Break Aim-Point Charts
Limitations for Learning Skills for Reading Putts
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Aim points per green speed, distance, and slope, from H.A. Templeton, Vector Putting: The Art and Science of Reading Greens and Computing Break (Fort Worth TX: Vector Golf Inc., 1984) (over 20 years ahead of AimPoint Golf and all others):
The Limitations of Aim-Point Charts
All breaking putts come down to LINE and SPEED. Two points make a line and the first one is the ball -- the second point for the LINE is the aim point on the fall line of the straight uphill/downhill putt thru the hole. The SPEED is "nicely into the hole". So breaking putts have a start line and a real curve down off the start line into the hole. The SPEED for the real curve is the same for the imaginary straight putt from ball to aim point as if there were a second hole on the fall line centered at the aim point and the golfer delivers the ball "nicely into the hole" at the end of this straight and level putt. This use of the fall line for performing touch has never been a part of golf lore for reading putts before the PuttingZone, and is not part of the aim-point charts even today. All aim-point charting is based upon an assumed speed pattern of the ball from start to finish that may or may not correspond to the speed used by a specific golfer, but does not in any event address the issue of how the golfer gets control of his speed. The golfer needs to understand HOW touch works, and specifically how touch and the fall line are related when the golfer reads any putt in order to identify the correct aim point.
The golfer of course needs to "perceive" the aim point and know how to get this done, but the charts that simply list the aim points for various putts give the golfer an aim point based upon the physics of ball-green interaction for all putts LIKE the one the golfer faces. But remember: perceiving THIS PUTT is MORE THAN the physics of a general putt likeTHIS PUTT. The charts simply get the golfer into the general ballpark, but then the golfer has to pay attention in perceiving THIS PUTT. Charts are "general" but each putt is "specific". In particular, the charts and aim points all ASSUME every golfer uses the same SPEED and that the green surface is TRUE so that nothing in the grass (apart from the slope and green speed and gravity) will alter the rolling direction or speed and energy of the ball. In the case of Templeton's charts, the assumed speed is one that would roll the ball about 12" past the hole in case of a close miss on most normal green speeds without substantial uphill or downhill past the hole. Other charts are based upon a different delivery speed or even a range of delivery speeds. A chart that uses 6-12" past the hole like the most recent one has larger breaks than otherwise, as this is a very "die in the hole" slow delivery speed that is not normal. So, charts are sort of "opinions" about your putt -- everybody has one.
Recent Efforts Using the Fall Line to Find Aim Points
The more recent efforts to model ball-green paths or use aim-point charts -- work by Lorensen and Yamron in 1992, Hubbard and Alaways in 1999, Vanderbei in 2000, David Ewing and others in 2004, AimPoint Golf by Mark Sweeney and Ray Penner in 2005, Britain's Adrian Fryer and his Spider Disk, and others -- all use the same or similar assumptions about surface and ball speed. AimPoint's televeision product and later charts are based upon the physics formulae for ball-green and ball-hole interaction detailed in A.R. Penner's article, The Physics of Putting, Canadian Journal of P hysics, 80: 1–14 (2002). (Neither Ray Penner nor AimPoint's Mark Seeney was aware of Templeton's earlier work and Penner's article does not explicitly identify the fall line as such.) Penner does not attempt to address the putter-ball interaction or the golfer-putter interaction. However, herein lies the whole question of SKILLED PERFORMANCE -- perception of line and distance and execution of the stroke for line and distance. At the end of his survey of the known physics for ball-green and ball-hole interactions, Penner concludes: "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." No matter how many Ph.D.s in physics someone may have, it's still not the arrow -- it's the Indian. That's a different laboratory and a different science library altogether.
For example, the assumption that the surface tilt and direction does not alter between the ball and the hole causes two BIG problems for using aim-point charts. First, at a certain level of resolution, the assumption always fails -- greens are only approximately flat over a typical radius out from the hole, usually around 3-10 feet. Second, charts don't handle double (or mltiple) breaking putts very well at all -- far too complicated to deal with. If a lion is charging into your camp on the savannah, you wouldn't want to stand there calculating his body mass, fang-bite pressure, and likely launch angle in the breeze, and then start measuring the black powder into your cartridge loader with a tiny spoon while he's closing the distance on you and your clipboard! A great deal of the fun and challenge of golf (as opposed, say, to shuffle board) derives from "the rub of the green."
The Use of Aim-Point Charts
To use charts like those of Templeton for aim points on the fall line or Zero Break Line (straight uphill or downhill putt thru the cup), identify first the green speed. Charts fin Templeton are for Slow (4'6"), Medium Slow (5'6"), Medium (6'6"), Medium Fast (7'6"), and Fast (8'6") greens. Then on the chart for today's green, identify the slope between 1% and 6%. Then idenify the distance of the putt (rightmost side of chart, from 2.5' to 25' in 2.5' increments). The large number in the chart's intersection of the slope and distance
is the number of inches above the hole on the fall line to aim the putter face at. The small numbers in the same box are for adjusting slightly for faster / smaller-break uphill putts (lower right corner) or slower, bigger-break downhill putts (upper right corner). The "touch" is based upon balls that roll 2-3 rolls past the hole in case of a miss (about 12"). (Templeton states that the "decay" phase kicks in when a certain slowness is reached in the retarding speed of the putt, and that this varies a little with green speed, but independent of green speed, once the "decay" phase begins, the putt is over in about one more foot in all cases. His data says the "decay" phase starts on a 4.6' Stimp green at 3.05 ft/s or 7.0 revs./s and on a 10.6' Stimp green at 2.06 ft/s. or 4.7 revs./s, page 62.)
