The law of reflection originally refers to the behavior of light. It’s usually written “the angle of incidence is equal to the angle of reflection. “[1] X Research source
Imagine a line from the cue ball to the rail, intersecting at right angles. Now imagine the cue ball traveling to the rail. This path is the hypotenuse of a right triangle, formed by your first line and a section of the rail. Now picture the cue ball bouncing off and hitting the object ball. Mentally draw a second right triangle pointing the opposite direction.
The law of reflection tells us that the two angles between the hypotenuses and the rail are equal. Both are right triangles, so they each have two 90º angles. Since the two balls started equidistant from the rail, we know the two sides between the ball and the rail are equal.
The two triangles still share the same angles, but not the same lengths. This makes them similar triangles: same shape, different sizes. Since the cue ball is twice as far from the rail, the first triangle is twice as large as the second triangle. This means the first triangle’s “rail side” is twice as long as the second triangle’s “rail side. " Aim for a point on the rail ⅔ of the way to the object ball, since ⅔ is twice as long as ⅓.
A dead-on shots overlaps completely. You could say it has a “fullness” of 1. If the cue ball covers ¾ of the object ball, the hit is ¾ full.
A direct hit (fullness 1) results in a cut angle of 0º. The object ball continues along the same path as the cue ball. A ¾ shot sends the object ball out at 14. 5º. A ½ shot sends the object ball out at 30º. A ¼ shot sends the object ball out at 48. 6º.
Imagine a straight line segment from the pocket to the center of the object ball. Extend this line slightly past the object ball. Imagine a “ghost ball” at this spot, squarely on this line and touching the object ball. To hit the object ball into the pocket, you should aim at the center of the “ghost ball. "
For example, if the angle with ball A as the vertex is about 45º, the cut angle you want to achieve is about 15º. The fullness rule above tells us that a ¾ full collision should produce this angle.
You’ll have trouble narrowing down the effects of English (side spin) if you’re not also controlling the amount of overspin and slipping. These effects are determined by the height you strike on the cue ball. Slipping is completely eliminated at 2/5 of the distance between the center and the top of the ball, but in practical terms 1/5 of this distance is often a better measure for optimal control and speed. [7] X Research source [8] X Research source
100% English or maximum English means you strike halfway between the center and the edge of the ball. This is the farthest from the center you can strike and reliably avoid miscues. 50% English means you strike halfway between the maximum point and the center (¼ of the way from the center to the edge of the ball). You can use any other percentage of English by striking at different points between the center and the maximum point.
The term comes from the analogy of two gears meshing smoothly together, transferring the motion perfectly.
If the cut angle is 15º, use slightly more than 20% English. (Remember, the cut angle is the angle between the cue ball’s original path and the path of the object ball. ) If the cut angle is 30º, use 40% English. If the cut angle is 45º, use about 55% English. If the cut angle is 60º, use about 70% English. As the cut angle approaches 90º, increase English to 80%.
This effect is called cut induced throw: the cut angle transferred a spin which threw the ball off the expected path. You can use this to your advantage to make seemingly impossible shots. If your only clear shot would put the ball slightly too far to the right, increase the amount of outside English to throw the ball into the pocket.
