Vector Putting – A Review

December 28th, 2011 by John Graham Leave a reply »

Vector Putting: The Art and Science of Reading Greens and Computing Break is a book published in 1984 by HA Templeton. It is the only book I’ve been able to find discussing the science of green reading. It covers a wide array of topics from appropriate make percentages, measuring green speeds, ball speed into the hole, balancing golf balls and green reading to cover a few. It is very difficult to find because it has been out of print for quite some time and there were only a few hundred copies printed. I’ve read the book a few times and I thought I would share some of its ideas with you.

It has some nice information on things that I would like to confirm the accuracy of like the phases of a putt and how the ball rolls on top of the grass for a majority of the putt. It only settles down at the very end and then obviously at the beginning as well. This end phase (decay phase) as he calls it is when the ball is most susceptible to imperfections in the green and causes the ball to wobble.[1] I thought he discussed some topics very well like time, grain and a talk about perception and normalization. Another thing I thought was interesting was his talk on time studies where he states that about 2.5 hours of a typical 4 hour round of golf is composed of the time the golfer is judging and deciding what to do. The other 1.5 hours included walking and actual execution.[2]

I also want to go over some of the information provided on the science of green reading and how Vector Putting works. First off, it’s important to understand that HA Templeton did not include any of the math or formula’s for how his break amounts or aim points were computed. He used a computer to run the numbers but mentions many times that the computer simulation was incapable of predicting where the aim point should be on it’s first try and needed mulligans, as he called them, to alter the aim points and velocity amounts to get the right answer (depending on the difficulty of the putt)[3]. He says that his computers accuracy on the first try was quite good for short putts(10 feet and less) on a theoretical surface.[4]

Now let’s talk about how the system works. First, let me define a key term with some quotes from the book. One of the main concepts is the Zero Break Line (ZBL) “when the ball lies on a line (above or below the hole) that is normal to the contour line that runs through the hole. This line, by definition, is the direction of the slope. “Zero Break Line is a line running through the center of the hole which defines the direction of the slope. The zero break line also represents the line of maximum slope at the hole location.” [5] To make it more simple, the Zero Break Line is just the fall line in that location. He recommended creating green books that have a 10 foot grid of ZBL’s and slope percentages so players could determine break direction and amounts. Here’s a picture of one of the green charts:

The arrows represent the zero break lines (fall lines) at those particular data points. The arrow points toward low. [6]You can see from the picture that the Zero Break Line is simply the fall line at different points on the green and the slope direction through the hole. He makes a point of saying multiple times the Zero Break Line is where no curve occurs. “Remember that the Zero Break Line is the line where the ball rolls absolutely straight, curving neither right nor left. If you stood above the hole and dropped balls or poured water out of a bucket the balls and/or water would roll/flow down the ZBL and into the hole.”[7]

These Zero Break Lines are used to help the player determine the break. Here’s how it works. If a player hit a put from 10 feet away from the hole directly perpendicular to the ZBL and aimed it at the center of the cup the ball would break below the hole. Assuming the player hit the putt with exactly a foot past the hole speed the ball would cross the lower ZBL at some distance from the center of the hole. That distance now becomes the gravity vector. All the player has to do is take that distance (let’s say 10 inches) and that becomes the point where the player should aim above the hole(on the ZBL) to make the putt. In fact, it is taught that this 10 inches above the hole aim on the ZBL becomes the single aim location for all putts from every angle of the same distance. [9]Templeton claims that this idea works very well for a theoretical surface without too much slope, from too long a distance or that is not running too fast.[8]

When putts become longer, steeper or the greens get faster, HA Templeton recommends using an elastic gravity vector to help with finding the correct place to aim. [9]“Elastic” means that the aim on the ZBL (fall line) moves away from the single point as your position around the hole changes. Charts were made in the back of the book that  players could use that listed the different gravity vector amounts and the amount of elasticity they would have but lack specificity as when and how much to apply them. Here’s an example of one. The subscripts and superscripts represent the elasticity feature of gravity vectors. pg 182[10] You can view a copy of the charts by following this link.

The final topic I want to cover in the book is the Effective Zero Break Line. This is Templeton’s attempt to deal with the real world. Here’s a quote from the book which is very telling. [11] “But what about situations in the real word of undulating or rolling greens where there are obvious changes in the direction of amount of slope between the ball and the hole?  How do you mentally calculate the direction and length of the gravity vector?  Alas the state of the art of Vector Putting is such today that unless you are pretty fast with mental arithmetic, you can’t, within a reasonable time at any rate.  A persistent individual with a calculator, a Green Slope Chart, and a Vector Table could calculate a Gravity Vector in a few minutes but his playing companions (and the foursome behind) might object to the delay.”

