cut stroke requires an open face angle. The inside-to-square stroke features a face that either remains square to the target direction at setup (or unchanged from the setup orientation) or that stays square to the stroke path itself even though the path is curved. The straight stroke features a face that remains square both to the target and to the path.
Billy Mayfair's "Cut Stroke". That's why a cut stroke like Billy Mayfair's can work to get the ball in the hole, but is not recommended generally -- the cut stroke is too complicated to get right consistently. A cut stroke has two separate aspects: a PATH moving from outside to inside thru the ball, and a FACE ANGLE slightly open at impact. The combination of these two aspects is wherein the trickiness lies. For example, roughly speaking, a path that cuts across the target line at a 30 degree angle, combined with a face opened 5 degrees, will send the ball more or less straight along the target line. If you placed your putter so the face matched the targetline so the toe pointed down the line and then opened the face in 5-degree steps until the face was "square" to the line, you would have to move the putterface in 18 equal steps; continuing until the toe points down the target line away from the target takes another 18 equal steps. So "5 degrees open" is 1/18th of the way back off square. Got that? Now, what is 30 degrees for the outside-to-inside path? One third of the way up from the target line to a path that is perpendicular to the target line (1/3rd of 90 degrees). Got that? There are other combinations of face and path. Way too complicated for consistency!
Bobby Locke's "Hook Stroke" is Inside-to-Square. The opposite of a Mayfair-style cut stroke is usually thought of as the Bobby Locke "hook stroke." However, Locke setup with his feet "closed" to the target line but his shoulders square to the target line, drew the putter back along his closed toe line while keeping the putterface with the same aim it had at address, and then delivered the putterface into the ball along this toe line slightly from inside to outside INTO impact but square and straight down the line thereafter. Locke's ball does not start out with hook spin, but rolls straight down the line. From impact and after, Bobby Locke's stroke was not unlike Jack Nicklaus' "push stroke" sending the putterface squarely down the line. Locke probably could have used a combination of inside-to-outside stroke PATH beyond impact with a slightly closed FACE ANGLE; and such a combination would be the true mirror opposite of the Mayfair-style cut stroke described above. Either way, whether with Locke's transformation of PATH at impact, or with a set inside-out path combined with a set closed face angle, these strokes are not recommended for general use because of the great amount of time and attention to attain and keep consistent accuracy with these complex movements.
Ben Crenshaw's Arc Stroke is also Inside-to-Square. Ben Crenshaw's stroke path is typically described as inside-square-inside. A closer examination of Ben Crenshaw's stroke reveals, I think, that his stroke path at and beyond impact is pretty straight, at least for that critical five or six inches past impact in which the ball-putterface contact occurs. So, Crenshaw's stroke has some similarity to Bobby Locke's, in that he delivers the putter on a PATH slightly from the inside but with the FACE ANGLE square and moving square at and thru impact, before the PATH again comes inside. The Crenshaw stroke PATH is more inside-to-square. Why does his stroke start back to the inside on the backstroke? Because his right shoulder rotates laterally to the back and only slightly rises -- his "stroke plane for the backstroke is not very tilted and is almost horizontal. Why does his stroke go straight at and thru impact? Because once his body retraces the backstroke path to the position it had at address (square to the target line), his stroke movement shifts so that the left shoulder rises instead of rotates back during that critical part of the stroke at and thru impact until the business is finished and then the shoulder relaxes and goes on back laterally carrying the putterhead inside -- thru impact, his stroke plane is very tilted and nearly vertical. His stroke movement pattern is not symmetric in that what happens behind the ball is not mirrored in what happens at impact and beyond. The shoulderframe "fans" the putter open going back and "fans" it closed back square coming towards impact, but from the squareness in the middle of the stroke forward, the shoulderframe ceases "fanning" closed and stays square as the square putterface moves square at and thru impact.
The strokes of both Locke and Crenshaw require a repeating recognition of the point of transition. This is partly a sense of body position during movement and a sense of timing. The key cue from body position is when the two shoulders return to square, as this relaxes the lower back and chest muscles, so it is a recognizable feeling. The key timing cue is probably mostly visual, watching the putterhead approaching the middle of the stance or the putterhead's former position at address. These cues prompt the transition from inside-to-outside path to square down-the-line path. Most golfers consider the management of this transition too complicated and unreliable.