Below are Templeton's five charts for Slow (4'6"), Medium Slow (5'6"), Medium (6'6"), Medium Fast (7'6"), and Fast (8'6") greens. (These are "Membership" green speed categories circa 1980, as compared to "Tournament" speeds that run from 6'6" as Slow to 10'6" as Fast. Templeton unfortunately does not include charts for these Tournament speeds, but one can extrapolate thusly: for a Stimp 9' chart, use the Stimp 4'6" chart for the slopes that are twice as steep as the ones on the Stimp 9' green. For example, the aim for a Stimp 4'6" slope 4% putt corresponds to a Stimp 9' slope 2% putt -- same aim; and the doubled slopes for the Stimp 5'6" chart correspond to the slopes for a Stimp 11' green.) The columns are slopes from 1% to 6% (6 columns), and the rows are distances from ball to hole in 2.5' increments over the range 2.5' to 25' (9 rows). So each chart has 54 "cells" with a number, and each cell gives the number of inches to aim above the cup along the fall line or the Zero Break Line. Click on the above live links to download each chart separately for printing out. The MAIN ones to get familiar with are 8'6" (medium) and 9'6" (medium fast) and 10'6" (fast), as these three charts probably account for 95% of greens the vast majority of golfers always play on a regular basis.
Small numbers. Some cells have small superscript numbers also. Inside about 10 feet, with usual slope, these adjustments are not critical. The upper right small negative number is the maximum to add for downhill putts with larger breaks. All (100%) of the number is added in for straight-downhill putts from the 12 o'clock position, about 50% for breaks in the 10-11 o'clock or 1-2 o'clock areas, and about 10-20% for breaks in the 9-10 o'clock or 2-3 o'clock areas (with 3 and 9 o'clock being straight-on sidehill putts). The small negative numbers in the lower right of the cells are for uphill putts, from straight uphill at 6 o'clock (subtract 100%), to the 4-5 and 7-8 o'clock areas (subtract 50%), and the 3-4 and 8-9 o'clock areas (subtract 10-20%).
Even though these charts are interesting and moderately informative, they are NO SUBSTITUTE for learning HOW to perceive the read correctly. Below is a detailed discussion of the HOW-TO for the perceptual process of reading a putt.
Nice Rules of Thumb:
Rules of thumb and a good sense of what is "small, medium, or large" are worth their weight in gold for playing golf compared to the analytical, abstract approach of numbers. Golfers need these rules of thumb more than a chart in their back pockets.
The most common slope is 2-3%, the most common green speed is Stimp 9', and the "money putts" are between 5' and 10'. Past 20', the green contour and distance essentially render aim-point charts useless. Looking at the most likely and meaningful putts focuses on normal green speeds and slopes in the 5-20' range, the "rules of thumb" and the slopes and distance ranges where they apply are":
Aim in inches "rule"
by counted steps minus 1
4 steps away (10') aim 3" up fall line; 7 steps aim 6"; 8 steps aim 7"
For a normal green speed (here 9.5'), the above rules of thumb apply pretty consistently, especially in the 3-8 step range (7.5' to 20').
When the distance changes, these rules of thumb indicate the approximate change in the aim:
one step (2.5') at a time
-- new aim spot is ~X % higher
from 1 to 2 steps (2.5' to 5')
from 2 to 3 steps (5' to 7.5')
from 3 to 4 steps (7.5' to 10')
from 4 to 5 steps (10' to 12.5')
from 5 to 6 steps (12.5' to 15')
from 6 to 7 steps (15' to 17.5')
from 7 to 8 steps (17.5' to 20')
When the slope changes, these rules of thumb indicate the approximate change in the aim:
one level at a time
-- new aim spot is about ~X % higher
from 1% to 2%
from 2% to 3%
from 3% to 4%
from 4% to 5%
from 5% to 6%
jumping up from 1% as base level
-- new aim spot is about ~X times higher
from 1% to 2%
from 1% to 3%
from 1% to 4%
from 1% to 5%
from 1% to 6%
When the green speed changes, these rules of thumb indicate the approximate change in the aim:
Speed Increase (Stimp ft)
one level at a time
-- new aim spot is about ~X % higher
from 7.5 to 8.5
from 8.5 to 9.5
from 9.5 to 10.5
Changing the delivery speed of the ball is not advisable, so the golfer needs to regard the Templeton charts as delivering the ball with 2-3 evolutions per second that would roll past the hole not more than 10-15 inches in case of a near miss.
A preliminary examination of the different combinations indicates that there is an apparent lack of cohesive patterning in the slowest greens, the shortest ranges, the longest ranges, and the fastest greens. In other words, the aim-point charts appear to be more consistent in a certain limit of parameters: green speed 8.5 to 9.5 and putt lengths 7.5 to 17.5 feet. Greens typically affect the path of the ball by as much as 1-2 degrees, moreso on longer putts. When the putts get too long, the variation introduced by the green surfaces alters the path of the putted ball as much as or more than the differences between aim points for adjacent ranges and slopes. An aim point for six steps (15') on a 9.5' Stimp green at 3% slope is 16" and the aim point for 4% slope is only 7" more, but the green variation can knock the ball off line about 6". The difference in aim points for a Stimp 9' green with 4% slope from 15'and from 20' is 9", and the green variation may sometimes affect the line on a 20' putt by 8". The implicit suggestion that the aim-point accuracy is precise at these ranges is likely not the case in the real world. The other end of the realm -- short putts and slow greens -- is also somewhat problematic because slow greens go hand-in-hand with non-true rolls and greater variation in ball speeds by the same golfer compared to longer putts. The mathematical modeling of the physics general formulae is most accurate on a perfectly flat marble surface putting balanced, round balls without dimples using a robot to make the strokes. From there, the physics is all downhill compared to reality.
Other aiming charts list different aim spot distances up the fall line, due to different assumptions. Here is the Breakmaster explanation of how slope affects putts on a given green speed:
How Much Will My Putt Break?
The BreakMaster will tell you accurate information about what's happening on the green that your eyes can never see: the exact break direction (downhill) as well as the exact amount of break (shown as degrees of slope).
But once you have this information, what do you do with it? How do you put BreakMaster data into practical use to adjust your putt?
At Exelys, we've done extensive testing in real-world situations to find out how much putts will actually break at various kinds of slopes. We've tested on greens of different types (bent grass, Bermuda grass) at varying green conditions and with various popular brands of golf balls. The following table can be a useful general guideline to helping you adjust your putt.
Note: all of these measurements were taken putting straight across the break, meaning at a right angle to the downhill line (the break or fall line) which is indicated by the arrow on the BreakMaster display.
