Thursday, September 22, 2011

Aimpoint as Poor Science

Aimpoint as Poor Science

I was asked recently to critique Aimpoint from the point of view of science. Aimpoint purports to chart exact aim locations for breaks for all golfers, with the exactitude matching the calculation of how far a car drives along a straight road at 50 mph in one hour. Golfers are fools for numbers, and believe anything wearing a lab coat and pocket protector must be a demigod sent from Heaven's own Science Department to explain to us poor dumb golfers "how things really are". The first thing the demigod intones stentoriously is: "To measure is to know!" So here come the numbers! Playing golf by numbers is like painting a Picasso by number -- it'll work, sort of, but that's not why the Good Lord created Pablo or you to begin with. So there's a basic problem in golf culture with how golfers regard science and the technologies of science.

Aimpoint is a great example of the pretense to reality and the claim to scientific truth versus the reality that such science is largely guess work and often way off base from reality and what golfers need to know about the world of the golf course. A leisurely examination of the sources of Aimpoint reveals its many flaws in applying physics to the skills of putting.


Hi Geoff,

Can I get your thoughts on Aimpoint? I am considering attending a two-hour session and wondered whether you thought it was worth it.

Kind regards,

Golf Coach


Dear GC, 

This webpage on the PuttingZone addresses these issues and more. Here in detail are EIGHT main problems with the "science" of Aimpoint's calculated breaks


Aimpoint is a bit odd because the whole physics is based upon a level of touch that its creator Mark Sweeney cut-and-pasted from a physics article written by a physics teacher not especially knowledgeable about the reality of putting and certainly not a teacher (Tony Penner at Malaspina University, BC Canada in the Canadian Journal of Physics for 2002), and he in fact cut-and-pasted this level of touch (6-12" past the hole) from another physics teacher who calculated the numbers rather than learned about touch (Brian Holmes, in California in the 1980s, in the Physics Teacher Journal in 1986). (This is all obvious from Sweeney's Patent Application in 2004.) The level in fact is not at all what is usual in golf, and is essentially how Ben Crenshaw would LIKE to have touch if he were really good one day, but is certainly not normal for the vast majority of golfers. This means two things: 

1. the aimpoint calculations are not suitable for the vast majority of golfers; 
2. golfers cannot use the aimpoint calculations without first learning an unusually superb level of touch on a consistent basis. 


The second problem is that the physics paper relied upon (Sweeney has little or no physics personally; it all comes from Malaspina University, BC) is a "model" and not physics calculations of reality. The difference is that a "model" is an assemblage and a modification of a set of standard general formulae from textbooks shaped and shaved until the formulae generate what looks like a reasonable approximation of reality when the theoretical calculations of the model more or less look like the numbers measured from reality in some manner. This is called "the model has a 'good fit' with the empirical data." The paper is AJ Penner, The physics of putting, Canadian J. of Physics, 80, 1-14 (2002). The "shaped and shaved" business requires making "assumptions" that simplify and vary away from the full complexity of reality. Here are ELEVEN poor choices made by Penner in constructing a "model" that Sweeney inappropriately applies to real putting: 

1. All greens are perfectly planar and flat: 

Penner (all quotations are from the 2002 article in the Canadian Journal of Physics): "Holmes [3] presented a detailed model of the capture of a golf ball by a hole on a flat [i.e., "level"] green. This model will be discussed briefly along with a correction that will be required to account for sloped greens [flat but tilted surfaces, actually meaning "a surface on a green that has one slope, one tilt, and is otherwise uniformly flat or planar]." 

Aimpoint charts are limited for use ONLY when the green surface between ball and hole is "flat" -- that is, the same planar surface without changes in slope, with the same tilt in space, and all fall lines arranged parallel to one another and all contour equal-elevation lines parallel to one another and also perpendicular everywhere to all fall lines. 

While it is true that greens are not usually "level" in gravity, the surface is "flat" only in discrete areas and then only to a reasonable level of resolution ("sort of flat" or "flat enough" for purposes of the read), and then the real "flat" areas are not very large. 

Below is a contour map of a fairly typical green (top of the two maps), with a "slope" area map of the same green (the lower map of the two). A "flat" area is a region where the contour lines next to each other remain parallel, and really this means that 3-4 contours lines stay parallel. Once these lines start to become NOT STRAIGHT anymore, the area is no longer "flat". So flat areas are areas where 3-4 adjacent contour lines are parallel LINE SEGMENTS without curving. And then there is another consideration: whether the slope percentage stays the same over the "flat" area. If the slope changes, that is the same as curling a sheet of paper: it's flat left-right, but rolling up concave or away convex in the up-down or near-far direction. This aspect is mapped in the bottom of the two maps below. 

So truly "planar" areas are 1. parallel contour lines, and 2. same slope percentage. BOTH maps below have to be consulted -- upper map for parallel, lower map for same slope.



Below, the areas that are "flat enough" to consider "planar" for purposes of reading putts with hole locations on those areas are few and far between. If the blocks of the top map are numbered vertically and horizontally top to bottom and left to right as in real road maps, there is one reasonably large "flat area" at 2-2 in the top third's middle section, a tiny area at 2-3 at the top far right edge of the green, a very small "flat" area at 3-3 in the top lobe, a flatish TIER at 5-1 to 5-2 in the middle that is too steep to serve as a pinnable hole location and so is irrelevant in aimpoint charts, and another sizeable "flat" area at 7-2 in the front lower left of the green, and a small flat area at 7-3 in the front right of the green. 

The grids are 5 yards x 5 yards, so the CIRCLED AREAS in total have these sizes: 2-2 is about 15' x 15'; 2-3 is 6' x 6', 3-3 is 6' x 6', 5-2 may be 7' x 7', 7-2 is about 10' x 10', and 7-3 is 7' x 7'. 

Checking BOTH maps for these areas shows that what at first appears flat from the contours is actually changing slope, so that the really flat area is further restricted to only one slope color inside the circled area. Consulting the bottom map for CIRCLED ONE-COLOR AREAS: 

For 2-2, the lighter orange is about 10' x 10'. 
For 2-3, the one-color area is 6' x 6'. 
For 3-3, it's 6' x 6'. 
The 5-2 area is just too steep but in any event its flat one-color area is not very large. 
The 7-2 area is curved into convexity except for a central area about 5' x 5'. 
The 7-3 is about 7' x 7'. 

That's a total of one area 5' x 5', two 6' x 6', one 7' x 7', and one 10' x 10'. As circles, these are areas of diameter 2.5', 3', 3.5', and 5' -- not very large, and none remaining "flat" for more than two steps away from the hole.

Even with that, speaking as a greenskeeper who set pins at four courses, the chances that the pin location will be centered within one of these four flat areas is exceedingly slim. What is REAL is that the top lobe in the left map is a large half-bowl shape draining off to the right at 4 o'clock off the front-to-back line of the green and the bottom lobe is another half-bowl draining off to the bottom right at about 5 o'clock. While it's a fairly simple green, it's not really one that offers many flat areas or flat areas that extend out very far before the surface contour and slope changes from that at the hole. 

USGA pin location guidelines want pins to be located basically where there is at least a 4' x 4' flat area if not a 6' x 6' area, so 2-3' out from the hole in any direction does not change slope or flatness. Greens always have plenty of these areas, but they are about the minimal size for flat areas. 

