It is very important to be able to predict and control where the CB will go. The most important goal in pool is to pocket the ball, but the 2nd most important goal is to leave the CB in a good spot to allow you to pocket the next and remaining balls. It is also important to predict CB motion when needing to detect and avoid a scratch, plan position routes, avoid “traffic” (obstacle balls), and to aim carom (kiss) shots and break-out (cluster separation) shots.
Below is an illustration of reference directions useful for predicting the path of the CB. For more information, examples, and video demonstration links, see: Fundamentals – Part V: CB position control (Billiards Digest, January, 2009).
Here are good video demonstrations of the reference directions predicted by the 90° rule (for a stun shot), the 30° rule (for a follow shot), and the 3-times-the angle (trisect) system (for a draw shot):
Shot speed also has a significant affect on the path of the CB. For more information and demonstrations see: speed effects. And a big part of controlling the position of the CB is developing a good feel for shot speed. See the speed control advice resource page for help with this.
For shots with spin amounts in between stun and full-rolling topspin or stun and maximum backspin, the CB heads between the reference directions. See tweener shots for more info and demonstrations.
The CB reference directions are also very useful for aiming carom shots, as demonstrated in this video:
and for aiming break-out shots:
Here’s a good drill, from Vol. II of the Billiard University (BU) Instructional video series, for practicing cue ball control:
More drills and advice can be found on the cue ball control resource page.