Bob Charles' "Straight Stroke". The main model for the straight back-straight through shoulder stroke is Bob Charles. The shoulders move in a single plane and the "triangle" shape stays intact. So long as the shoulderframe is moved in a single plane, and there is no "fanning" open and closed of the shoulderframe, and no hand or wrist changes, the PATH is "straight" and the FACE ANGLE stays the same as it was at address.
THE "PATH" OF A STRAIGHT STROKE
The Projected Path, the Plane Path, and Perspective. The reason there are quote marks on "straight" in the last sentence is that, if the plane of stroke is tilted, it depends on your perspective whether the PATH looks straight or arcing.
The plane of motion of the shoulders intersects the (flat) surface of the green in a straight line. Two planes always intersect one another so that the intersection is a straight line -- here, the plane of shoulder motion and the plane of the surface. THIS INTERSECTION LINE NEEDS TO COINCIDE WITH OR AT LEAST PARALLEL THE START LINE OR TARGET LINE OF THE PUTT. Even so, the putterhead rises going back and rises going forward inside the plane, in a symmetric arc above the surface. If the path of the putterhead in a tilted stroke plane is viewed from directly above the putterhead and the path marked on the ground like a projected shadow at noon with the sun vertically overhead, the PROJECTED PATH on the ground will not be straight, will not match the target line or startline of the putt, but will describe an arc inside-square-inside. But if the sun (or your eyes) were located near the body inside the same stroke plane, and the shadow of the putterhead were projected onto the ground, the putterhead motion would coincide with the LINE of intersection of the stroke plane and the ground. In other words, the PLANE PATH of the putterhead is actually straight in a tilted stroke plane (and matches the target line of the putt), so long as the putting stroke stays in plane. The rising of the putterhead on either side of the bottom of the stroke combined with the tilt is what leads to the arcing PROJECTED PATH in a tilted stroke plane.
Tilted versus Vertical Stroke Plane. The extent to which this arc in the PROJECTED PATH separates from the target / intersection line to the inside going back or going forward of the starting address position depends upon how tilted the plane of shoulder motion is to the ground. If the plane of motion is NOT TILTED at all, and the plane of shoulder motion is vertical and perpendicular to the surface, then the PATH will not arc off the target line at any point in the stroke. Both the PLANE PATH and PROJECTED PATH are then the same regardless of perspective -- they both run along the target / intersection line.
If the plane of motion is TILTED off vertical, then the PATH will definitely appear to arc inside going back and then arc inside going forward, but this is if you are watching from directly above the targetline. In fact, if your eyes were located at the center of your stroke pivot and also in the plane of the stroke motion, and watched the putterhead move in plane from that perspective, the eyes would see the putterhead describe a straight line. As it is, your eyes are neither in the plane nor directly vertically above the putterhead, but in bewteen, so watching the putterhead from your actual eye position, you WILL see some arcing in relation to the ground, but not as much as a person looking straight down at the putterhead.
Handsiness and Putter Face Twists out of Plane. This brings us to the meat of the confusion. To have a "square putterface moving square at and thru impact," one needs the COMBINATION of PATH and FACE ANGLE that best promotes consistent accuracy. The problem is that the term "square" has two meanings: square to the target, and square to the path (and "path" also has two meanings - plane path and projected path). When golfers speak about the toe opening on the backstroke, they don't usually distinguish whether they mean the toe is opening with respect to the target, or the path, or both. A toe opening to the target going back is not all that big a deal, so long as the face remains square to the PLANE PATH and the golfer can return the putter on the same path. This is the Crenshaw inside-square stroke. In the Locke stroke, the putterface in the backstroke does not stay square to the stroke path, but is kept square to the original direction with a counterclockwise manipulation of the wrists that continues to the top of the backstroke, where the wrist angle is then fixed for the balance of the stroke. This takes considerable practice to get right, and also poses a different problem for delivering the putterface into impact without wrist changes. In effect, the backstroke is similar to that of Crenshaw, but going forward the stroke is more of a shove or push powered by a lateral move outward of the back shoulder.
When the shoulders move in a plane that intersects the ground so the intersection matches the putt line, there is only one way the putterface gets twisted open or closed in the PLANE PATH from the way it started at address -- changes in hand or wrist position rotationally with respect to the forearm. This points the putterface out of the plane of motion. (NB: If the wrists flap or hinge like a pet door attached at the end of the two bones on each forearm , and the forearms are inside the stroke plane or at least moving parallel to it, then this hinging lifts the putterhead, but does not point the face out of plane. The "right sort" of wrist break does not hurt. Just ask Billy Casper or Bob Heintz.) So if you want to keep the putterface square to the PLANE PATH (the one that matters), use a "dead hands" stroke (stable shape and pressure), and for added insurance, keep the forearm motion parallel to the stroke plane.
