The diagram above can represent both side and overhead views of how a shaft can pivot (exaggerated here) on your bridge. Any vertical or horizontal movement of your stroking arm will cause the tip to pivot in the opposite direction. If you pull or push your elbow up, down, right or left, your cue tip mirrors the action to a degree dictated by the length of the bridge.
Perfect aim can be negated with a poor hit on the cue ball. Any movement of your elbow that does not contribute to a smooth, straight stroke through the point of contact on the cue ball can cause a myriad of deflection errors, including miscues. Does this happen to you? One test is a long, straight-in shot.
Set the object ball in the center of the table and cue ball about halfway between the head string and head rail in a straight line to the opposite corner pocket. Shoot the shot with your normal bridge (usually 6 to 8 inches from the cue ball.) Use an absolute center hit on the cue ball. If the cue ball drifts right or left after hitting the object ball, you may not have struck the object ball where you aimed. Now, shorten your bridge to 2 inches behind the cue ball, and shorten your stroke (with good follow through). If the cue does not drift after the hit, it is a good indication that your normal stroke pivots on the bridge.
One way to improve your stroke is with the use of Elephant Practice balls. The cue ball is designed so as to allow the "chalk mark" following the hit to be easily seen against the black ring around the ball. The smaller circle, which provides a guide for maximum english hits, also helps you determine where you hit the ball with the tip. The object ball is divided directly in half, with red on one side and black on the other. This makes it easier to see the spin on the ball, and is also helpful in other tests that are explained in the instruction booklet that comes with the balls. The practice balls are endorsed by Robert Byrne, probably the best know instructor in the game. I am not suggesting that the practice balls are absolutely vital for improvement in your stroke, but they are very helpful if you use them as instructed.
Billiard World 1998 Edition
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