The pins on this green are highly likely to be located on areas with very minimal flatness at the hole on a general "inside of bowl" contour, with the bottom of the bowl being tipped to "pour" the water off the green a specific direction. Yes, the bowl is very shallow, but it's still a bowl. Aimpoint charts don't work to give targets on the inside of a bowl. 

This means that aimpoint charts based upon the assumption that greens are "planar" or else the aimpoints aren't valid are not really useful much past about 5-8' out from a hole, and almost never are valid for 10' to 20' out. If I had to guess the percentage of real hole locations for which the aimpoint charts are actually correct for 10' putts, I would guess the percentage of real 10-foot putts and real pin locations are not "flat" or "planar" for purposes of the charts except in perhaps 20% of the putts, and that for 80% of real 10-footers, the charts are incorrect. (Aimpoint has obviously found this fact out, but claim they can handle it by telling you something extra other than what the charts say, in an advanced session for more money. Uh, okay boys.) 

2. The friction in the grass can be estimated reliably without direct measurement by calculating how much friction is at work stopping the ball at Stimpmeter distance X given the ball's off-ramp initial velocity off the bottom of the Stimpmeter [and Penner borrows a calculation about the Stimpmeter ball speed that is in error, so his calculations of green speed are skewed]: 

Penner: "The speed of a green will be directly related to the deceleration of the golf ball and will, therefore, be a measure of the value of g. The speed of a green is typically measured by a device called a stimpmeter, which is basically an inclined plane with a V-groove running down its centre. Holmes [9] has shown that the initial speed of a golf ball when it leaves the end of a stimpmeter is 1.83 m/s. For what would be considered a very fast green the ball rolls, after leaving the end of the stimpmeter, a distance of approximately 12 ft (3.66 m). For what would be considered a very slow green the ball rolls a distance of only approximately 4 ft (1.22 m). Using the speed of the golf ball as it leaves the stimpmeter (as determined by Holmes), the above extreme roll distances, and the acceleration of the golf ball as given by (5), the range of values for g with golf greens can be found. The result is that for golf balls rolling on golf greens 0.065 less than g less than 0.196 (6) with an average value of 0.131." 

Balls come off ramp differently depending upon whether the ramp presents "sliding" friction or "rolling" friction. A V-shaped ramp like the Stimpmeter alters the "rolling" friction from that of a ball down a flat ramp rolling on only ONE bottom point to that of a ball rolling down perched on two angled edges with TWO friction points. The physics teacher that Penner borrowed from for the Stimpmeter off-ramp speed is Brian Holmes, who mis-calculted the off-ramp speed by about 10% due to his error using only the one-point rolling friction. Holmes predicted about 6.0 feet per second ball velocity off the ramp (72 inches per second), but measured speeds are closer to 5.4 feet per second (64.8 inches per second), a difference of 11.1% (1/9th too fast). This results in OVERESTIMATING the ability of the green friction to slow and stop[ the ball at X feet away. Penner uses Holmes to calculate the co-efficient of grass friction of a Stimp 8' green as 0.131, and this is the basis for all aimpoint calculations. So that is too large by 11.1%, and the calculated coefficient of grass friction should be 0.116 instead of 0.131, even assuming that is the way to guess the friction coefficient. In engineering, engineers say the coefficient can only really be determined by direct empirical measurement. Neither Holmes, Penner, nor Sweeney has ever measured green friction, so not only is it error in the aimpoint calculation; it's a crap-shoot even if calculated correctly. 

3. Green speed does not vary anywhere on the level surface: 

Penner: "Experimental measurements of a golf ball rolling on a green by Hubbard and Alaways [8] have indicated that there is a dependence of the deceleration of a golf ball on its speed, with the retarding force increasing at lower speeds. However, the dependence was found to be small, i.e., a 10% variation over a 14 ft (4.3 m) putt (1 ft = 0.3048 m), and for the purposes of this paper the golf balls deceleration, and therefore the value of g, will be taken to be constant." 

A 10% variation in real green speeds from the beginning of the putt to the hole is not negligible. This is especially the case when the green has grain and also varies depending upon whether the surface is exposed to and faces directly into the midday sun (southern slope) or away from the sun (northern slope) and whether the green has any invasive grasses or weeds or disease areas (pretty common really). On some Bermuda greens, the different green speed up-grain versus down-grain played with the same putt force results in one 20-foot putt stopping as much as 6 feet short and the other putt racing 6 feet past the hole. And green speed also varies with time of day, growing strongest shortly after midday, and changes with mid-day watering. This is all in addition to the fact that one green differs from another because one green is high and exposed to sun and wind and the other is low and shaded in a boggy area hidden from the wind and sun. 

4. Green speed does not differ when the ball travels uphill or downhill so that green speed is always assumed to be the speed of a level green surface: 

Penner: "For the more general case of a rolling golf ball on a sloped green, the value of g will be taken to be the same as is found with level greens, and the equivalent contact point on the golf ball will be taken to be along the direction of travel. These approximations will greatly simplify the analysis and would be expected to have only a secondary effect on the determined paths." 

In actuality, the friction is the interface between the grass and the bottom shape of the ball compared to the center of gravity of the ball. When the ball heads uphill, the center of gravity presses MORE of the area of the bottom of the ball against the uphill grass slope, the way the prow of a boat plows into the opposing water. Downhill has less friction because the center of gravity presses the rear half of the bottom of the ball down at the downhill slope and this rear half does not have a "prow of boat" effect like the uphill putt. Indeed, the friction of a cross-hill or side-hill putt is also less than the friction across level green or uphill green. 

5. No putts have balls that skid and all balls start true rolling immediately off the face of the putter: 

Penner: "Both Cochran and Stobbs and Daish indicate that a putted golf ball will be in a state of pure rolling after traveling approximately 20% of the total length of the putt. However, this would, in general, depend on both the loft of the putter and on the nature of the impact as a golf ball can initially be given top spin or bottom spin depending on the relative position of the putter at impact. For the purposes of this paper the ball will be taken to be in a state of pure rolling immediately after it leaves the face of the putter. This will greatly simplify the analysis and this approximation would be expected to have only a secondary effect on the actual path of the putt." 

This means the touch calculations are off up to 20% depending upon what the specific golfer's stroke produces for skid-roll pattern. Any skid-roll means the aimpoint is not correct for that golfer, and ALL golfers generate some skid. The usual range is between worst-case 45 degrees backspin to 45 degrees forward spin, and NO ONE generates 360 degrees of true roll off the face of the putter without any skid. Skidding resulting from putter design alone can alter distance (and delivery speed and capture speed) between a loss of 20% of the energy up to a loss of 35% of the energy, so this is not a negligible issue. Assuming the balls start with perfect rolling means the aimpoint calculations are all off, as the distance of roll and final entry speeds of the calculations don't match reality by up to 15% (one-seventh). 

"A badly designed putter can give so much backspin that the ball loses 35% or more of its initial energy through skidding before it gets rolling. (High topspin putters can reduce this to 20% or less.)"

6. Any ball launching into the air doesn't alter the distance or the line:

Penner: "For the more general case of a rolling golf ball on a sloped green, the value of g will be taken to be the same as is found with level greens, and the equivalent contact point on the golf ball will be taken to be along the direction of travel. These approximations will greatly simplify the analysis and would be expected to have only a secondary effect on the determined paths."