Stroke Motion Not Staying in Plane - the True Inside-Square-Inside Path. If the shoulder sockets are not coordinated in the same plane as they move, then the line of motion of one socket lies in a plane that is not the same plane in which the line of motion of the other socket lies. In plane English, when the lead shoulder moves down toward the target line in the backstroke, the rear shoulder moves laterally backwards in a plane not aimed at the target line. In even plainer English, the stroke plane itself fans, sways or swings open. Even if the hands, wrists, and arms stay dead without FACE or PATH manipulation, the FACE ANGLE will nonetheless "fan" open to the target line going back and "fan" closed to the target line going thru on either side of the center of the stroke path. It is as if you defined the plane of a good tilted stroke, but instead of keeping both the lead and the rear sockets in that same plane as the movement progressed, you keep only the lead socket in plane and allow the rear socket to wander laterally back out of plane. This particular flaw in stroke movement also moves the head and center of the neck curling back following the arcing out of plane of the rear shoulder. It is as if a tilted stroke plane is "hinged" along the edge from lead shoulder to target line, like a door, and flaps open and closed on the rear side. If you aim the flat plane of a Compact Disc at a target line, held on the left by the left hand fingertips, and held on the right by the right hand fingertips, and then rotate the CD left hand down and right hand up, that describes a good stroke plane. If, however, you rotate the left hand down in plane with the CD but use the right hand to "open" the CD by pulling laterally back, the CD plane swings open. That's why the FACE ANGLE "fans" open even if the "triangle" is kept intact with a "no hands" technique.
A second "flawed" pattern in stroke motion is just like the above, except there is no "hinge" along the lead edge. This second flaw may have no head motion, and so is deceptively subtle and may occur without recognition. Instead of a "hinge" fanning, there is a pivot for the fanning of the plane of motion in the center of the neck (or elsewhere) so that -- although both the lead and back sockets rotate the CD (to illustrate the stroke plane in action) -- the CD's left and right edges twist laterally so the whole plane swings open as the putter goes back and closed as the putter goes forward. The ultimate example of this flaw is where the shoulder sockets move purely horizontally above the ground -- lead shoulder towards the ball, rear away from the ball in the backstroke, and reversing this in the thrustroke. This movement pattern is a pure "fanning" (only) of the putter. Every "fanning" action of the stroke has this horizontal component infecting it in some degree.
HOW TO MAKE IT HAPPEN -- MOVEMENTS
How to Stay in Plane. The way to stay in plane is to move both shoulders in one (non-horizontal) plane both back and through -- whether the plane is tilted or vertical, so long as that stroke plane intersects the ground along the target line or along a parallel line. The "rule" that the hands have to be below the shoulder sockets for the stroke to stay straight is not really correct. What really matters is the coordinated direction of movement of the shoulder sockets. So long as the positions and shapes of the rest of the system out from the shoulder sockets stay stable during the stroke (no changes in elbows, forearms, wrists, hands or fingers) and the setup positioning places the putter squarely behind the ball aimed on target, a movement of the shoulders in plane will produce a PLANE PATH of the putterhead that moves straight along the target / intersection line, with the FACE ANGLE staying square to the target line at all times.
Hand position with respect to the shoulders only relates to how the putter sole is oriented to the ground (flat, toe up, or heel up). Of course, this depends also on the design of the putter in length and lie.Optimal positioning of the elbows, forearms, and hands (in my experience) keeps the putterface in plane and helps dampen out changes in positions so that the golfer can concentrate solely on keeping the shoulder move in plane.
To me, this is elbows vertically below the shoulder sockets (like stubby logs each suspended on a short piece of rope from the socket), arms fully but naturally extended to take almost all of the play out of the elbows, the plane of the two forearm bones vertical, the wrists cocked down as if pointing the thumbs down the line of the forearms and also like the action of casting a flyrod (Dave Stockton's "high hands"), and the palms opposed in a neutral grip. The length and lie of the putter should fit the setup, and not the other way around. While variants are possible, the sole ought to be flat regardless of hand positioning. For example, if the hands are vertical below the shoulder sockets but not "high," then the lie will have to be flatter. In my setup, the lie is pretty upright.