Templeton's aim-point charts are below, and following is a discussion of how to perceive break -- slope direction and steepness / grade, green speed, ball speed, fall line, aim point or target on fall line, start line, distance reference, curve path into hole, and more. To JUMP straight to the "how To" discussion, click here.
USING CHARTS vs READING THIS PUTT
Perceiving the Fall Line and Slope and Green Speed and Ball Speed for THIS Breaking Putt
All breaking putts depend upon four factors: slope (as indicated by the direction and steepness of the fall line that runs straight uphill-downhill thru the hole), green speed, ball speed, and position of ball relative to the fall line thru the hole. In order to predict the correct LINE of a breaking putt, the golfer starts with perceiving the fall line, the base line (straight line from ball to hole), and the speed of the putt nicely into the cup, and then imagines what curve rolls the ball on the high side of the base line as far as the hole so the ball falls nicely into the cup. The "tangent" of this predicted curve at the very beginning of the curve at the ball at address establishes the start line, not the so-called "apex" of the break. It's as if you had a small model car with headlights instead of a ball, and backed the car all the way from hole to ball on the "curved highway" of the predicted putt -- the headlights when this car arrives backwards to the ball at address shine straight along the correct start line at a point up along the fall line. That point is the aim point of the charts for that putt.
However, so-called science often purports to be worth more than it is really worth. Science is always presenting a GENERAL rule, and not a "firing solution" for a SPECIFIC targeting problem in a specific real-world context. This is especially the case when "science" offers a "chart" for all golfers to use on any putting green for different putts. For specific putts, the golfer does not want a general rule. He MAY use general parameters to get a better "ballpark" handle on the situation, but then he goes BEYOND the general science to deal with the specific situation. For this, the human instinctive brain is vastly superior and more important to successful reading of putts than any chart or any "algorithm" of mathematics and physics. So, HOW TO perceive the read instinctively, intuitively, and smartly for accurate and consistent perfomance in golf is the task and the responsibility of the golfer. Thinking that a chart can "just show you" or that this is effective learning of the perceptual requirements for the skill of reading putts is simply misguided and wasteful effort.
Perceiving the Green's Stimp-measured Speed
Since the charts use Stimp measurements, a golfer using the charts will need to know the green's Stimp or a close approximation. The Stimpmeter is simply a device that delivers the same ball speed off the bottom of the ramp, and that speed is about 76 inches per second (or equivalently, 6.3 ft/s, 1.93 m/s, or 14.4 rev/s). A backstroke of about 15 inches with a simple pendular downstroke without the golfer adding to the swing but simply allowing the putter to swing will closely duplicate the ball speed of a Stimpmeter for almost all putters. A golfer using a quicker, more violent stroke who once duplicates the distance of roll of a ball off a Stimpmeter and notes the length and timing of his stroke to do so has a repeating action that makes him into a Stimpmeter. This is useful on the practice green when there is no other source for learning the Stimp speed of the greens for that day.
In general, USGA testing shows that golfers cannot tell the difference between two green speeds closer than about 1/2 a foot. Hence, it makes little sense to try to discriminate green speed at a level of precision that purports to separate Stimp 9.5' from Stimp 9.75'.
More broadly, most greens today in weekday condition Stimp between 8.5' and 9.5'. Agronomy for healthy greens does not currently allow maintaining green speed chronically much above 9.5', and faster greens are occasionally prepared for tournaments or result from untypical weather patterns. Greens are generally faster in fall than in sping or summer, and during the course of a typical day with changes in temperature, moisture, and wind, green speeds don't change more than 1/2 a foot except rarely, often peaking in the afternoon.
Each green varies in Stimp speed a little, but usually not that much. Greens that are high on a hill with good drainage exposed to the sun and wind tend to be faster than usual, and definitely faster than greens tucked low near water without good drainage and protected by shade trees from the sun and wind. The maximum difference may be 1' in Stimp or so.
"The USGA frequently receives requests for guidelines with respect to selection of hole locations on the putting greens, particularly during competitions. There are no rules regarding hole locations, so there is no such thing as an "illegal" hole location. However, we do have some guidelines.
Many factors affect selection of hole locations. The first and most important is good judgment in deciding what will give fair results. Do not be tricky in locating holes. There should be enough putting green surface between the hole and the front and the sides of the green to accommodate the required shot.
In any case, it generally is recommended that the hole be located at least five paces from any edge of the green. If a bunker is close to the edge, or if the ground slopes away from the edge, the distance should be greater, especially if the shot is more than a pitch.
An area two to three feet in radius around the hole should be as nearly level [wrong word; should say "flat"] as possible and of uniform grade. A player above the hole should be able to stop the ball at the hole. Consider the condition of nearby turf, especially taking care to avoid old hole plugs that have not completely healed."
The above boils down to: a) in from fringe about 5 steps or more; avoid too severe slope where ball won't stop; area around hole is flat and has no significant change of steepness. Because pins should not be located where the combination of slope steepness and green speed will not allow the ball to come to rest, the fact that a ball will stop near a pin limits the green speed. If you know the slope, you can estimate the MAXIMUM green speed near a hole. The maximum speed for a 7% slope is about Stimp 8'. The maximum speed for a 6% slope is about Stimp 9.5'. The maximum speed for a slope of about 5% is Stimp 11'. The maximum speed for a 4% slope is about Stimp 13'. This approach is mainly helpful for pin positions on steeper slopes. A slope under 4% can have pin locations even when the speed or the surface exceeds Stimp 14'.
Max. Stimp (Lemons)
Examples of pin / hole locations that ended up being unplayable in major tournaments include the 18th at the 1998 US Open second round at Olympia Fields where the slope-spped combination resulted in balls rolling off the green and Payne Stewart 3-putted en route tofinishing second, the 7th at the 2004 US Open final round at Shinnecock Hills (where withholding watering killed the green before the final round started and officials watered between groups to slow the speed down to playable) and the 15th at the 2009 British Open third round at Turnberry. Also at the 2004 US Open, Mickelson came to the 71st hole (par 3) with a 1-shot lead, but double bogeyed with a 3-putt from 5 feet, the first putt getting taken by wind across unfairly fast surface 5-6 feet. ""I hit an easy putt because I knew it was quick, but it still shouldn't have gone 6 or 7 feet by," Mickelson said. "The wind certainly took the first putt. It broke quite a bit the other way, left to right, and the wind was right to left. It affected it quite a bit and kept taking it down the hill."
