If there's one thing we all eventually learn about pool, it's that nothing we learn always applies. The words "always" and "never" can rarely find their way legitimately into a pool conversation. Invariably, it seems that we no sooner learn a rule or a principle than we discover an exception to it. The game would be so much easier if we knew that everything we learned worked all the time exactly as we learned it-easier perhaps but also a lot less interesting.
With that in mind I'd like to flip things over a bit to offer a couple of generalities that apply in every case without fail. The first relates to what may be the game's most powerful principle or reference. Because there is no straight line going from anywhere on a rail over the table's center spot to a pocket, a cue ball rebounding from a rail and rolling over the center spot cannot scratch. Players who learn that early and practice finding the table's center with a variety of shots place themselves on the fast track to greatness. Here's our first unwavering rule: All great players have a cue ball that tracks through the center on auto pilot, whether they learned to do so consciously or not. For those like me, who learned unconsciously, the principle needs a lot more time to take hold. I hate to think about all the time I could have saved and how much better I might play now if someone had introduced this principle to me way back in my formative years.
In the diagram we see two shots and a lot of lines on the table. The solid lines show how the center diamond from each rail can be used to connect a path to the table's center spot along with a slight touch of running english, right in this case. This simple concept lays the foundation of the Monk's 2-7-2 system and remains one of the great contributions to pool instruction. Beginning there we can examine the concept further to uncover several additional principles. Note that if the path traced by the solid lines were the only route to the table's center spot, it would only be useful for the small handful of shots that could put the cue ball onto the first line and thus hardly worth remembering.
If we dig a deeper we can observe that a cue ball approaching the top rail on a line that's parallel, or roughly parallel, to the first solid line will also track to the center. Now we have a principle that can apply in many situations. And with that in mind, look at the dotted line running from the foot spot to the corner pocket, noting that it's perpendicular to the first solid line. So, for any object ball on the dotted line, between the foot spot and the corner pocket, with a cut angle to the left, a sliding cue ball, or stun shot, will put the cue ball onto a track that will take it to the center of the table. To simplify, because the first solid line is the tangent line to the dotted outlined ball, an object ball anywhere on the dotted line will have a parallel tangent line that ultimately takes the cue ball to the table's center. Wait, it gets better.
While the principle detailed above is an extremely valuable guideline, different tables will require slight adjustments with english to make it work precisely. But here come two principles that never change, regardless of variations in equipment. With the table's center spot in mind, always think of stun or a sliding cue ball for an object ball on the dotted line. For an object ball between the dotted line and the side rail, e.g. the solid ball in shot A, you will always use follow to hit the table's center spot. When the object ball lies between the short rail and the dotted line, like the striped ball in Shot B, you will always use draw to find the center spot. Both of these shots will also require running english, right in both cases, for natural rebounds from the cushions. Also, the precise location of the object ball and the precise cut angle will determine how much top or bottom spin, and english to use. But the basic principle always applies: Follow for balls closer to the side rail, draw for balls closer to the top rail. In case you're wondering, a stun for shot A would send the cue ball too wide and make it come out well short of the center for a possible scratch in the left side pocket. Stunning the cue ball on Shot B would miss the center on the long side and possibly scratch in the lower left corner.
As we navigate pool's sea of surprise it's nice to find an occasional guideline that applies consistently regardless of the shot's setup or the equipment's idiosyncrasies. Practice the shots in the diagram, along with some of your own variations, until you observe your cue ball finding the table's center with the same consistency that these principles offer.