This article discusses lining a putt. The relevant mathematical concept starts with tan(θ) or the tangent of an angle, θ. For those of you traumatized by eleventh grade trigenometry, this article, by I. Newton, does not require an understanding of the tangent function. It is simply a much more commonsense idea which mathematicians shorthand as the tangent function, which is the theme of understanding golf better, as God gave it to us. We then move to reality, and understanding the true importance of misalignment. For mathematicians and physicists, as some simple graphs may persuade the reader, this is a matter of discussing the problem as though it existed not on a flat plane, but on a 2-dimensional Riemann surface. For golfers everywhere, we end up learning how misalignment is affected greatly by break – the speed and slope of a green.
One of the most frequent things a golf does, perhaps second after gripping the club, is to line up a putt. Let’s leave aside the important issue of trying to read the putt — that is, the task of determining the direction and speed that one should try to give the ball with the putter. Having figured out the line, our question today is how best to line it up.
There is of course no “right” or “wrong” way. There are advantages to different methods depending upon the individual, their physical abilities, their stroke, and the like. Today, we hope to explain why alignment is such a tough, but important thing. I suspect all golfers under the “basics” below. Most don’t really appreciate the “insidious,” which is more the norm on a putting green.
Let’s abstract out.
There is a spectrum, and I will posit the two ends of the spectrum as, first, the “line drawn on the ball” method; and, second, the “Dave Stockton” method. These, to my mind are essentially diametrically opposed. Let me explain, after discussing each a bit, why I believe Stockton has concluded his method works best, and I agree, because of the mathematics at bottom.
I am going to digress into some simple mathematics. It is really much simpler than understanding the tangent of x. It goes back to elementary geometry and what, to put a fancy name on it, are “similar triangles.” Two triangles are similar … what does this mean? It is really just a fancy way of saying that the two triangles “look the same” while one is a larger version of the other. In elementary high school geometry, we would learn things like two triangles are congruent if we have “SSA” – meaning that if two adjacent sides and the far angle are the same, the triangles are ‘similar.’ If we draw a diagram, we get this picture of two congruent triangles:
Notice that the side of the triangle opposite the angle marked θ grows the farther away one gets from “the origin.” In the case of a putt, one has a ball (the origin) and an intended line (the side of the triangle “extending out” of the ball) and an actual line (the side of the triangle determined by the angle theta).
It is a truism that one wants the intended and actual paths to be the same. The greater theta, the more one’s path is off, and the more the side opposite theta will diverge from the hole (or intended target).
Everyone intuitively understands most of this. The tricky part is that as the length of the putt increases, the more a small theta can result is a large miss of the target. Take some simple measurements. Suppose one has a 5 foot putt. That is roughly 1.5 meters. 1.5 meters is 1500 millimeters. If one thinks of the triangle formed by the ball the intended line and the line in which the putter is actually pointing, one can show easily that a 1 mm deviation corresponds to a theta of about 1.1 degrees. So if one is off at the putter/ball place by 1 degree, one will be off by 1500*.02 (tangent(1.1 degrees) = .02), or 30 millimeters at 5 feet. 30 millimeters is about an inch.
At 5 feet, then, a 1 degree misalignment (not much) results in a 1 inch miss of the intended target. The cup is about 4 inches wide, so this may not be much. On a 50 foot put, however, one will be off by 10 inches. And this is surely enough to miss a putt. If one is off not by 1 degree but by a little less than 3 degrees, the misalignment near the target will be about 3.1 inches. This is easily enough to miss a putt. If one has a 10 foot putt, one will be off by 6 inches. On a 20 foot putt, one’s alignment will be off by a foot; on a 50 foot putt, one’s alignment will be off by 3 feet.
That’s right. One will be aiming 3 feet to one side or the other of where one thinks they are aiming. Why this stark misalignment? Because the function tangent of x grows very rapidly. One gets a bit of leeway at 5 feet but being precise is important even at that distance. A mere 1 degree misalignment of the putter head leads to being an inch off — definitely enough to miss a putt if one isn’t picking out a target that is dead center of the cup.
At 50 feet and 3 degrees off, one ends up so far off, that it’s a question of whether the second putt will be a make-able knee-knocker. Let’s hope it is a friendly game where “short” putts are conceded. Plenty a touring pro misses a three-footer.
Now all this is assuming that one is aiming on a completely flat green. I haven’t it put it that way, but this reveals how much more important it is to get alignment right. If the putt breaks one way or the other, that 50 footer may end up not 3 feet off after its movements back and forth, but 10 feet or more off. A sure 3-putt, not a knee-knocker. In other words, when one has to read the green (it is not absolutely flat) even very very small misalignments at 50 feet can ensure a 3 putt. (That’s why, incidentally, even touring pros often 3 putt from over 50 feet. It’s just not that easy to be precise enough, after factoring in the slope of a greeen this way and that, to get it close, much less in the hole. Some putts therefore amaze me, like Nicklaus’ putt on the 18th hole at Turnberry in 1977 – sinking a breaking 40 footer to force Watson to make his 3-footer to win [link].)
It’s a matter of degree. That’s right. And the margin for error is every so tiny.
Part two will complicate this picture a bit.