Although use of the charts requires some estimation of the Stimp measurement, the Stimp is mostly irrelevant to golfers using instinctive touch. These golfers don't want the abstract numbers of measurement according to Western culture and its concepts of science. Instead, the instinctive golfer deals directly and only with the facts of the world and his body. This means he needs to appreciate what the green surface speed allows when he makes strokes with his putter and usual tempo and rhythm. To perceive this, the golfer should choose a stroke size going slightly wider than his stance and rear foot and his usual tempo and timing and then produce two strokes with identical force. Two balls then roll a specific distance across the green, the same distance, and this is a personalized analog report from this green in its present condition ONLY to this golfer. The golfer then accepts, absorbs and appreciates this distance in an aesthetic mode perhaps like savoring the taste of a cookie to discriminate the amount of cinnamon in the recipe. This process calibrates the golfer's usual stroke tempo and timing and his body to the day's green speed. The golfer is personally tuned to the green.
The "Fall Line" and How to Perceive It
To perceive the fall line, first identify the general direction or line connecting uphill between the highest point in the local terrain and the lowest point in the local terrain, looking as far to the horizon as hills and trees allow. The clubhouse is very often on the highest local hill, and knowing roughly the direction to rivers, creeks, ponds, lakes, and sea is a good start on gauging the local terrain. Second, take stock of the general or overall slope of the green as a whole to see the line connecting the lowest point of the fringe of the green straight uphill to the opposite highest point of the fringe. Third, focus in on the flat area 3-10 feet in radius around the specific pin location and hole to perceive the "fall line" of the putt thru the center of the hole that runs straight uphill or downhill without any break. This specific "fall line" will usually be fairly close to the first two directions but also slightly off due to specific, localized contouring of the green.
Five redundant ways to perceive the fall line's direction thru the hole and arrive at a "best guess" consensus:
1) identify the highest spot on the uphill side of the rim of the hole, as the fall line runs thru the center of the cup and this highest spot on the rim (difficult to do unless the slope is steep so there is a bigger difference in elevation between the lowest spot on the rim and the highest spot across the width of the hole);
2) identify the lowest point on the rim where a hole filling with water like a stopped-up toilet would first overflow and leak out of the rim onto the surface of the green headed straight downhill;
3) identify the axis of tilt of the hole where left-right of the fall line thru the center of the hole all points on the ground have the same elevation, as if preparing to lean down to a sloped beach and place both hands for a push-up so that neither hand was at a lower elevation on the surface, as the fall line is then the same as the spine perpendicular to this left-right axis;
4) imagine walking in a circle around the hole about 6-10 feet out tethered on a rope like a donkey with four feet and perceive in the feet the first step when the circling changes from uphill to downhill, as this point above the hole is on the fall line; and
5) stand near the hole flat-footed to the surface and suspend the putter in the finger tips gently between the legs and start it swinging by placing it initially between the ankles and releasing it and then wait until gravity makes the swinging line first circle a bit and then align itself with the uphill-downhill direction.
Of these, the "push up" seems to be the stongest and most reliable and accurate approach. The "inclineometer" technique in number 5) will not work if the golfer steers the swinging to and fro by participating in the directional changes with subtle "helping" with the fingertips, which is difficult to know how to avoid. But whenever done correctly, a swing line that starts incorrectly off the true fall line will result in the end of the shaft near the putter head "circling" gently to conform to the influence of gravity before finally swinging along a single line (conforming to the fall line's orientation up the hill). If the golfer deliberately stands askance the fall line direction he guesses roughly to make sure there will be some "circling", and then he sees the "circling", this means he is getting a pretty accurate reading from the final "line" swinging up and down the fall line once the "circling" is over.
As a matter of "mapping", a "contour map" is a map showing lines / curves of "points of equal elevation" in regular steps up or down. For example, a map of a perfect cone-shaped volcano island 100 feet tall starts at sea level with a large circle for all "0" points, and then next shows the curve of all points at 10' as a smaller concentric circle, then shows all 20' points etc., until a "bullseye" of eleven concentric circles is drawn. All "fall lines" are always perpendicular to the contour equal-elevation lines.
The big clue is to locate the drain-off areas. Greens today very often have one main drainage line and one or two side-off drains. You can usually find these side-off areas by looking for greenside "collection areas" with a grate at the bottom. Drainage is never directed at a downhill greenside bunker (unles there is substantial mounding to send the run-off around or away and never thru the bunker) -- so that's another clue to fall lines. As a greenskeeper, I've been assigned many times to go to the back nine with a vehicle loaded with replacement sand for bunkers where the sand got washed out by a storm by green-surface runoff channeled thru a bunker. Each of the above green maps show two drainage patterns off each green (arrows going off green). At left the two areas are top / back and bottom / front. Center, the areas are left front and right front. At right the two areas are back right and front.
The arrows on these maps are the fall lines, everywhere perpendicular to the contour lines. Here are green maps focused upon fall lines and slope:
On a clockface at any specific point on the green, the contour line runs 3-9 and the fall line runs 6-12. In effect, any contour map of a green contains in it all the fall lines, so it is really a question of the scale or resolution of the contour map for how close the contour lines have been shown (e.g., 1-foot, 5-foot, 10-foot separations). A really fun way to experience this is to play the putting game at Stracka.com, which shows the contour lines for different greens and challenges you to putt across the slope to a hole.
The "Core Break" and How to Use It to See the Aim Point
In general, on the practice green before a round, find a slope that is pretty representative of the majority of slope you will face on the course and putt a sidehill putt directly at the hole with the usual delivery speed to see how far below the hole it breaks and then crosses the low-side fall line. This distance will be the "core break" to use to vary aiming depending upon whether the on-course putt has steeper slope (higher aim spot), or faster surface speed (higher aim spot), or a longer distance (higher aim spot), or you use a slower delivery pace (higher aim spot). For example, a medium fast green (Stimp 9.5') from 10 feet will break 7 inches below the cup on a 2% slope and 10 inches on a 3% slope. So then you know that shorter putts on similar slope have aim spots lower than 7-10 inches, that longer putts have higher aim spots than this, that steeper slopes have more break than this, etc.