Here, Templeton basically says, Vector putting can’t handle changing slopes without the aid of a computer. But even the computer struggles on the first try. Here’s the next paragraph in the book. “However, the computer simulator can find a Gravity Vector for any situation in a matter of seconds. In fact, each time the simulator runs through a mulligan putt it is compiling information as to the ‘effective’ ZBL and slope.”[12]

Runs through a mulligan putt? You mean it can’t do it on the first try either? Basically, to compute Effective Zero Break Lines the player would need to be able to weight average the ZBL directions across the length of the putt in terms of degrees (0 to 360) to determine where to place the gravity vector relative to the hole being played and then determine its elasticity to see if adjustments are needed to the chart.[13]

Personally, I think the books attempt to explain and predict green reading falls short. Really complicated and according to Dr Grober (A leading golf scientist) the break amounts aren’t even accurate. Here’s a copy of a paper Dr Grober wrote discussing the problems with the book Vector Putting. Click on this link to view the paper. Dr Grober Paper – The Geometry of Putting On a Planar Surface. This paper discusses how Templeton’s break amounts are about 20% too low and explains why. He also shows that the single aim location due to the gravity vector is also incorrect.

I still think Vector Putting is worthy of a read if you can get a copy of it. Maybe not for the green reading information but for some of the other stuff. It’s remarkable that it’s the only book on green reading. Too bad the information is overly complicated and inaccurate. Might be why it’s been out of print for so long and has no acceptance on any professional tour. After all, Templeton does have a chapter called “Golf is a two putt game”.[14]

JG – AimPoint Green Reading Certified Instructor


[1] H.A. Templeton, Vector Putting, (Vector Putting Inc., Fort Worth, 1984). pgs 61-62

[2] H.A. Templeton, Vector Putting, (Vector Putting Inc., Fort Worth, 1984). pgs 83-85

[3] H.A. Templeton, Vector Putting, (Vector Putting Inc., Fort Worth, 1984). pg 18

[4] H.A. Templeton, Vector Putting, (Vector Putting Inc., Fort Worth, 1984). pg 147

[5] H.A. Templeton, Vector Putting, (Vector Putting Inc., Fort Worth, 1984). pg 93

[6] H.A. Templeton, Vector Putting, (Vector Putting Inc., Fort Worth, 1984). pg 94

[7] H.A. Templeton, Vector Putting, (Vector Putting Inc., Fort Worth, 1984). pg 135

[8] H.A. Templeton, Vector Putting, (Vector Putting Inc., Fort Worth, 1984). pgs 135-136

[9] H.A. Templeton, Vector Putting, (Vector Putting Inc., Fort Worth, 1984). pg 153

[10] H.A. Templeton, Vector Putting, (Vector Putting Inc., Fort Worth, 1984). pg 156

[11] H.A. Templeton, Vector Putting, (Vector Putting Inc., Fort Worth, 1984). pg 156

[12] H.A. Templeton, Vector Putting, (Vector Putting Inc., Fort Worth, 1984). pg 156

[13] H.A. Templeton, Vector Putting, (Vector Putting Inc., Fort Worth, 1984). pg 157-158

[14] H.A. Templeton, Vector Putting, (Vector Putting Inc., Fort Worth, 1984). pg 147



  1. Bobbin says:

    Please tell me how you can make someone hit the ball at the correct pace…… Surely a putt is dependant on line AND SPEED?

  2. David Leet says:

    Thanks for the info, Very informative and has answered my questions regarding this system. David

  3. Sara_PGA says:

    Like David echoed, this answered a few remaining questions I had about the Vector Putting. Thanks for putting this together JG.

  4. John Graham says:


    Of course a putt is dependent on line and speed. Learning to control touch requires a great amount of practice on drills specific to this exact area.


  5. John Graham says:


    Thanks for reading. I hope you had a great 2011 and hope for a better 2012. Hope you are well.


  6. Martin says:

    John! Well written article putting science into laymans terms is not always easy. You did a good job. Thanks for the post it will allow future students to make an informed decision. The choice will be obvious.
    Martin Mills

  7. Rick says:

    Hey John, thanks for sharing. I understand the book is out of print. Any idea where to find a copy? I’d like to learn more and of course I’d like to learn more about Aimpoint and compare/contrast what Mark Sweeney developed versus what H Templeton developed. In my quest, there are some instructors who swear by Aimpoint and then there is a group that believes in Templetons developments. I’d like to do my own research. Both are confusing to me, but I’m not well versed in either theory.

  8. Jason Sutton says:

    Thanks for breaking down the book. I know we have talked about this before but this makes it very clear. Great job

  9. Geoff Mangum says:

    Dear John,

    I’m not sure you why you don’t tell people where you got your copy of Vector Putting, since it came from me for free. Those are my ink marks on the text you display. Anyone wanting a free copy of this book can have it by emailing me at I’ve been giving it away for free for years.

    Robert Grober is not a leading golf scientist; he is a physics guy at a university playing around with golf. He says Templeton is PROBABLY 20% too low and that a high school physics teacher is PROBABLY correct because the high school physics teacher PROBABLY uses a more realistic speed of the ball off the Stimpmeter, but that no one really knows what is correct to use for calculating breaks without actually measuring the speed off the ramp. So Grober doesn’t know either.