"Figure 2 shows the overhead view for a golf ball launched at a speed of v and a launch angle of towards a hole that lies on the y-axis."

The Penner "model" ignores launching the ball into the air when calculating "launch speed". The basic physics starts with acceptable range of capture speed and works backwards to "launch speed" off the face of the putter along some "launch angle" on the surface plane. Penner is using the term "launch" as a special term of art in physics to indicate the "launch parameters" of the ball at impact, and this specialized jargon meaning obscures the fact that the launch equations in the "model" do not include a term for vertical motion in the z-axis or up-down off the surface plane, which lies in the x- (near-far) and y-axis (left-right).

The launching and bouncing of balls off the face of the putter vertically off the surface is the MAIN source of divergence of putts off line and less than the intended distance and break expected and used in the read, not the skid-roll issue. Typical putts with modern putter designs and usual stroke motions launch balls at least 3" and out to 8" or more sometimes. The greater the distance and force, the greater the launch. No break occurs while the ball is in the air; no grass friction slows the ball while the ball is in the air; and a ball that lands and bounces tends to bounce off line due to hitting grass stems or roots, ball marks, and dimple edges. The bottom line is that launching balls into the air "swiss cheeses" the break used to aim the putt and the bouncing typically drains the energy of the putt so these putts end up high for read and short for distance, aside from the bouncing knocking the ball off line too. In other words, failing to account for this factor renders the aimpoint charts inaccurate. 

7. Golf balls do not have dimples: 

Penner: "The above model ignores the fact that the surface of a golf ball is dimpled, however, as the dimpled surface would be expected to have only a minor effect on the path it seems a reasonable approximation to treat its surface as smooth." 

Of course they do, and dimples affect friction with the grass, interaction with the putter face for line and distance, and interaction with the hole rim. While it's not reasonable for Penner to have to factor the effect of dimples into the equations he builds up for the "model", it is instructive to see that all of the "assumptions" are really simplifications that IGNORE admittedly relevant factors in the HOPE that so ignoring the factor will not seriously undermine the "model"'s capacity for faithfully APPROXIMATING empirical experience to some reasonably satisfactory degree. 

8. The capture speed of a ball depends upon the length of its path across the circular column of the hole and upon the interacting geometry of ball and rim or back wall of the hole, and calculations borrowed from another physics paper (Brian Holmes) reliably approximate reality, and only approximate adjustments are made with respect to tilted rims located on uphill or downhill slopes: 

Penner: "In the case where the probability of a player making a putt is small, the scatter in the launch speed and launch angles in the putts of the given player will be much larger than the range in the launch conditions required to make the putt. The probability of the player making a putt will in these cases then be approximately proportional to the areas of the required launch conditions as given in the launch-speed launch-angle space. Pelz [10] found that professional golfers make approximately 50% of putts from a distance of 6 ft. Using this value to scale the areas of required launch conditions, as given in launch-speed launch-angle space, allows for the probability of making putts for other distances and other conditions to be determined. The result for a level green is shown in Fig. 11 with the probability of making a putt shown for hole distances ranging from 6 to 30 ft. Also shown is the range of success of professional golfers, as given by Pelz, in making putts at these same distances. As is seen, the general dependence of the probability of making a putt on hole distance, as predicted by the putting model, agrees well with the results of professional golfers." 

That's okay as an approximation IN GENERAL, but real golf holes are 1) not cut straight into the earth all the time (off perhaps 20% of the holes), 2) and damaged during play by golfers' rough handling in retrieving balls and removing and replacing the flagstick. While the tilt of the hole's rim doesn't have a very large effect on ball delivery or capture speed, the downhill slope past the hole resulting in unacceptable rolls past the hole matters quite a bit in changing the golfer's motion towards the hole for stroke timing, size, tempo, rhythm and the like. Downhill slope plus steepness and downhill slope plus slick or fast green speed REALLY alters what capture speed will work out in total for getting the ball ONLY as far as the hole and not too far past the hole. 

Oddly, Penner calculates hills as 5 DEGREES, which exceeds the slope for any pinnable position even when the green speed is exceptionally SLOW. Even as slow as Stimp 7', the maximum slope golfers will face for a hole location is between 3.5 and 4 DEGREES of slope, which corresponds to about 6-7 PERCENT GRADE. His modeling of uphill-downhill putts on 5 DEGREE contour/slope is then pretty far out on the fringe of relevance. 

9. All captures speeds are assumed to be equally good, except that the maximum number of sinks occur when the touch delivery / capture speed is near the lowest end of the capture speed range: 

Penner: "As is indicated in both these figures, the greatest range in acceptable launch angles corresponds to approximately the minimum value of acceptable launch speeds. In the case of putts on average speed greens, such as is given in Fig 14b, this also corresponds to putts near the maximum allowed launch angle." 

This ignores the real problem of avoiding three-putts by going too far past the hole, which is what sets the upper limit on delivery speed in actual golf. The vast majority of golfers need help setting the upper limit of their delivery speed -- not setting the delivery speed nearest the low end of the physics possibilities. So aimpoint chooses the fundamental parameter that underlies all calculations of all aim targets in a backwards manner at war with real golf. 

The reality is that delivery / capture speeds that race past the hole more than 2-3 feet are beyond the maximum acceptable velocity, and keeping the delivery speed within this maximum takes priority over achieving a delivery speed nearest the low end of the total acceptable range. Penner does not discuss a maximum range that does not send the ball too far past the hole, but in fact this speed is the upper limit and the golfer is perfectly happy with anything between the least acceptable speed and this. In other words, the acceptable delivery speed is not singular or even tightly constrained, but is a nice comfortable zone of speeds that result in the ball that misses stopping just past the front lip of the hole or stopping 2-3 feet past the back of the hole, where a comeback putt presents little threat of turning into a miss and a three-jack. 

In neuroscience, if the golfer guards against the too-far speed while perceiving the spatial situation and in forming his intentionality about the outcome, he is basically rendered SAFE in terms of the too-far speed. Anything less than that down to a speed that still gets to the front lip is sort of gravy. The main deal is to sort out NOT going too far past the hole. The brain is designed by DNA trained by evolution to protect the human and itself against harm, pain, injury and death during movement. The rule of movement in the brain is safety first, then maybe success second. With this brain, ruling out too far past is the key to getting success, defined as at least as far as the front edge of the hole and safely within the safety zone but never too far past and beyond the safety zone.

The brain regards "safe success" as any putt for which the ball ends up "not any short" and "not too far past the hole as to create a problem in the comeback putt". This means that any ball ending up in this "safe house" is regarded by the brain as "children safe in the home loved equally". There is no sense for the brain discriminating in favor of one child who arrived safe inside only 1" past the hole and against another child who arrived safe inside but who stopped 21" past the hole, when a 21" comeback is never a problem. So the brain does not try to have a touch skill that delivers all balls within a nice, tight go-by distance other than "inside the home safely", as this sort of nit-picking perfectionism doesn't make any putt "safer" or really increase the rate of "success" significantly or avoid "unsafe" in putts going too far past the hole and incurring extra strokes significantly less likely. Why bother?

