Where will the cue ball go after it hits an object ball?

For a good basic tutorial with demonstrations of most of the stuff below, see the CB control tutorial page first. The following figure also provides a good visual summary:

cue ball control reference directions

For a stun shot, most people know the right answer: in the tangent line direction, perpendicular to the OB direction. This is the 90° rule (see “The 90° rule: Part I – the basics” – BD, January, 2004). If you want a more precise answer that accounts for various effects (e.g., friction and english), see the following instructional articles:

FYI, here is a convenient one-page summary of the 90° rule.

For a rolling CB, the cue ball changes direction by about 30° for a wide range of cut shots (1/4 to 3/4 ball hit). This is the 30° rule (see “The 30° rule: Part I – the basics” – BD, April, 2004). If you want to be more precise, the angle is a little more (about 34°) closer to a 1/2-ball hit and a little less (about 27°) closer to a 1/4-ball or 3/4-ball hit (see TP B.13 for even more details and precision). If you want to know how to account for speed effects, see “90° and 30° Rule Follow-up – Part V: the final chapter” (BD, June, 2005). If you want an easy way to use your hand to accurately visualize the cue ball direction, use the Dr. Dave peace-sign technique. FYI, here is a convenient one-page summary of the 30° rule.

For a draw shot with good draw action, and for cut angles smaller than about 40° (i.e., ball-hit fraction greater than about 3/8), the trisect system is your answer (see “Draw Shot Primer – Part III: using the trisect system” – BD, March, 2006). You can use a modified version of the Dr. Dave peace-sign technique to predict the cue ball direction (see the article, NV B.43, and NV B.67 for illustrations and examples).

For shots “in between” all of these different cases (i.e., “tweener” shots), see tweener shots.

To see how speed and table conditions affects CB trajectories, see speed effects.

For more info, see Vol. I and Vol. II of the Video Encyclopedia of Pool Shots and:

See also:

What if the cut is very thin or hit very full?

For roll shots, there are good approximations for the CB deflection angles.

For a fairly full hit, with a ball-hit-fraction greater than 3/4, the CB will deflect about 3-times the cut angle.

For a fairly thin hit, with a ball-hit-fraction less than 1/4, the CB will deflect about 70% of the angle between the aiming line and the tangent line.

See “Rolling Cue Ball Deflection Angle Approximations” (BD, November, 2011) for illustrations, examples, and more information.

There are similar rules for draw shots. For more information, see “Draw Shot Cue Ball Directions” (BD, December, 2011).

As with the 30° rule and trisect system, the full-hit and thin-hit rules apply to the final direction of the CB. The actual final path of the CB is shifted down the tangent line with higher speed.

Video demonstrations of these types of shots can be found in Vol. I of the Video Encyclopedia of Pool Shots.


from Neil Murphy (Toronto, Canada) via e-mail:

Neil’s Unified CB Control Theory

As my aiming system, I start each shot along the target line of the shot, and mentally create a rectangle between the contact point of the cue ball and the contact point of the object ball (see the diagram below).

I started exploring how to predict where the natural angle of a rolling cue ball would go. I extracted deflection angles from one of your charts in your technical papers and put them into a spread sheet. I calculated where the natural angle would intersect the line below the cue ball, if extended backwards. For all angles from 0-85°, the natural angle extends backwards and cuts the vertical line below the cue ball consistently at the 30% mark.

But what about draw shots? I extracted deflection angles from one of your charts and started playing with the geometry on my spread sheets. What if I extend the draw angle back the same way I did the natural rolling shot? Again the height of the division is near 30% of the total vertical axis! In this case we are closer to a 1/3, but given the greater degree of variability in draw shots, 30% is an excellent estimation and provides better visual symmetry when lining up the shots.

So now we have a system that allows us to accurately predict the cue ball path. By standing perpendicular to the target line, you can see the shots accurately. However, most shots you can get a reasonable estimate facing down the target line as well. It is also possible to view this in other ways. I will sometimes visualize the rectangle extending to the right, and then pick out the 30% point for both draw and follow.

unified CB theory

from Jal (from AZB post, which contains additional information):

When the balls are close enough to each other and/or you’re hitting hard enough such that the cueball doesn’t lose any significant backspin on the way to the object ball (or gain more topspin), there is a method of determining the cueball’s direction once it reaches natural roll after the collision. I call it the Bottom-Center-Arrow method, or B-C-A for short, in that it’s easy to remember.

Imagine a circle centered on the ghostball with the bottom of the circle running through the center of the cueball. This circle represents the face of the cueball from the shooter’s perspective. To determine the CB’s roll direction after the collision for any vertical offset (no sidespin applied), draw a line from the center of the real cueball parallel to the line of centers between the ghostball and the object ball. This will intersect the tangent line at 90°, call it point A. Thus, we have a triangle with the CB at vertex B (bottom of the circle), the ghostball at C (center of the circle) and point A from which we’ll draw an arrow such that it intersects the vertical axis of the large circle. This yields the CB’s direction once roll sets in, given that vertical tip offset on the face of cueball. Here’s a diagram:

BCA draw shot aiming method

… friction, amongst other things, has an effect on this idealized geometry.

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