    I have explained all this to Grober and to you and others numerous times. The AimPont calculations are too high for TWO reasons: 1. the go-by speed of ball at the hole is far too short for real golfers, and Templeton’s is better, and Grober’s is more like Templeton’s, but clearly Grober has no real hands-on practical experience with this stuff — he’s just playing around with formulae; and 2. the off-Stimp ball speed used to calculate the aim points is not known and uses the high-school physics teacher’s “guess” and is not measured in reality by anyone either.

    Thewhole approach of AimPoint, Grober, AND Templeton is a bit funny and peculiar. Golfers don’t play golf that way. That’s why I suggest people need to read Templeton for all the interesting background, but not for the charts. So now you seem to agree. But the same goes for AimPoint and for Grober. The real way to teach putting is to teach perceptions and get touch and then learn how much break goes with YOUR touch. The PuttingZone has been past Templeton now for 20 years on just this.

  10. Mark Sweeney says:

    Here is my test comparing Vector Tables to AimPoint charts:

  11. John Graham says:


    Thanks for your comment. It’s always nice for others to see an opposing opinion.


  12. Geoff Mangum says:

    I just watched Mark Sweeney’s comparison of breaks on YouTube and can;t let that pass as valid science. He used the same ball speed to test Templeton’s breaks and his breaks but the two calculations use different ball speeds. Sweeney is testing ONLY his speed, and his speed surely doesn’t work with Templeton’s faster ball speed. That’s bogus.

    Besides, who wants golfers to think the slowest delivery speed is the one they have to use or else the aims are all wrong? I have to say again, it’s not about the charts and formulae, guys, it’s about the touch skill know-how and the perceptions accurately sought out and used knowingly.

  13. John Graham says:


    I don’t agree that only Sweeney’s ball speed was used. I don’t think anyone would argue that was a scientific test. Thanks for watching. Hope 2011 was a success and that 2012 is even better.


  14. Mark Sweeney says:

    Geoff, those Vector breaks were all about 18″ past if you watched, except the last one which would have missed by even more at a faster speed. And given that Tests 1 and 2 were all about 50% too low, there is no physical possibility that a slightly faster ball speed would make up the difference.

  15. GolfHappy says:

    Hi John, great to have found your blog, I’m going to be spending several hours here for sure, but I really want to ask a question (yes, I know it’s cheeky!)

    I’d appreciate it if you could define geometrically the proper way to hit PUSH-DRAW with a driver.

    Can you please crunch the numbers for D-plane (trackman stats) for a PUSH-DRAW with a driver hit at +5° assuming the feet are SQUARE to the target line.. I figure you’d need to be “swinging out” with the base of the plane pointed considerably right of target?

    Thanks in adv…..

  16. John Graham says:

    Golf Happy, I have copied you comment and moved it with my reply over to the comments for the D Plane page.


  17. Geoff Mangum says:

    To anyone familiar with Galilean physics of balls rolling down inclined planes, the ONLY determinant of ball speed off the ramp is the height of release (all other factors about the ramp and ball being the same). The height of release is the same when Sweeney tests his reads as when he tests the Templeton reads, so that is simply bogus as a matter of fact.

    If the test of Sweeney’s reads first establishes the height of release that makes the balls go in the hole, and then he reproduces that on film, that’s fine. But then using that same speed to test Templeton’s reads, when they are based upon a different and faster delivery speed, is obviously not going to result in sinks. To make the Templeton reads works, just like the Sweeney reads, one would first have to adjust the exact release height to match what Templeton uses, and then sinks start to happen. That release height is then wrong for the Sweeney reads.

    What is really odd is that Sweeney would not know how high to release the ball for his own reads without first trying a few to get the release height and ball speed to be what is required by the reads. That is not a way to test the validity of the reads; that is a way to jerry-rig a film so it looks right.

  18. John Graham says:


    It clearly states in Vector Putting that he prefers his optimal terminal velocity at the lip to be 2.37 fps and says that the player should try to hit the ball 1 foot past the center of the hole on a level green. He states this would also apply for sidehill putts. He also states that because he prefers a constant velocity at the hole that uphill putts would not stretch to a full foot past and downhill putts would go beyond the foot.

    This is one of his reasons for the elastic gravity vector. The putts shown in the video are so nearly to the above distances, I’m surprised you would bring it up. Based on the optimal terminal velocity described by HA Templeton in his book, the video is quite appropriate. His aims are too low for the speed he recommends and for the speed we recommend.

    Surely, there must be a speed that would go in at his reads, assuming it is below maximum terminal velocity, but that’s not what’s being discussed in the videos.



  19. RoyD says:

    Why is the Sweeney not available for public viewing on YouTube?

  20. John Graham says:

    because of the ongoing lawsuit between them.

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