Similarly, you can test how much break there is in this sidehill 10-foot putt as a way to find out the slope. If you aim straight at the hole from 10 feet and the putt breaks 11-12", this tells you the speed and slope might be:
5-6% on a slow green
4-5% on a medium slow green
4% on a medium green
3.5% on a medium fast green
3% on a fast green
If you know the speed of the green, then you know the slope. If you know the slope, then the 10-foot "core break" putt tells you the green speed.
The "Core Slope" and How to Perceive It
Using the "Core Break" does not require perceiving the steepness of the surface slope, as the steepness is implicit in the imagining of how low a straight-on sidehill putt will curve below the hole. But in order to use the aim-point charts, the golfer needs to perceive the percentage of slope. The percentage of slope is not the same as the angle of surface off horizontal, and aids that provide the slope meausrement in degrees are not nearly as helpful as the "grade" or percentage of slope. A percent slope is rise/run, so that a rise in elevation of 1 foot over a run of 100 feet is a 1% slope, and a rise of 2 feet is a 2% slope, etc. Most green slopes near hole or pin locations are between 1% and 6%, since slopes steeper than this combine with usual green speeds so that a ball will not come to rest on such a surface -- one of the guidelines for locating pins so that play is fair. A "core slope" is the most common slope the golfer expects to face as he plays the pin positions of the specific course over 18 greens. For most golf courses and greens, this "core slope" is likely to fall in the 2% to 3% range.
Perceiving the "core slope" starts with standing at the lowest point on a green's fringe and looking across to the opposite highest point and estimating the far height in terms of the golfer's body: how high up the legs does the height of the opposite highest side of the fringe rise? A golfer 6' tall is the model. If the height reaches the golfer's knees 2 feet high and the far fringe is 100 feet away, the slope steepness is 2% (2'/100' = 2%). If the far fringe is only 50 feet away, the height will rise up the legs only halfway to the knees or 1 foot, and this is also 2% slope (1'/50' = 2%). If instead a fringe 100' away rises all the way to the golfer's hips (3' high), then the slope is 3%. A far fringe 100' away that rises to the bottom of the golfer's sternum and diphragm is 4%. A far fringe 100' away that rises to the golfer's chin is 5%. A far fringe that rises to the level of the top of the golfer's head is 6% (the golfer's eyes are at 5.5' or 5.5%). Slopes over 10-12% don't exist except possibly on steep tiers between levels of greens.
Body of 6' Golfer
for Run 100'
for Run 50' (2x)
for Run 25' (4x)
Halfway up shin
Bottom of Sternum
Top of Head
In all cases the reference distance for the "run" needs to be known. Conveniently, the usual green is about 90-100 feet in diameter, as a circular green with a radius of 45 feet gives a green a little larger in area than 6,000 square feet, the averrage size green played on the PGA Tour. If the reference distance uphill is half this at 50 feet, then the rise is only half as high as the slope percent, with a 1-foot rise over 50 feet of run indicating a 2% steepness of slope grade. Double the rise when using 50 feet. Quadruple (4x) the rise when using only 25 feet. Multiply the rise in feet by 10 when using a run of only 10 feet.
So what is 100 feet? What is 50 feet? What is 25 feet? What is 10 feet? The gofer needs to know this so he can judge the steepness of different greens. A run of 100 feet is 1,200 inches and the normal step length of adult males is about 30 inches each step, so 100 feet is about 40 steps away and 50 feet is about 20 steps and 25 feet is about 10 steps. A run of ten feet is 120 inches, so that is about 4 steps, but the rise is likely to be perceived in inches (not feet) and will have to be converted to feet, as in 6 inches is 0.5 feet. When using short distances of run like this, it is more convenient to use 100 inches, not 120, and this is about three steps or 8.3 feet away. In this case, a rise of 1" over 100" run is 1%; 2" is 2%; etc.
Estimating the rise is a bit of a trick. The ideal technique would be to get the eyes level and horizontal with the same elevation as the far side of the run uphill. Getting the eyes low enough is tough sometimes. If the golfer squatted at the lowest point on the fringe and looked across 100 feet to the far fringe and the far fringe is level with the height of the eyes while squatting, this is about 3%. If the golfer sights across the top of the handle of a conventional 35-inch putter poised vertically and this hits the far fringe 100 feet away, the green slopes generally 3%. If the far fringe at this reference distance is sighted level with eyes 2 feet up the shaft, the green slopes 2%. But getting the eyes level to heights lower than 2 feet involves something other than squatting and even getting the eyes as low as two feet is pretty challenging. So, instead, imagine while squatting that you are patting your hand on the elevation of the far fringe, and then look to see how high off the low fringe your hand is patting, or compare this height to a point up the shaft of the putter and estimate the height in inches or feet. If shorter reference distances are used, multiply the rise accordingly.
However, the above technique is only for estimating the steepness of the green IN GENERAL. What really matters is the steepness of the flat-but-tilted surface area right near the hole 3-10 feet out. This SPECIFIC SLOPE steepness can only be gauged in inches, so the 100-inch run is best here. Look straight up the fall line direction from the hole 3 steps, 100 inches, and 8.3 feet away to a spot on the fall line and try to estimate how many inches this height rises from the top edge of the hole. You can also fixate this spot 100 inches up the fall line and look at the rise from the side perspective, standing a respectable distance off the fall line (the 6-12 line on a clockface) at the 3 or 9 o'clock position. Standing 11 steps along the axis of tilt to a 3 or 9 o'clock perspective and holding up a "movie director's box" about 20" out in front of the face with thumbs touching horizontally and aiming one index finger tip at the hole, the other index finger tip aims about 100" up the fall line. "Touching" the fall line with one index finger tip and holding both finger tips level (level eyes and head with good upright posture) will show the hole slightly lower on the finger nail; each 1/3rd of finger nail from top to bottom is about 1% slope, so a full fingernail low is 3%.