Aimpoint approaches the issue backwards, regarding the situation solely in terms of sinks. The brain balances sinking one putts with avoiding three putts. In a typical round of golf at the Tour level, a player reaches 12 greens in regulation and takes 29 putts. Of those 12 first putts for birdie, the golfer typically sinks no more than 3 putts inside 10 feet and the 9 rest are two putts from outside 10 feet. All 9 second putts are from inside 10 feet, without a serious danger of three-putting. Of the 6 missed GIRs, the pro chips and 1-putts from inside 8 feet 4 times and two putts for bogey usually from 10 feet and out 2 times. Total 21 putts on GIRs and 8 putts on missed GIRs. Only 7 putts are one putts and all are inside 10 feet; there are 11 putts from outside 10 feet and all are two putts.

The accuracy demanded and available for line control inside 10 feet is no more than +/- 1 degree off line left or right and the putt still will probably sink if the speed is mild. But by the same token, not may putts inside 5 feet actually have break outside the hole, and line accuracy demand is not over +/- 2 degrees left or right. That's a double benefit greenlighting putts in this range without a big risk of changing one putt into three: greater allowable error in line plus using the hole's backstop. In contrast, putts out to 20 feet have +/- 0.5 degree as the maximum error in line and the distance control is more of a threat of being seriously off. This all means that the putts that require care are much more numerous at the long range than putts in the short range requiring similar accuracy for line and distance. In the typical case, about 11 putts are pretty dicey from outside 10 feet whereas putts in the 5-10 foot range number usually only 3 to 5 of the total. STOPPING long putts skillfully no longer past the hole than 2-3 feet is more important by a factor of 3 or 4 times than delivering putts ONLY 6-12" past the hole in order to match some read. 

In so many words, the objective in putting is not one putting the first attempt nearly as often as the objective is to try to sink a longish putt without running long past the hole and making a safe two-putt turn into a dreaded three-putt. Clean up putts are more about smooth rhythm and hitting the intended line than they are about perfecting one specific delivery speed. 

10. All putts feature square, solidly centered, and moving online impacts of the putter head thru the ball: 

Penner: "For the more general case of a rolling golf ball on a sloped green, the value of g will be taken to be the same as is found with level greens, and the equivalent contact point on the golf ball will be taken to be along the direction of travel. These approximations will greatly simplify the analysis and would be expected to have only a secondary effect on the determined paths." 

"In the case where the probability of a player making a putt is small, the scatter in the launch speed and launch angles in the putts of the given player will be much larger than the range in the launch conditions required to make the putt. The probability of the player making a putt will in these cases then be approximately proportional to the areas of the required launch conditions as given in the launch-speed launch-angle space. Pelz [10] found that professional golfers make approximately 50% of putts from a distance of 6 ft. Using this value to scale the areas of required launch conditions, as given in launch-speed launch-angle space, allows for the probability of making putts for other distances and other conditions to be determined. The result for a level green is shown in Fig. 11 with the probability of making a putt shown for hole distances ranging from 6 to 30 ft. Also shown is the range of success of professional golfers, as given by Pelz, in making putts at these same distances. As is seen, the general dependence of the probability of making a putt on hole distance, as predicted by the putting model, agrees well with the results of professional golfers." 

The above two passages indicate that Penner assumes golfers do not always execute putts according to the optimal or even acceptable launch parameters for speed and line. However, once the delivery speed and accepatble entry lines are set, the success or failure of the putt assumes the golfer will execute the correct line and distance (that is, a putt that enters the hole centercut with optimal delivery pace). The calculations of the model ASSUME all putts are started solidly on line. Given the aimpoint, the golfer actually will have some room to perform sloppily and still have the ball captured by the hole, but the aimpoint system has such fine-grained precision that it suggests otherwise. 

Obviously golfers don't really hit all putts on the exact sweetspot with perfectly square faces moving thru the center of the ball directly down the intended line. Pros have an impact profile on the sweetspot that is about 0.5" wide left-right and half that up-down. Amateurs have an impact profile about twice that large. Any one putt falls somewhere within this profile 95% of the time, but even that does not tell how often the face of the putter makes impact while SQUARE to the intended start line or whether the sweetspot trajectory thru impact travel straight down the intended line. Not all that often, I would say, having observed amateurs and pros hitting putts with cut-stroke and arcing paths and with open faces slicing putts off to the outside. 

What difference does this make? The unwarranted assumption would appear to help make the aimpoint system less subject to criticism, but in fact the implied precision required to do what the aimpoint approach commands is ill-advised. Golfers are far more successful in putting generally by NOT being overly precise on the aim and line. Ben Crenshaw, for example, does not use any line when he visualizes the read and the putt path: instead, he sees a ribbon along the green that is about as wide as his putter head from heel to toe, or as wide as the hole itself. Brad Faxon sees the swipe of a paint brush across the surface. Geoff Ogilvy reported in Golf Digest that he never uses targets or lines when reading putts. And in general the phenomenon of getting "line bound" at the expense of touch is well known among golfers. 

11. Calculations of the full range of possible ball trajectories passing the hole will include only a given percentage of successful capture trajectories depending upon the golfer's skill and the difficulty of the putt, so that comparing this capture probability figure to existing putting statistics will serve as a good judge of whether the "model" has a "good fit" with reality. 

Penner: "In the case where the probability of a player making a putt is small, the scatter in the launch speed and launch angles in the putts of the given player will be much larger than the range in the launch conditions required to make the putt. The probability of the player making a putt will in these cases then be approximately proportional to the areas of the required launch conditions as given in the launch-speed launch-angle space. Pelz [10] found that professional golfers make approximately 50% of putts from a distance of 6 ft. Using this value to scale the areas of required launch conditions, as given in launch-speed launch-angle space, allows for the probability of making putts for other distances and other conditions to be determined. The result for a level green is shown in Fig. 11 with the probability of making a putt shown for hole distances ranging from 6 to 30 ft. Also shown is the range of success of professional golfers, as given by Pelz, in making putts at these same distances. As is seen, the general dependence of the probability of making a putt on hole distance, as predicted by the putting model, agrees well with the results of professional golfers." 

As noted, this coefficient of friction is not calculated accurately, but even so, the comparison of the "model" predicitions / calculated results and the pro empirical data is comparing apples and oranges. Pro stats reflect putting on Stimp 11' greens, not Stimp 8' (0.131 friction) greens. A Stimp 11' green in Penner's erroneous calculations is about HALF 0.131, so that is a VERY BIG DIFFERENCE. If pro stats generated on Stimp 8' greens are compared to the Penner "model" predicitions, the pros would be VERY MUCH MORE SUCCESSFUL than the "model", so the "fit" between "model" and real data is not really as "good" as it is claimed to be by Penner, and is likely not a good fit at all.


Summarizing the above "assumptions", Penner uniformly notes that each factor has a real role in reflecting reality but the "model" cannot handle the complication, so the factors are all ASSUMED to be safe to IGNORE. That's just the nature of the whole enterprise of building a "model" -- there's an "art" to it in the choices, and there's also a degree of veracity that is set as the standard for when ignoring a factor is NOT allowed and more serious effort has to be expended in the structuring of the "model". The trouble comes in two main forms: the CUMULATIVE effect of multiple simplifications is likely to be more undermining of the "model"'s efficacy than supposed without deliberate analysis to this issue, and here there is none; and the persistent ignoring of admittedly pertinent factors tends to create an insurmountable BIAS that the end product has not suffered grievously from the slashing and cutting off of whole body parts in pursuit of a stub of a "model" that can handle calculations without great effort. That's basically what we have here.


