Assuming you have a perfect stroke, and that you can always shoot the CB exactly where you're aiming, you can make a straight-in shot anywhere on the table 100% of the time, since you have a definite aiming point on which to focus (the center of the OB). However, even with a perfect stroke, you have no such guarantee potting any cut shot, since the point at which you aim might be flawed. For a cut shot, there is no definite aiming point; it must be imagined visually. Either you're visualizing the precise location of an imaginary ghost ball, or you're trying to guess the location of the contact point on the CB and match it up with the contact point of the OB (or you may have some other system). Either way, there is a certain degree of guess work, and always the possibility of error.
However, other than the center of the OB, there is another definite point on the OB at which to aim. This is the edge of the OB, or a half-ball hit. Assuming the cut angle is precisely 30 degrees, with a perfect stroke and the edge of the OB as your definite aiming point, you can make this shot 100% of the time (let's disregard throw for simplicity). The problem is how can you tell if your shot is exactly 30 degrees without carrying a protractor in your back pocket? Sure it's easy to tell a straight-in shot, but not so for a 30 degree cut.
This is where the knowledge of geometry and the properties of 30-60-90 right triangles might help. For a right triangle containing a 30 degree angle, the hypotenuse (the side opposite the 90 degree angle) is exactly twice the length of the side opposite the 30 degree angle (sin 30degrees = 0.5). So how can this knowledge help your pool game?...
The shot above shows a cut angle of 30 degrees. The 8 ball is the OB and the 1 ball is the imaginary ghost ball. A 30-60-90 right triangle is formed, such that the hypotenuse of the right triangle is the line connecting the center of the ghost ball and the center of the pocket (red arrow) and the cut angle is the 30 degree angle of the triangle. If the cut angle is exactly 30 degrees, then the red arrow should be exactly twice the length of the blue arrow.
When determining if your shot is 30 degrees, measure the distance of the red arrow with your cue stick. Point the tip of the cue at the ghost ball's center (not OB's center) and mark the place on the stick where it's over the pocket with your hand. Then rotate your cue about the pocket such that the cue is perpendicular to your aim line (CB through the OB edge, green line in figure).
If the aim line splits the distance measured by your cue, then you know the cut angle is 30 degrees, and that you should aim exactly at the OB's edge. If the intersection point is closer to your hand than it is to the tip, then you know the angle is less than 30 degrees and you should aim slightly inside the edge of the OB. If the interection point is closer to the tip, then the angle is greater than 30 degrees and you should aim slightly outside the edge of the OB.
Note: I know this methodology is most likely impractical on shots where the OB is close to the pocket, since you still have to guess distances. However, it may help on some of your longer shots. Just thought I'd throw it out there...
However, other than the center of the OB, there is another definite point on the OB at which to aim. This is the edge of the OB, or a half-ball hit. Assuming the cut angle is precisely 30 degrees, with a perfect stroke and the edge of the OB as your definite aiming point, you can make this shot 100% of the time (let's disregard throw for simplicity). The problem is how can you tell if your shot is exactly 30 degrees without carrying a protractor in your back pocket? Sure it's easy to tell a straight-in shot, but not so for a 30 degree cut.
This is where the knowledge of geometry and the properties of 30-60-90 right triangles might help. For a right triangle containing a 30 degree angle, the hypotenuse (the side opposite the 90 degree angle) is exactly twice the length of the side opposite the 30 degree angle (sin 30degrees = 0.5). So how can this knowledge help your pool game?...
The shot above shows a cut angle of 30 degrees. The 8 ball is the OB and the 1 ball is the imaginary ghost ball. A 30-60-90 right triangle is formed, such that the hypotenuse of the right triangle is the line connecting the center of the ghost ball and the center of the pocket (red arrow) and the cut angle is the 30 degree angle of the triangle. If the cut angle is exactly 30 degrees, then the red arrow should be exactly twice the length of the blue arrow.
When determining if your shot is 30 degrees, measure the distance of the red arrow with your cue stick. Point the tip of the cue at the ghost ball's center (not OB's center) and mark the place on the stick where it's over the pocket with your hand. Then rotate your cue about the pocket such that the cue is perpendicular to your aim line (CB through the OB edge, green line in figure).
If the aim line splits the distance measured by your cue, then you know the cut angle is 30 degrees, and that you should aim exactly at the OB's edge. If the intersection point is closer to your hand than it is to the tip, then you know the angle is less than 30 degrees and you should aim slightly inside the edge of the OB. If the interection point is closer to the tip, then the angle is greater than 30 degrees and you should aim slightly outside the edge of the OB.
Note: I know this methodology is most likely impractical on shots where the OB is close to the pocket, since you still have to guess distances. However, it may help on some of your longer shots. Just thought I'd throw it out there...