Making a Stroke in the Vertical Plane. The easiest way to make a vertical stroke is to setup with shoulders square to the line and level and simply move the lead shoulder straight down and then come straight back up and continue up past the starting height. The right shoulder will reciprocate. The hands and the putterhead describe an arc that rises on either side of the bottom of the stroke, and the maximum height of the rising is set by the extent the shoulder goes down or up from the starting height. Ordinarily, the shoulder should go up above the starting height the same length it goes it goes down below the starting height. Clearly, the shoulder not only goes straight down, but also laterally back a bit as the shoulderframe "rocks." But the feeling in the shoulder is, for all practical purposes, the same as if moving the socket straight at the balls of the foot. A helpful image is to think of the two hands holding short pieces of rope attached to the front and rear of a battering ram, and then moving the shoulders so that the battering ram swings in a straight line. Another helpful notion is that the shoulderframe rocks like a coathanger hanging on the closet rod of the spine at the top of the neck. Harold Swash teaches that the spine at the top of the back / neck needs to parallel the surface, so the shoulderframe will rock in a truly vertical plane. This vertical stroke plane maximizes the time the putter's sweetspot runs above the target line going back and then thru impact. You should note that the shoulders move in a vertical plane, but it is not really necessary for the hands to be vertically below the shoulders or for the putter shaft to stick vertically down -- only that the putter sole rest flat in your setup, and high hands are preferable.
Making a Stroke in a Tilted Plane. A tilted stroke plane works pretty well also. Both planes keep the putter's PLANE PATH headed straight along the target / intersection line. The trick is to keep the sole flat to the surface. If your setup or your putter's design encourages the toe to rest higher than the heel (which is more typical than the heel being up), then the loft on the putterface brings the toe-side of the face closer to the outside quadrant of the ball, and that menas the ball heads offline to the inside. But if the putter sole is managed properly, a tilted stroke works as well as a vertical stroke. In the vertical stroke, the shoulderframe is square at address and the left shoulder socket moves vertically down towards the ball of the foot. In the tilted stroke, the reference that replaces the ball of the foot is some spot on the ground on a line that parallels or coincides with the target line. So long as the shoulder movement stays in plane, the lead socket will move towards this ground spot going back and the rear socket will move towards a similar spot on the rear section of the target line. If the socket move to spots located exactly ON the target line, so much the better. But it's also okay if the spots are just back inside (or even outside) the target line. These two offset spots form a line that parallels rather than coincides with the target line.
Identifying the exact tilt of the stroke plane, so the shoulder sockets move in this plane, is helped by thinking of the base of the neck. If a person is guillotined, the base of the neck forms a plane just above the shoulders. In a vertical plane with eyes gazing straight and physically located vertically above the ball, the plane of the neck is vertical, too! In a tilted stroke plane, with the head tilted forehead-up off horizontal but with the eyes gazing straight out of the face at the ball, the plane of the neck intersects the ground in a line parallel to the target line! That's very useful. Just keep the shoulder movement in plane with the neck plane -- so you have a very reliable BODY CUE to KNOW the stroke plane for a tilted stroke, one that avoids fanning the face open and closed. If the shoulderframe is rotated in this neck plane, it is also easier to avoid the trouble of a sway or movement of the pivot during the stroke.
Another helpful image is to think of pulling on two handles connected by a single cable passing through a pulley anchored at the ball -- keeping the arms at constant extension and making the pulls from the shoulder sockets. This image is similar to that of moving the socket straight at the balls of the foot, and must be understood as simultaneously moving the shoulder down and also laterally back in a "rocking" motion beneath the base of the neck. The main point, I guess, is that the sockets move directly at the target line, so perhaps this is even slightly better than moving the sockets in the plane of the neck!
HOW TO MAKE IT HAPPEN -- TRAINING AIDS
Stroke Plane Trainers. Two putting training aids have recently come on the market based upon the Conics mathematics of Apollonius of Perga from ancient Greece. Each is designed to train an effective stroke plane for a stright roll.
The idea of the Conics is that when a plane intersects a cone, the intersection defines an ellipse, and the vertical projection of this ellipse to the surface gives the PROJECTED PATH described above for a straight stroke in plane.