Some useful guidelines are: The tip of the thumb from last knuckle to end of thumb tip is about 1 inch; the length of the last two knuckles of the index finger tip is about 2 inches; the length of the forearm is typically 1'; the height of the putter head is often 1"; holding the putter grip level about 20" out from the eyes about 7 steps back from the hole marks a line on the ground that is about 100" long from top of handle to end of handle; 100" is about 3 putter lengths; 100" is around 3 steps; standing at the hole extending the arm and putter horizontally reaches the putter head to about 50"; making a "movie director's box" with thumbs touching horizontally to spread index fingers apart held at 20" from 11 steps back from the hole marks 100" on the ground.
for Run 100'
for Run 50' (2x)
for Run 25' (4x)
1/3rd up shaft
1/2ve up shaft
2/3rds up shaft
Bottom of grip
Top of handle
Putter, Hand, Ball
for Run 100"
3 steps or 8.3'
for Run 50" (2x)
1.5 steps or 4.2'
for Run 25" (4x)
1 step or 2'
Top of Putter Head
Last 1 Knuckle of Thumb Tip
Last 2 Knuckles Index Finger
Top of Foot
First Bend of Hosel
"Thumbs Up!" gesture
Hand Wrist to Fingertips
The Stimp 6.5' Templeton chart can be compared to modern green speeds by proportionately incrteasing the 6.5' by 50% (multiply 6.5 * 1.5 = 9.75). Similarly, shifting from the Slope 2% column by 1.5 indicates that the Stimp 6.5' 3% slope column is the equivalent of a Stimp 9.75' green and a 2% slope. Templeton's numbers then would be:
Slope 2% from 2.5': 1.6"
Slope 2% from 5.0': 4"
Slope 2% from 7.5': 7"
Slope 2% from 10.0': 10"
Slope 2% from 12.5': 13"
Slope 2% from 15.0': 16"
Slope 2% from 17.5': 19"
Slope 2% from 20.0': 22"
These numbers can be mapped onto the other slopes by similar proportioning from the 2% slope: 1% is half; 3% is 1.5, 4% is twice, 5% is 2.5, and 6% is three times as much break as the 2% slope. With that, Templeton's numbers indicate break on modern greens:
These figures yield an interesting and convenient rule for this common Stimp speed: the break across flat slope is 1" for every foot of the putt's length when the slope is 2%, 0.5" when 1%, 1.5" when 3%, 2" when 4%, 2.5" when 5%, and 3" when 6%. A similar "inches of break for each foot of putt distance" figure can also be empirically established for different Stimp speeds, or can simply be mapped by proportionality. A Stimp 12' green compares to the Stimp 9.75' figues by a factor of 1.23. Not too complicated!
But the best use of these numbers is to consider them as ballpark breaks and then adjust for the specific situation faced on the course.
These drawings illustrate slope in terms of a 6' tall person standing on a 100-foot run of surface. So the 7% slope at the right is elevated 7 feet out of the level base.
Ball delivery speed is not best perceived by how far past the hole a ball rolls, but by how deeply the ball enters the cup. A centercut putt that hits the dirt at the back of the hole between the top of the cup liner and the rim on the surface is traveling about 8 revolutions per second at the front lip as it first crosses over the opening of the hole, which is about the same rate of rolling as the tires on a tractor-trailer truck on the Interstate at a speed of 75 mph or so. As the entry speed of the ball slows, the ball strikes the rear wall on centercut putts about 1 inch lower for each 1 rps drop in speed. So 7 rps strikes the wall about 1 inch down the liner, 6 rps strikes 2 inches down the liner, 5 rps strikes 3 inches down the liner and 4 rps strikes 4 inches down the liner where the wall meets the liner floor, then 3 rps hits the floor between the flag hole and the back wall, 2 rps strikes the flag hole, and 1 rps centercut falls to the floor between the flag hole and the front wall.
Golfers don't hit centercut putts often enough and such a target is only one dimple wide any way, so golfers need a wider hole. A crossing path that is half the centercut path makes 86% of the area of the hole available. These two "half paths" are only 2 1/8th inch long front to back, but are close to the left and right sides of the hole (<1/8th inch in from the edge). When the ball crosses a line half as long as the centercut line, the above drops are reduced in half, so that a 4 rps entry hits the dirt just like a centercut 8 rps ball, and a 2 rps ball on a half line across the hole hits the intersection of floor and wall. A 4 rps putt is dangerous on these half-paths, because slightly too much speed or slightly too far to the edge causes the ball to "rim out" in a gravity sling shot and go farther from the hole with a speed higher than 4 rps, in the same manner NASA uses the planet Jupiter to "sling shot" the Voyager satellite into deep space after a close fly-by. A power lip-out like this is worse than a pure miss, as the ball powers out with more speed than it arrived with and also heads off to leave a sidehill comeback with lots of break, instead of finishing near the fall line for a fairly straight comeback. And a 2 rps putt is not really "safe" until the right side of the ball is closer to the center of the cup than the right edge of the hole. What is really "safe" is a line across the hole at least half a ball in from the edge, or 0.84" inside right or left. The "red" balls below are"safe" from rimming out, while the "blue" balls have a high chance of rimming out. That is a hole effectively 4.25" - 1.68" = 2.57" wide on center (60% of the apparent left-right width of the hole).
Roughly speaking, the safe width of the hole doesn't change much for putts arriving with 1-4 rps delivery speed (all holes are effectively 2.1" to 2.5" wide). Interestingly, even at the higher delivery speeds for ball capture up to about 8 rps, the effective "safe" hole width is never less wide than 2". It would be better for golfers if they ignored the diameter of the hole and thought of all holes as box-shaped 2" wide and 3.4" deep, and catching ANY part of this "hole" at ANY allowable delivery speed results in a sink.
The above is probably the underlying reason why top putters like Ben Crenshaw don't see a thin-line curve from ball to hole when they visualize a read, and instead see a "ribbon" nearly as wide as the putter head curving from ball to hole. I recommend seeing a ribbon about 2-inches wide. This means the "aim points" are not really precise points, but fat areas. And in this vein, it should be noted that golfers are not really able to discrimiate aim points that are not separated by about 1/2 inch from 10 feet away from the cup and fall line, as this is a mere 0.2 degree. By comparison, the diameter of a dime is 0.7", so perceiving points on the fall line ten feet away requires looking for targets about as large as a dime. At 20 feet, a dime is a bit too small for targeting.