Aimpoint lacks know-how about how touch works in the human brain-body or on real greens with real golfers, and hence cannot and does not teach touch. Instead, the sessions attempt to get golfers temporarily successful stopping balls within about 10" of the hole with two strings separated that far apart and golfers standing off at various ranges away trying to stop balls inside the two strings. That's NOT teaching "know-how" that travels from putt to putt, course to course, or hole to hole over the weeks and years. Neither can aimpoint teach how to perceive the basic factors reqired to turn to the correct page in the chart book and look up the correct row and column of numbers to find the correct aimpoint. This requires teaching golfers to perceive green speed as a Stimp measurement number (not really possible or normal); to perceive Slope as a percentage or degree (nothing taught except use an instrument of some kind to map the greens and get used to what the instrument reveals); to perceive fall line orientation straight uphill and downhill thru the hole (aimpoint teaches one technique that I taught David Orr, who then taught it to Mark Sweeney, and apart from that, aimpoint cannot teach perceiving the fall line orientation) -- so what use is the chart booklet if golfers can't look up the appropriate calculation (which, by the way, is incorrect)? 

Studies by the USGA have proved that even pro players with years of experience cannot discriminate a slow green from a fast green unless the difference between the two green speeds is at least 1/2 a foot on the Stimp. That is, pros cannot tell which of two greens is the fast one and which the slow one when one green is Stimp 9.5' and the other green is Stimp 9.75'. Interestingly, the USGA made no attempt to determine whether pros can accurately rate the Stimp measurement of any one green with any degree of precision. Probably, pros are not better than guessing green speed within 1' of the actual value. Personal experience over the years and observation of others convinces me that the vast majority of pros aren't all that astute at calling out the number of a green's speed based solely upon visual examination and perhaps a bit of walking on the green. Getting that skill takes more attention and practice than offered merely by long familiarity / experience alone. 


Over 90% of all golfers including pros do not aim inside the hole from 10 feet away, and even at 6 feet away, probably 60-70% aim outside the hole, are not aware of this, and lack skill to aim correctly and accurately. Aimpoint gives these golfers a target, and perhaps during the session the aiming gets finessed okay, but once the golfer leaves, he has no ability to aim the putter and the body and the stroke motion in a manner that succeeds in using the aimpoint calculation at all. So why bother without also teaching how to aim accurately? Aimpoint does not know how to teach this, and at best suggests that a different putter made by David Edel might somehow reduce the misaiming to a tolerable level at least for a while. Sad, really. 


Because golfers don't ever aim correctly, they are at the mercy of a variable stroke to figure out some way to get the ball to end up where they hope it should end up. Typically, golfers mis-aim to the outside and this teaches them at a non-conscious level that only a pull stroke can possibly work. The pull varies with the distance, so even the pull is not a steady action. But golfers typically do not know they mis-aim and also do not know their strokes don't go where the putter face aims -- 90% of them are in this boat. Hence, what sense does it make to give a golfer a target to aim at, since even if he gets aimed at the target accurately, he won't stroke the ball at the target unless he overcomes his usual pull stroke? Lacking experience as putting teachers with real knowledge, aimpoint folks don't seem to know this is a problem, so you get a situation where the blind are leading the blind in the session and later, after the session, the aimpoint isn't useful to the pull-stroke golfer. (This is the same reason that aiming a line on the ball correctly "looks left" to golfers with a pull stroke as their habitual pattern. A line on the ball "looks" right ONLY to a golfer who putts the ball the same direction the putter face aims at address, which comprises perhaps 3-5% of all golfers on the planet at most. This is just another instance of NON-instructors, unfamiliar with real skills and real golfers putting, assuming that they have a good bead on things with a few math and physics calculations. 


The USGA equipment czar approved aimpoint charts as not in violation of the Rules in March 2008, but in November 2008 the USGA and R&A main bodies entered into a Joint Statement on Electronic Artificial Devices such as iPod apps and laser range finders that unequivocally reaffirmed the general rule that ONLY DISTANCE is allowable information that can be included in booklets and in range finders, and that ELEVATION and CONTOUR information ("slope", "gradient" etc.) cannot be used to assist golfers in planning or executing a stroke, as that undercuts skills and tradition. Aimpoint thinks they are legal because the equipment czar issued a ruling that was not correct according to the Rules he applied, and is definitely not correct in light of the Joint Statement, and has simply not been officially withdrawn or corrected. Golfers who bet that use of aimpoint charts will be approved for use in competition such as the US Open or the British Open or any other stipulated round when the governing bodies convene to refine and clarify the Rules of Golf in their 2012 session are, in my view, a little over-optimistic that their skill-debasing ways will be overlooked and allowed to continue. The basic desire to use a chart like these is very anti-golf for skill and tradition, regardless of what the current occupants of Golf House might opine. I vote for golf, not folks unhappy that they lack skill and want merely a lower score by cheating. 


Colonel H.A. Templeton actually road-tested his charts and used a more realistic delivery speed for the main touch in his calculations (in his 1984 book, Vector Putting: The Art and Science of Reading Greens and Computing Break, long out-of-print and almost entirely unread by golfers). His charts have less break than aimpoint breaks. Templeton's 9.5' Stimp 2% slope from 10 feet sidehill has 7" break. Aimpoint's 10' Stimp 2% slope 10-foot sidehill putt has 9" break. This pattern is replicated throughout all the charts for all the slopes and green speeds and distances. 


The REAL way the brain uses perceptions and movements based upon perceptions is NOT by using numbers generated by abstract general formulae out of physics texts. The brain uses FACTS without converting the facts into or out of numbers and measurements and calculations. The brain is a Picasso perceiving the world and then responding, and Picasso does not paint by numbers.

One better way is to imagine a straight line from ball to hole and then predict what exactly would happen if the golfer putted straight along this line with his personal good delivery speed, accepting whatever the slope and green speed and contour shape that is present, and then "seeing accurately" exactly how far below the hole such a putt would pass the hole with nice stopping speed, and then aim exactly that same distance to the high side of the hole and repeat the same touch in a straight stroke at this high-side target. Another way is to generate SPECIFIC knowledge by learning how to perceive green speed and slope and then find a typical slope (say 3%) that one is likely to encounter many times in a round on the specific course and then step off sidehill to 10 feet and putt dead straight at the hole with good delivery pace and observe and mark exactly how low this PARADIGM 10-footer breaks. In fact, putts on this slope and green speed form anywhere on a 10-foot circle around the hole use this one same aimpoint with only very minor adjustments for uphill putts and downhill putts. On the course, all the same putts with the same slope and green speed will break the same from sidehill and 10 feet, and then the golfer can adjust for fine-tuned complications. The adjustments are: steeper slope breaks more, so that one-third more slope breaks about one-third more; faster green speed breaks more, and as a rule of thumb each 1' increase in Stimp speed requires about 20% more break; and greater distance breaks more, and as a rule of thumb each 2.5' (one military step) increase in distance adds about 25% more break. 