Dr Roger Brooks at the University of Lancaster, UK, has written a study of the mathematics of the shape of the putting stroke. Based upon this study, Dr Brooks has created the Trueplane Putting Trainer. The aid is based on the notion that a good pendulum stroke has the shoulders moving in an inclined plane and the putterhead path straight-back and straight-through within that inclined plane, but the path describes an elliptical arc as seen from directly above. The Trueplane trainer uses a tilted sheet of plexiglass along the puttline with a "smiley face" section of the inclined putt path on the tilted sheet. Running the heel of the putter along the red curve on the tilted plexiglass allows the golfer to feel and learn a straight stroke.
The Putting Arc is a similar training aid being distributed in the US, based also on the notion that the natural stroke has an arcing putterhead inside-square-inside trajectory above the ground. The Arc device is a long and heavy flat-bottomed piece of wood to set on the green, with the near side straight and parallel to the putt path and the far side curved in a slight arc inside-square-inside. The more modest version of this aid is plastic and is used by securing the aid to the green with tee pegs and running the heel of the putter along the arc.
Both the Putting Arc and the Trueplane are using the same mathematical approach to define the curve; the main difference is that the Trueplane plexiglass sheet defines the vertical dimension of the stroke as well.
Both training aids are somewhat arbitrary, in that each is based on one particular tilt of the stroke plane. While the Trueplane's plexiglass plate is tilted to one of two specific angles and the red curve on the plate presupposes the size and shape of the golfer and his putter, the Putting Arc likewise makes similar assumptions. The makers of the Putting Arc recognize this openly, and offer custom-made arcs fashioned with reference to a specific golfer's stroke pattern, setup and putter design -- and hence his stroke plane. Both aids assume that a tilted stroke plane is preferable to a vertical plane, on the belief that a tilted plane is more "natural."
The two aids have one major difference. The Trueplane ensures that the heel of the putter (butted against the tilted plexiglass plane) keeps the putter FACE ANGLE square to the target line at all times, although the sweetspot "appears" to wander inside-square-inside during the stroke as viewed from directly above the target line. The standard-issue Putting Arc, however, presents a vertical surface to the heel of the putter but this surface is not a plane, and is instead curved in a way that intersects the ground in an elliptical path. So, running the heel along the vertical surface actually encourages a "fanning" of the putter open to the target line going back and closed to the target line going forward. The FACE ANGLE may stay square to the PUTT PATH, but not to the TARGET. This feature makes ball position along the curved path of the putter critical to directional control. In the Trueplane, in contrast, the FACE ANGLE stays square to the PUTT PATH and to the TARGET at all points in the movement, so ball position only matters for whether the impact blow is descending, level, or ascending and what the dynamic loft of the face is at impact, and NOT for whether the FACE ANGLE matches the TARGET LINE at impact.
In a sense, the Putting Arc design accepts the flawed stroke movement pattern of the largest "demographic" in the golf market -- that is, golfers who putt poorly and score between 90 and 100 -- and seeks to regularize the flaw so that the golfer can find a good setup and ball position for his flaw that results in the ball going where he aims his setup. Interestingly, in contrast to the accompanying description and the demo by Mike Shannon offered by the Putting Arc at the PGA Merchandise Show just recently, the putter is supposedly encouraged to fan in the path as the heel stays in contact with the vertical surface, but the ROBOT demonstrating this ran the putter straight in an unfanning tilted stroke plane, and the heel of the putter separated from the Putting Arc going back and going forward of the center.
Better golfers need the individualized, custom-shaped Putting Arc to get closer to an optimal stroke pattern without the flaw, but what they really need is an optimal stroke pattern to begin with, that reduces or eliminates the importance of ball position or the timing and other issues for repeatedly finding the transition point in the path from inside to square.
Every inside-square-inside stroke path that "fans" the FACE ANGLE is generated by one or the other of the flawed patterns of a stroke plane fanning on a hinge or about a pivot in the shoulderframe, with the whole plane connecting the shoulder sockets with the target line either twisting on a hinge at the lead shoulder or rotating about a pivot along the shoulderframe. The degree of fanning is worse with the hinge pattern. In either case, the inside-square-inside pattern is not good because inconsistency in ball position AND / OR repeating the return to the cetnter of the stroke and keeping the pattern symmetric on either side of the center produce BAD RESULTS from putt to putt. This pattern also does nothing especially helpful about keeping the putter sole flush to the surface. And accepting this flaw and "fixing" the golfer with ball positioning strikes me as gimmicky and not a sound approach to how to play the game with optimal results. Making a straight stroke with both shoulders staying in plane just isn't that hard!
