It's a bit odd to imagine I guess, but when using the 2.25" diameter/width of the ball as it is viewed, aiming 1mm left or right of an aiming reference on that 2.25" line ends up being 0.5mm on the actual fat surface of the ball (its circumference or equator), which is where the contact points are located. And each 0.5mm on the equator is a 1° change in shot angle.
So when using contact points one has to be able to work in 0.5mm increments instead of 1mm increments to create the same cut angle. That means you have to be twice as accurate when using contact points. As the cut angle gets larger the numbers change a little bit, but for any shot thicker than about a 3/8 overlap, a 1mm fractional aim adjustment is about 1°, and that same 1° adjustment would only be 0.5mm if using contact points.
Here's the nuts of it.... If you're off by 1mm on the contact point, the shot will be 2° off. If you're off by 1mm on a fractional aim point the shot will be 1° off.
Let’s take a look at fractional aiming.
The ball is just a bit over 57mm in width
A quarter ball hit is an eighth of that or just over 7 mm wide, just over 49°.
The last quarter ball, roughly 7.15 mm covers the remaining ~40° of angles.
Rough math shows that each lateral mm encompasses an average of 5-6° of angles.
The last mm rates to include closer to 10°+ based on the receding surface dynamics.
This reminds me of a diagram from Freddy the Beard.
He reminded us that the ball to ball contact involved a flattening of both surfaces at impact.
Using carbon paper on the equator he measured the flattening using various speeds.
Higher speeds equaled more flattening.
The flattened area we know as the tangent line.
Just something to consider.
By directing the reference line with my cue line using a convergent version of applying small amounts of side, in this case a midpoint convergence, I can bring the impact area dynamic back to the cue ball visually.
The pivot from center exactly represents the two fold adjustment that occurs with contact points.
To help explain I’m going to start with a just miss line.
I can set my vision line for the outside edges to be aligned about a mm apart then shift to center ball.
That line would miss the ball.
Taking the midpoint of that line and pivoting the cue butt to the outside, at a pivot of a mm at the core center of the cb. the cue line now contacts edge to edge.
The lateral movement at one end is echoed at the other.
The mm pivot shift of the butt away from the reference line brings the cue line a mm closer at the other.
On shots such as the one presented here instead of aiming to miss I aim to overcut the ball by about a half ball.
I then pivot from the midpoint by between a mm to a mm and a half as seen from the cb center extended from the tip contact point past the core center to the midpoint.
The overcut starting reference line allows for minimal outside english to be used and the aim line adjusted for distance in one single process.
This combination allows us to use all of the Dr Dave research insights at the table constructively.
Having an echo location of the contact position right under our noses at the cb center, adds a 3D element representation.