Here is another "ballpark" system for estimating the break / aimpoint above the hole on the fall line in inches, after which the golfer has to pay attention to the complex reality and fine tune the read. For any given slope grade, the golfer counts the number of steps the ball sits out from the hole and applies the following formulae to get a good "ballpark" sense of the real break or aim in inches above the center of the cup along the fall line:

1% slope: Steps - 1 (e.g., 4 steps away, aim 4-1 = 3" up fall line) 

2% slope: (Steps x 2) - 1 (e.g., 4 steps away, aim 4x2 - 1 = 7" up fall line) 

3% slope: (Steps x 2.5) (e.g., 4 steps away, aim 4x2.5 = 10" up fall line) 

These approximations apply pretty well on Stimp 9.5' green speed between 7.5' to 20' out. For each additional slope increase, the break grows by about one third (about 33%) (e.g., break of 10" at 3% becomes 13" on 4% slope; and then on 5% slope this becomes 17").

To perceive the slope percentage, orient to the fall line straight uphill-downhill thru the cup, walk three paces plus 10 more inches straight downhill, or walk three 35" putter lengths downhill, and compare the spot 100" below the cup to the elevation at the cup. An elevation difference onto the toe of the shoe located at the downhill spot is 2" and a 2% slope. A difference onto the tops of the laces of the shoes is 3" and a 3% slope. A difference onto the ankle bone is 4" and a 4% slope.

Do the aimpoint charts work despite all these flaws? Not really. There is no quantification of the actual touch, aim, and stroke straightness or the arrival speed of balls to CHECK whether the results in a training session or by one golfer attempting to apply the charts in perceiving slope and green speed and distance and delivery speed actually involves using the charts correctly or getting the expected results or simply getting a happy result in a sloppy way. Golfers who think the charts are giving good results and teaching good green reading skills are simply reacting to getting something to drink after crawling in from the desert wasteland after years baking in the sun of skill-lessness. Well, perhaps the drink is not really wholesome.

How about the television computerized line? First, that line cannot be generated by a human or even by a computer unless 1. the green surface is surveyed with precise laserometry in tens of thousands of small data points, and then 2. fed into a computer until its memory banks are ready to burst wide open, and 3. then the high-powered computer number crunches all the surface data points and the physics formulae to generate a point-to-point fine-scaled curve from ball to hole across the contour that represents the computer's read, not the golfer's. This limits the tv usage to about three greens maximum per course, since the computer will not hold more data; the greens must be lasered days in advance; the computer calculations have to be short-cutted to reduce the time the calculations and plotting takes to fit within the time from "ball lands on green" to "golfer strokes putt", since without this short-cutting there is not enough time to use the tv system at all. At the end of the day, the curve drawn on the green for tv is not the golfer's read, but the computer's read. The golfer's putt may not match the tv curve, but this does not indicate that the golfer misread the putt or failed to execute the putt he read. And in any event, this system is completely useless to real golfers -- hence the chart limited to "planar" surfaces and 20 feet out. 

Here's how Penner ends his "model" building -- claiming comparison of Stimp 8' calculations with Stimp 11' pro stats works out fine but then doubting any of this matters to real golfers: 

Penner: "The model of the path of rolling golf balls on sloped greens that has been presented has provided reasonable results. However, it must be made clear that the model can only approximate the actual behavior of a real putt. This is not only due to the approximations made in the treatment of the contact force and the initial motion of the golf ball but also because the grass surface will have small but numerous imperfections that will result in deviations in the golf ball’s path."

"The dynamics and the resulting paths of the golf balls that have been presented provide a reasonable model for the motion of a golf ball on sloped greens. To further improve the model would require an investigation on the position of the contact area for a rolling ball on a sloped surface and the resulting contact forces and moments. The resulting required launch conditions that were determined from this model, along with Holmes model, allowed for the determination of the dependence of the probability of making putts on the putt distance. The result agreed well with the actual performance of professional golfers."

"The model presented in this paper could be applied, in general, to the topology of any green and it would be interesting to consider the variety of possibilities.
Whether the results presented here would help a golfer improve their putting is debatable and, unfortunately, this author has not noticed any improvement in his game.

As it happens, Mark Sweeney has said that Penner's physics accurately represents what happens in real putts as if the calculations of the aimpoints are "calculated facts," unassailable in the same way that 153 yards is not arguable and is simply the measured FACT. He sold the charts on this basis to the equipment czar at the USGA, who also thinks the calculations are no different from saying the measurement of the distance is 174.5 feet. But obviously, the "model" calculations are way off being mere measurements or infallible, unassailable statements of FACTS. Sweeney does not appear to recognize the difference between a "model" of cobbled-together formulae simplified for convenience and physics that accurately and veridically portrays reality with quantitative and numerical preciseness. 

In essence, aimpoint is a "suggested read" -- or even merely an "opinion" -- and not a very helpful one at that. Aimpoint is similar to your caddy reading putts for you without first watching to see how you putt. And in this case, the caddy has no great track record as a reader of putts and has a few issues in his vision, his basic familiarity with greens and the skills in play, and his capacity to make sense of what he's looking at. Since it's science, with numbers and physics and formulae and a professor and all that, it must be right, huh? Golfers, though, should not be misled about this. 

To summarize the MAIN points, the unreal touch skews all the targets too high, the calculations are based on a very dubious "model" with lots of simplifications that move the model away from reality, the whole is worthless without perception skills required to look up the numbers in the charts, the whole is cheating and not real golf, the comparison with pros is apples and oranges, it has all been done better by Templeton, the brain doesn't work that way, and there are easier ways to do the same thing better.

Other than that, aimpoint is the greatest thing since bounce on a sand wedge.

Instead of getting entangled in all these issues and trying to salvage something of value from the mess, golfers would be better advised to learn how to perceive slope, fall lines, green speed, ball delivery speed, elevation differences, and typical putting paradigms and patterns, and then knowing how to put all this together on real greens facing specific putts by paying attention to the space with the golfer's personal sense of delivery speed. Read with YOUR speed to see YOUR break for THIS putt, and then build the aim for start line and execute the putt with the touch that brought you to the dance. 

Applying science appropriately to a sport skill like putting requires quite a bit more than mere familiarity shuffling formulae about. In general, if someone claims that a certain science has applied answers for golf, the first question has to be, "What makes you think you know about golf?" In the case of putting in particular, it would be unusual in the extreme for someone to understand what is involved in putting skills without years of focused attention, observation and study. It's not something amenable to "cut-and-paste" expertise.


Geoff Mangum 
Putting Coach and Theorist

Monday, September 12, 2011

Brain Science and Putting

In golf strokes, the non-conscious body-brain is oriented to the objective world-as-it-is, and not concerned with the subjective state of the conscious mind for "feel" of the body.

"Feel" is the worst term bandied about without clear definition in golf. Golf psychologists who use this term certainly should know better, if they have been keeping up with the incredibly rich and important new brain science spawned since 1990, but of course they have not read any of this new science at all, as is pretty evident to anyone who has.

What is "feel", and why is it poison for golfers?

"Feel" is a subjective registering in the conscious mind of a state of the body for position or movement, used to allow the mind to "judge" whether the "feel" comports with expectations and memories of what the golfer "thinks" is the correct and appropriate body action for the immediate stroke.

What's poison about that?

What is absolutely bad about "feel" is:

first, what gets elevated to the conscious mind is not especially accurate and real, but is an assemblage of ad hoc sort-of's about the body that may or may not be accurate reporting of the body state; 

second, the conscious mind is not an impartial judge of "feel" but is tainted by habits and expectations and also false or partially false memories; 

third, the implicit notion that unless the conscious mind "approves" the current "feel" as correct and appropriate for the stroke, then the golfer is unlikely to execute the shot well, is a formula for de-emphasizing the world-as-it-is in favor of the body-as-it-might-be-if-that-matters, which promotes error in performance; and 

finally, routing the movement thru the conscious mind prevents or at least obstructs and interferes with reliance upon the body processes at the non-conscious level of the brain-as-organ/not-awareness and the body-as-organ-operated-by-the-brain-as-organ.