HOW TO MAKE IT HAPPEN -- DRILLS
These drills can all be used to help focus practice upon an in-plane shoulder stroke that moves the putterhead on a straight path with a face staying square to the target.
You can make up your own drills as well as anyone, but just keep the focus where it belongs -- training the feeling of the movement of a good straight shoulder stroke that keeps the face square.
WHAT IT ALL MEANS
Although it is true that by far most golfers do not use a straight shoulder stroke with a vertical stroke plane -- instead using either an arms, wrist, or hands stroke or a shoulder stroke running inside-square-inside, or a hybrid stroke running inside-square, or a shoulder stroke with a tilted stroke plane -- the vertical stroke plane is the most consistent and reliable movement pattern of the lot. This is mainly because the verticality of shoulder movement is easily recognized and repeated, whereas the "tilt" direction is variable, harder to visualize, and does not correlate well with an easily learned series of shoulder positions. This pattern also reduced or eliminates the importance of ball position, and promotes recognizing the bottom of the stroke as a transition point.
Both the Vertical Stroke Plane and the Tilted Stroke Plane produce a straight, square motion of the putterface, with the sweetspot staying directly above the target line back and thru as viewed from inside the plane. The Tilted Stroke Plane is not all that much more difficult than a vertical plane, and mostly requires attention to keeping the sole flat, the hands dead, and the forearms moving paralell to the tilt of the stroke plane. Between the Trueplane and the standard-issue Putting Arc, though, the Trueplane appears to give the better physical guidance, because the sweetspot of the putter stays on line throughout the stroke and the plexiglass plane discourages fanning the stroke plane. In contrast, the standard Putting Arc encourages the putter's sweetspot to drift inside going back and then beyond impact because it encourages the stroke plane itself to fan the FACE ANGLE out of square to the target. This places a premium on ball position and movement consistency and timing that is more complex than a straight-line stroke, and in fact twists the face off square to the target (although still square to the path's arc). A do-it-yourselfer like Beth Bauer simply uses a 4x4 timber and runs the heel along the wood in a straight line. The tilt of the Trueplane's plexiglass adds a little to the 4x4, but not that much, because the surface of the heel is not an angled plane that rests against the plexiglass in a flush way, but only contacts the plexiglass in a point. The tilted stroke does come inside and the 4x4 blocks that action, but the 4x4 works just fine with a vertical stroke plane.
MAKE THIS PART OF YOUR GAME
I recommend an in-plane stroke, either vertical or tilted depending upon your preferences and equipment design, using the shoulders to move the system and keeping the shoulder sockets inside the plane going back and thru. Both stroke planes give a very straight path for the sweetspot, and a no-hands approach keeps the putterface as square as it was at address to the target. Between the two, however, I recommend the vertical stroke plane. There is really no arcing at all off the target line in this stroke pattern -- only the natural rising of the putter on either side of the bottom. It also maximizes the length of the path for which the putter sweetspot is on the target line. This reduces the importance of ball position (which is still a minor factor or importance in the tilted stroke plane), and variable ball position probably accounts for a large percentage of so-called "pushes" and "pull." This stroke path also allows a little more freedom in hinging the wrists without changing the face angle, so long as the hinging stays in the stroke plane (like a pet door). That's comforting, and allows a more relaxed grip pressure and frees up attention for more important matters.
To learn this, try the 4x4 as a stroke plane trainer, or purchase either of the above aids. They all work as well indoors as outdoors. On the green using a vertical stroke plane, be mindful of the image of moving the lead socket straight down at the balls of the foot and then coming straight back up and higher. The image of moving a battering ram hanging from two ropes at the ends also helps. On the green using a tilted stroke, think of the base of the neck as setting the plane of the stroke or aim the sockets right at the target line itself, think of the image of a pulley at the ball, move the shoulders inside the plane in a reciprocating rocking motion, and keep the sole of the putter flat above the surface. Set up on some long straight putts over 30 feet and drain them!
For more tips and information on putting, including a free 10,000+ database of putting lore and the Web's only newsletter on putting (also free), visit Geoff's website at http://www.puttingzone.com, or email him directly at firstname.lastname@example.org.