Shoe 4" wide with dime directly below with eyes 5' away
(400px and 2 thumbs wide at arm's length viewed with one eye)
Shoe 4" wide with dime seen with eyes 10' away
(250px and 1 thumb wide at arm's length viewed with one eye)
Shoe 4" wide with dime seen with eyes 20' away
(125px and 0.5 thumb wide at arm's length viewed with one eye)
The above images are sized for eyes viewing from 20" away from the screen, and are the actual apparent sizes of dimes seen from 5', 10' and 20'.
In case of misses, balls typically stop about 1 second after passing the front lip and hence a 2-3 rps ball stops within 2-3 rolls of the center of the hole. Each roll of a ball covers 5.28" on the ground, so 3 rolls past the cup is about 12"-13" past the hole. A golfer with consistent touch skill delivers all balls to all holes with about the same delivery speed, and so golfers need to watch and learn this falling-in and going-by pattern. Knowing this pattern provides "feedback" for all putts by any golfers about the surface speed and slope and break, so golfers can interpret what their playing companions' putts mean to them personally by watching the arrival speed of the companions' putts and translating this to the golfer's personal touch and appreciation for slope contour and green speed.
The Break and How to Perceive It
Now with a sense of slope direction and steepness, green speed, and ball delivery speed, and with a sense of the "core break", a golfer can imagine the break for a specific putt by visualizing exactly how low a putt from the ball's actual distance from the hole -- started straight along the baseline at the center of the hole -- would curl low when it crosses the fall line with the usual "nice" speed of the golfer's touch. The number of inches low is how high the aim point is located up the fall line above the hole. This is the SPECIFIC read, and the charts should "more or less" confirm this, but do not replace it. The SPECIFIC read is more detailed and takes into account more variables from the unique situation of the green and the golfer's personal touch than does the general aim point of the charts.
Bottom line: The charts help get oriented to where the break aim point is located "in the ball park" of reality, but the accurate imagining is what really predicts the future path and startline and aim point.
The "Apex" is Irrelevant and NOT the Aim Point
The so-called "apex" is not the aim point for the aim of the putter face and the start line of a breaking putt. The "apex" is simply the widest separation of the breaking curved path above or off to the side from the base line. The direction of the breaking curve at the apex is PARALLEL to the base line, and a golfer cannot simultaneously start the ball off at the apex and have the direction of the roll then change back down towards the base line while also reaching the apex with a direction that parallels the base line. The ball will always break between the start and the apex back towards the base line and so always pass below the apex. Aiming at the apex guarantees either that the ball misses to the amateur side or that the golfer changes his delivery speed by speeding up the stroke in order to prevent the ball from falling low. Either way, the golfer is not in control with a good read.
Nor is the "apex" the point along the curve where "gravity takes the ball the rest of the way downhill into the cup". This is tremendously confused thinking. Gravity doesn't sit and wait to engage the ball until the ball reaches some magic point along the ground, but is operating (obviously) all the time. But more importantly, this sort of thinking misunderstands breaking putts and doesn't even apply to 75-90% of breaks. Breaking paths do not generally run "uphill and then downhill". Uphill putts NEVER run downhill in any meaningful sense, but enter the hole while still heading uphill. Likewise, downhill putts ALMOST NEVER start out uphill and then turn downhill. Most downhill putts are downhill all the way into the hole. The only putts that start out uphill and then turn downhill are sidehill putts between about 2 o'clock and 3 o'clock or between 9 o'clock and about 10 o'clock. And even among these sort of breaks, gravity is not what provides the energy that gets the rolling ball to cover the real estate between the apex and the hole. If gravity were the sole energy, only those slopes and green speeds where the ball cannot stop will suffice to allow gravity to carry the ball all the way downhill from the apex to the hole and that is very unlikely since these slopes are not suitable for pin locations to begin with. On rare occasion, the short distance from apex to hole combines with the short roll to a stop of a ball on a slope and green speed suitable for a pin location, and this ending roll is long enough to reach the hole. What really happens is the golfer gives sufficient pace to the ball so that it makes it all the way to the hole and never dies out short and high of the hole.
In reading putts, the golfer always aims "high enough" in light of the delivery pace, but never aims "higher than necessary". The expression of sending the ball along a curving path "to the point where gravity will take it the rest of the way downhill into the hole" has a positive tendency to focus the golfer on the far ending area of the putt on the high side, and to encourage a gentle entry pace into the cup, but also unduly promotes leaving putts too high -- high and short.
"Hole High" is not the Correct Touch Reference
At the end of every read, the putter face is set aiming along a specific start line, and the success or failure of the putt boils down to TOUCH. A golfer in control when he deals with the reality of the world for putting across sloped grass surfaces MUST read with the same sense of delivery speed he actually uses when he executes the putt. One speed, one read -- one read, one speed. Because the physics of a flat-but-tilted planar surface depends upon the directional orientation of the fall line thru the center of the hole and upon the steepness of the tilt, the fall line is ALWAYS the spatial reference for touch -- the same way tossing a ball in the air to "tickle a leaf high on a tree branch" uses the leaf as a reference and the way a basket 10 feet above the floor in a basketball court sets the reference for a foul shot. Using a reference near the hole perpendicular from the base line straight from ball to hole, or reading the break as "so many balls left or right of the hole "hole high"" can be misleading and not promoting of the usual, consistent delivery speed used to read the putt in the first place. Golfers reading putts this way tend to read the putt and THEN try to guage "how hard to hit the putt" or try to generate a "conscious feel for the force". Great putters don't need this and really great putters only need tempo and rhythm. Using the fall line as the touch reference properly INTEGRATES the instinctive imagining of the break with the USUAL consistent delivery speed, so there is never any question about how hard to stroke the putt. All breaking putts are always stroked with the USUAL tempo and rhythm and sense of delivery speed into the cup.