So what is superior to "feel" -- what is the better way to play golf? Non-consciously, with the body. 

But isn't that what golf psychs teach -- to play golf non-consciously? Yes, that's what they "say", but "feel" is NOT playing by non-conscious processes -- "feel" is only "feel" when it is in the conscious awareness. Evidently, golf psychs don't really know the difference between the mind and the non-mind.

Golf is a game played in the six inches between the ears? Well, sort of. Golf is 100% physical and mental in assessing what to do and getting prepared for the stroke, then it's 100% physical and 0% mental in executing the stroke. How's that?

I guess you'd have to have been keeping up with brain science to realize how this is all VERY DIFFERENT from how golf psychologists talk about the mind and the non-conscious. The non-conscious is FAR, FAR MORE than simply shutting off the mind, Bob.

In modern neuroscience, "consciousness" means "subjective awareness", and non-consciousness means "brain and body processes of which we have no subjective awareness".

In a nutshell, the BODY and it's processes (especially for movement) comprise the non-conscious processes of the brain as organ operating the body, and those processes account for about 90% or more of ALL brain processes. And the "conscious" experiences in the MIND don't seem to have much purpose, at least for human movements such as those in golf. But then that knowledge is pretty new, compared to the pop psychology of the 1970s and 1980s that infuses all "golf psychology" today, which is uniformly ignorant of the new brain science.

The better way is to play golf "non-consciously" with the body, not with the mind, and this means, frankly, that reliance upon "feel" is not only ill-advised, but counter productive by blocking off use of better ways of getting it done.

This brings us to the odd crux of the matter: the body is not concerned with "subjective" states and instead is "all about the external world". "Huh, come again?" the golf psychs mutter incredulously.

Your non-conscious brain and your body -- when it comes to moving in the world -- basically could care less what your mind thinks about things.

Contrary to what golf psychs and most motor sports experts believe (as evident by their writings and teachings), the body is not unintelligent compared to the mind, as in the old attitude that the body is the dumb brute and mind is the cultivated human part of ourselves. This notion is utterly pervasive in western society. 

Golf psychs certainly believe that playing non-consciously is little more than turning off and not using all the usual stuff that accounts for intelligence, such as analysis and language and avoiding error with check lists. That's the problem: modern brain science says that the non-conscious brain-body processes ARE intelligent in ways that the mind has no clue about. Turning off the mind is not at all what is needed to play golf with the non-conscious brain-body informed by current science. The golfer needs to KNOW about the body's movement intelligence and know also how to operate these processes to take advantage of the body's knowledge for movement.

So let's get serious and stop pretending it is unnecessary to incorporate the NEW brain science in golf. Teaching wrong stuff is just bad teaching. Teaching out-dated wrong stuff is bad and LAZY.

In what sense is the body in its non-conscious processes intelligent and educated?

The way the world and objects in the world including the body operate together in motion is called "physics". The BODY knows more specific and accurate physics about the world and body movement in the world than the MIND by a factor of 50 to 100 times. That's because the ONLY physics the MIND knows is the physics the mind assumes or the physics that a high school teacher implanted to replace misconceptions about how the physics of the world works. That is also because the world trains the BODY according to how the physics of world-body operates, and does not train the MIND at all. In fact, the MIND is completely ignorant that the world is training the BODY so that the BODY "knows" and "accurately uses" the real physics in movement planning and execution. The MIND believes and claims that the only the MIND could comprehend such a sophisticated science as physics and that the brutish BODY couldn't possibly hold a candle to what the MIND knows. This is the problem.

Ask any high school physics teacher what he faces when a new crop of bright-eyed students occupy the chairs in his or her classroom at the start of the academic period: all high school teachers know the students, be they ever so intelligent, are invariably besotted with firmly held but mistaken beliefs about the physics of the world. Among teachers, this is called "the usual collection of beliefs of naive physics". That's why the teacher has a job, and always will.

For example, Aristotle around 500 BC contemplated which mass will drop faster from the same height and reach the ground sooner: a bowling ball weighing 20 pounds or a golf ball weighing 45 grams (a little less that 2 ounces or 1/8th of one pound, 160 times less than a bowling ball). his answer, supported by sophisticated reasoning as usual, was that the bowling ball gets to the ground sooner. He didn't actually perform any experiment to check this, as Greek thinkers didn't do such menial things as experiments.

And for the ensuing 2,100 years ALL humans who inhabited the earth SWORE that the more massive object will always outrace the less massive object to the earth when released from the same height at the same time. Until ONE PERSON actually checked it, and found the claim and the belief to be wrong.

Galileo in about 1600 AD checked, and he was the first person who said, no, ANY two objects always fall side by side when dropped simultaneously from the same height, regardless of even the largest differences in mass of the objects. All masses always fall at the same rate of accelerated motion, side by side, no matter what!

And then for the following 400 more years to today, all the humans STILL get this wrong unless they take a physics class and hear the gospel, and remember it when asked the question. Otherwise, since Aristotle, every human on the planet, without specific education to correct this error, has a firmly held and completely incorrect belief that can be invalidated instantly by simply checking OR by observing what actually happens all the time on the planet.

This is the nature of the the MIND's stupidity about the real world and it's physics.

A similar misconception in the MIND is that two arms held out to the sides away from the thighs, with one being held a short distance and small angle off the thigh and the other being held a large distance and angle off the other thigh, when dropped down to the thighs by relaxing, reach the thighs in different times -- the closer one hitting the thigh first, followed by the farther-off arm and hand striking the thigh later. Wrong, and not only wrong, but always and forever happens a different way, but the MIND for some reason doesn't ever see the real answer.

As to these two fundamental examples of important physics for movement on earth (free fall of all objects and pendular motion of arms and legs and sticks and metronome rods pivoting on a point), the BODY knows the accurate physics and always gets this correct, and the MIND firmly believes an obviously incorrect if not to say stupid notion of real physics.

Okay, just how educated is the BODY? Very, and very specifically. 

An example is how the world trains the body to ONE TEMPO. A tempo is how long a stick takes to swing from top to top in pendular motion. The world's physics for this is set once and for all time by the size of the rock we live on, which has been the same for about 4 or 5 billion years and isn't likely to change this week. The earth swings ANY stick in ONLY one timing or tempo, and the timing depends solely upon the length of the stick, not the weight or mass of the stick (remember free fall, where mass is irrelevant?) That applies to the human arm of the adult as well, since the arm has finished growing longer and has been the same length now for years.

When a human moves about, the arm separates from the body by turning or by voluntarily swinging it away from the side, against the force of gravity, and then the earth swings the arm back down to the side according to the laws of earth's gravity. The timing of ALL these motions down are always and forever ONE TEMPO -- short or long swings all get returned in exactly the same timing every single time when the earth swings the arm down. Roughly speaking, every human BODY gets about 857 doses or trainings of the earth's tempo for the arms every single waking day since adulthood.

