Vector Putting – A Review

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: http://puttingzone.com/graphics/VP/VP096Map300x410_78k.jpg

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. http://puttingzone.com/graphics/VP/VP182.jpg

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

Footnotes:

[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