Getting the Line without an Aim Point
Quite a few top putters on the PGA Tour like Loren Roberts, Ben Crenshaw, Brad Faxon, and Geoff Ogilvy don't ever see an aim point, or want to. Instead, these golfers intuitively aim "high and slow" and get a "gut feeling" for the break. This may entail visualizing the curving path of the putt, but it need not. The implicit "rules" for this sort of aiming use a consistent delivery speed into the cup combined with a refusal to aim such that it is possible for the ball to curve low-side of the hole, crossing the base line between ball and hole to the "amateur" side. Using the base line and the fall line as parameters, any golfer can do this sort of intuitive "reading" and aiming to get the putter face aimed at the correct angle off the base line for the usual touch delivery as follows: Always putt on the startline where the putter face aims; always putt for distance as if the imaginary "straight putt" would roll the ball "nicely" to the fall line; beginning with aim straight along the base line and then ranging the putter face to higher aim, the correct aim is reached when the gut feeling tells the golfer the aim is "high enough" so that when he putts straight towards the fall line with the correct pace, the ball will not coss to the amateur side of the base line. Once the aim is "high enough", the courageous and experienced golfer STOPS aiming any higher and simply pulls the trigger with the usual rhythm and tempo to roll the ball straight at the fall line as if a straight putt would arrive nicely all the way to and slightly past the fall line. Then the real curving putt curls down off the start line and dives nicely into the cup.
The base line and fall line together always establish a "corner" at the hole that can only be approached from the high side along an aim line that is integrated with the usual touch delivery. In some respects, this is similar to basketball free throws into a "basket" in the corner after a nice high trajectory -- "swish"!
Inappropriate Use of Aim Points
When teaching intuitive aiming to golfers at ANY level of play, there is a widespread habit of golfers to misue any target. Instead of starting the ball off online "AT" the target, golfers unconsciously (not SUBconsciously) send the ball off higher than the correct startline as established by the target and in fact try to get the rolling ball "TO" the target spot, with the ball curling downhill "ONTO" the target spot, high and short of the hole. This means these golfers don't use targets other than the hole. (That's why disciplined professional golfers have to learn the hard way to "commit to the line" of their read, and why this continually is a difficult task.) Pity, because these golfers don't have any understanding of how exactly reading putts intuitively works, and this lack of KNOW-HOW results in streaky performance. The above "intuitive reading" does not use targets mostly for this very reason. And introducing any target to almost all golfers, as is the intent of aim-point charts, always results in the golfer having to learn what it means to "putt straight where aimed". Phil Mickleson, for example, has only started learning how to do this in the last year of so (2009), according to his recent book and presentations on the Golf Channel. Unless the golfer knows how to make a straight stroke, the aim point hurts and doesn't help, because the end result is the "intuitive reading" with the hole as target goes out one window but the straight-at-the-aim-point-other-than-the-hole putting does not come in another window.
The real shame is in failing to understand that using different methods to read putts is not hurtful in any sense so long as the golfer is reading the SAME putt. Some teachers and many, many golfers believe that there are two "styles" or "types" of golfers for reading: so-called linear readers and curvilinear readers. In fact, there is no conflict, and golfers may be mostly one or the other, but that only means they should get as good as they can in both styles. Unfortunately, golfers who believe they are "feel" readers get the idea that this means a) they are curvilinear readers and see curves and energy, and b) this means they do not "naturally" see lines and targets, and c) that this is the "natural" method of real atheletes, and d) that analytical golfers are more likely to be "linear" readers, and e) that thinking is stinking and bad for golf because analysis causes paralysis, and f) trying to learn how better to read putts in a linear manner will harm the "natural" curvilinear reading and never be as good. I hear this personally from very experienced PGA teachers and many golfers echo these sentiments. These golfers likely will run from aim charts.
There is absolutely no science that says reading putts linearly and curvilinearly are in any wise mutually exclusive or incompatible in any degree. This notion merely has arisen from the defaulting of golfers to one approach or the other, to their detriment. It's an observation and not a reasoned conclusion about human modes of perception. Any golfer who believes there are two incompatible methods of reading putts and he should choose his "natural" approach and ignore the other approach effectively "cuts off his nose to spite his face." He limits skill rather than protects and enhances it.
This current state of golfer skill and knowledge means that in general the use of aim-point charts, unaccompanied by sound instruction, is likely to cause a detriment in reading skills to a large number of golfers. At the very least, many golfers will temporarily forsake their deeply engrained approach for a novel approach, without being aware of the need to extinguish the old habits to make way for the new. This doesn't happen just because someone implies using the aim-point charts in itself is sufficient.
The best way to introduce aim-points and targets other than the hole is first to explain the motor learning problem and to clarify that different methods of reading putts are compatible so long as they are reading the same putt. All putts with the usual delivery speed (the norm for golfers with touch) never result in more than one read, so golfers with touch need not be afraid of different approaches to reading putts. Golfers without consistent delivery speed are generally in a fog reading putts anyway, and aim points present the implict message that line is more vital than speed, when of course it's the other way around. Golfers trying to use aim points without consistent touch skill are in for regular doses of frustration and confusion. NOTHING much helps reading, in the long run, if the golfer does not first attain skill at controlling the delivery speed of all putts. But once this is accomplished, such a golfer should have redundant and mutually complementing methods for reading the same putt -- since then the agreement of the methods is a solid basis for confidence in the read that is truly earned.
Three Ways to Read One Break
Three ways to read the same break all result in the putter aiming down the same line and with the golfer using the same delivery pace for speed. First, imagine the straight-on base line putt to visualize how low the ball rolls nicely over the fall line and then aim that high above the hole and putt to the fall line. Second, imagine the ball arriving from the high side curling into the hole over the final 3-4 feet of the putt, and then "back a car with headlights" from the hole along the curve back to the ball, and aim wherever on the fall line above the hole the lights are shining when the car backs up to the ball, with a delivery that would arrive nicely across the fall line if the putt in fact were straight and level to an imaginary cup located where the headlights point. Finally, range the putter face to the high side of the base line while planning on putting straight at the fall line until the aim is "high enough" so the ball will not roll low across the base line, and then stroke the putt with the usual tempo and rhythm as if the ball would roll straight all the way nicely to the fall line. All three reading techniques end up the same -- "one speed, one read" and "one read, one speed". These techniques may differ slightly from the aim points in the charts as computed generally, but that's exactly what is supposed to happen when a golfer pays attention to the world of THIS PUTT uniquely as it is and to his own movement timing and sense of touch.