What is that timing or tempo? It simply depends upon the length of the human's arm. For most people, the arm is about 3 feet long from shoulder to fingertips. How long does the earth's physics take to swing a stick that long from top to top? A smidgen less than one second or 1,000 milleseconds, perhaps around 980 milleseconds. That's because a second (1,000 milleseconds) is the time required to swing a "meter stick" from top to top, and a meter stick is slightly longer (39.37") and slower than a human arm at 36", but not by much. Yes, each individual has a somewhat "unique" timing because each arm has a unique length, but that's dicing the matter too finely, and the reality is that the different lengths of adult human arms aren't all that different, and the overlap is very prominent among a random group of people.

The MIND is utterly unaware of this on-going, ceaseless, "mind-numbingly the same" BODY training that the world carries on. And golf psychs and motor sports experts are also completely unfamiliar with (ignorant of) this training relationship between the BODY and the WORLD.

How things fall from any given height is also trained into the body, and likewise how much force is required to SEND a given mass up away from the earth thru its gravity is also constantly trained. There is one and only one force that sends a golf ball to a height of 16 feet, ever, for every human who wants to send a golf ball that high.

This brings us to the OBJECTIVE nature of the NON-CONSCIOUS brain and body processes.

The essential purpose of the BRAIN is to record the WORLD and it's invariable physics so that the unchanging BODY can use this knowledge to make safe and successful motions, and avoid pain and injury as the top priority and achieve success as the secondary priority. The BRAIN is midway between the WORLD and the BODY.

That's the odd thing. The WORLD is what it is, regardless of what you or anyone might think. And, as it happens, the same is true about your BODY, since you won't be sprouting an extra arm in the next few days or hours. So the BRAIN is recording the physics of this WORLD as they objectively operate in terms of moving the only BODY it knows. For the BODY motion to comply with the objective requirements of the WORLD, then, the BRAIN in moving the BODY has to meet the objective requirements of the WORLD. Otherwise, the movement fails or at worst incurs pain and injury.

This all means that the BRAIN in movement of the BODY is not at all concerned about internal states of MIND. Of course, MIND can completely ruin a movement, but MIND actually is irrelevant otherwise to the BRAIN and BODY for safe and successful movement.

Okay, you say, this is way too theoretical. No, it's not. It's ACTUAL.

But how do you use it? Touch or pace control in putting is an excellent example of how this new brain science applies to golf.

First, the BRAIN cannot change space or mass, and can only influence the TIMING of movement of BODY parts. The BRAIN times movement. Period. Given a mass, such as the hand, or the arm and hand plus a putter, the timing defines the force. There is no calculating the force in the BRAIN -- there is only timing the mass in relation to the requirements of the WORLD. And timing is OBJECTIVE -- you either play the music in compliance with the conductor's tempo, or you get kicked out of the orchestra as a poor musician.

Second, the intentionality of a movement to a space and the definition of the space's perception in terms of what matters for the movement is what determines the force required for a given movement. In order to fly a ball 150 yards from tee to par-three, the force required is X ergs for all comers, Sally or Tom. You either deliver the goods required or you're short or long of the target. The MIND is not part of this except when the self-reflective human starts asking what's going on. What's going on is making a good stroke so the ball goes correctly to the space. That's pretty much it for the MIND, and that only comes up if you feel a need to be reflective. But it need not and should not come up at all, unless perhaps you suck at doing what is required when you play golf, or just don't like the challenge. Then perhaps the MIND has a role to keep you on task with your perceiving and your intentionality.

For force control in putting, the BRAIN uses the perceptions of the WORLD as it is with the clear intentionality to LIMIT the force first and foremost to insure safety in the motion by avoiding and ruling out "overshoot" or spastic movement that poses a substantial risk of pain or injury. But the BRAIN does not limit the force unreasonably so that success is thereby sacrificed: the limit is only imposed when the force reaches 100% of what the WORLD requires. 

Specifically, the force of a putting stroke starts with tempo and then the velocity of impact at the bottom of the swing is simply a matter of the SIZE of the backstroke, as the size determines how much downward acceleration the stroke undergoes to peak at a specific velocity at the bottom of the stroke. That's what the BODY knows specifically. The BODY knows for the given main tempo the WORLD daily installs in the BODY what exact size stroke goes with what exact velocity. The "knowing" of this is not knowing in the same way a student answers a test in a class, but in terms of using the knowledge reliably and consistently. The BODY for this specific tempo very intimately knows exactly how an entire spectrum of backstrokes correspond to velocity of impact, and when a specific putter mass is used familiarly, the BRAIN/BODY then also knows every backstroke size in terms of the force of impact, since force is mass combined with velocity.

Now, to simplify: the BRAIN pays attention to the WORLD as it is and this sets the SIZE of the backstroke using the main tempo to 100% of what the WORLD requires, using the BODY that is essentially unchanging as is what it is. With the size of the backstroke set, and the tempo in place, a backstroke uses one dose of tempo to reach the full size of the backstroke and then expends this energy by repeating another dose of tempo from top of backstroke to top of thru-stroke. Anything else will be short or long.

Eh, that means the BODY processes of setting the backstroke and getting the touch correct are COMPLETELY OBJECTIVE. Here's the "check list" of things that the golfer either does or does not do, in a yes/no or black/white sense:

1. Did the golfer formulate the intentionality with seriousness and commitment to move accurately all the way to and not too far past the hole? Yes or no.

2. Did the golfer pay attention to and take into account whatever matters for the WORLD's force requirement, such as distance, green speed, and elevation change uphill or downhill from ball to hole?  Yes or no.

3. Did the golfer then respect and allow the toss-back impulse used to send the arms and hands and putter into a backstroke swings that achieves the only correct size (safe and sufficient) for the WORLD's requirement for force in this putt? Yes or no.

4. Did the golfer's backstroke persist for one full dose of the chosen tempo? Yes or no.

5.Did the golfer's thru-stroke match the backstroke timing with another dose of tempo? Yes or no.

None of this is subjective or at all dependent upon anything subjective or even conscious, with the possible exception of sticking to the task and keeping the perceptions going after useful and relevant perceptions.

But when it comes to the actual stroke motion, assuming the intentionality and perceptions have accurately set the size of the backstroke that will take place, nothing is subjective and everything is completely "do it right or mess up." Respect the impulse without knowing or having any awareness in advance (or even needing a practice stroke or any memory of what to expect, and certainly no judgement of the size as the stroke unfolds). Comply with the WORLD's tempo in the backstroke. Allow the WORLD to handle the thru-stroke, since that will always comply with the WORLD's tempo. Basically, touch is simply pay attention to the WORLD's space for the putt with movement intentionality and then start the backstroke with good tempo and whatever impulse that the non-conscious BODY has set by prior tempo-force training from the WORLD.

You can work math problems while you putt so long as you stay on movement task and comply with the tempo, without any effect at all on the safety of success of the touch.

So teaching that golf should be played non-consciously by turning off the mind is half-assed teaching that leaves out the positive information about HOW to employ the non-conscious processes. Turning off the mind is not really necessary OR sufficient to use the non-conscious processes effectively. That requires some real knowledge about how those processes are structured and operated.

From touch in putting to all human movement, it's a new century, folks. Catch up and stay up, and if you're a golf psych too lazy to incorporate the new knowledge about the BRAIN and the BODY, I would suggest you shut up about the MIND and the Non-conscious.


Geoff Mangum
Putting Coach and Theorist -- golf's most advanced and comprehensive putting instruction.