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**30-degree and 90-degree Rules for Cue Ball Control in Pool and Billiards**

... how to predict cue ball motion to prevent scratches, aim break out shots, aim caroms, play position, and get through traffic.

- 30-degree rule
- 90-degree rule
- ball condition effects
- carom and kiss shot aiming
- Dr. Dave's peace-sign technique
- half-ball hit "gems"
- largest deflected angle
- poetry
- resources
- safety and ball-in-hand examples
- speed effects
- when the 30-degree rule applies
- where the CB goes for different cases

(external web-links) for more information:

see Sections 3.03, 3.04, 5.05, and 7.02 in The Illustrated Principles of Pool and Billiards

and Disc I of the Video Encyclopedia of Pool Shots

*What is the 30-degree rule?*

The 30-degree rule states that for a rolling-CB shot, over a wide range of cut angles, between a 1/4-ball and 3/4-ball hit, the CB will deflect by very close to 30° from its original direction after hitting the OB. If you want to be more precise, the angle is a little more (about 34 degrees) closer to a 1/2-ball hit and a little less (about 27 degrees) closer to a 1/4-ball or 3/4-ball hit. The rule is described and illustrated in the following video:

The is very useful in applying the 30-degree rule. Also, if you want to know how to account for speed effects, see " Dr. Dave peace-sign technique90° and 30° Rule Follow-up - Part V: the final chapter" (Download) (BD, June, 2005). And if you want to see how numbers change a little with typical pool equipment conditions, see "Rolling Cue Ball Deflection Angle Approximations" (Download) (BD, November, 2011).

Here a video demonstrations showing examples of how the 30-degree rule can be used in different shot situations:

Here a video demonstrations showing examples of how the 30-degree rule can be used in different shot situations:

and here are some others: (Videos)

Here's a convenient 1-page summary resource page (Download) summarizing all of the important points of the 30-degree rule.

For more info, see "The 30° rule: Part I - the basics" (Download) (BD, April, 2004) and where the CB goes for different cases.

- NV 3.7 – Using the 90° rule to check for and prevent a scratch
- NV 3.10 – Using the 30° rule to check for and prevent a scratch
- NV 5.1 – Using speed and angle-control to pocket a three-ball sequence
- NV 5.2 – Using speed and angle-control to pocket another three-ball sequence
- NV 7.2 – Cue ball billiard shot
- NV 7.3 – Object ball carom shot
- NV 7.4 – 30° rule billiard shot
- NV B.43 – CB position control stun, roll, and draw reference lines
- NV B.46 – CB path scratch avoid, cluster break-out, and carom example

Here's a convenient 1-page summary resource page (Download) summarizing all of the important points of the 30-degree rule.

For more info, see "The 30° rule: Part I - the basics" (Download) (BD, April, 2004) and where the CB goes for different cases.

*How do you aim carom and kiss shots?*

The following instructional articles explain how to use the 90 and 30 degree rules to aim carom and kiss shots.

- The 90° rule: Part III - carom and billiard shots" (Download) (BD, March, 2004)
- "The 30° rule: Part III - carom vs. cut" (Download) (BD, June, 2004)
- "VEPS GEMS - Part II: Basic Shot Making and Position" (Download) (BD, February, 2010)

Also, here are some video demonstrations: (YouTube)

and here's a good demonstration from Disc I of the Video Encyclopedia of Pool Shots (external web-link)

If you need to plan a carom or kiss shot that cannot be conveniently set up in the 90 or 30 degree directions, the 90 and 30 degree rules still give you good points of reference. The amount of cue ball vertical spin (follow, stun, draw) will determine where it goes relative to the 90 and 30 degree directions. With full stun, the cue ball will head exactly in the tangent line direction. With complete roll, the ball will deflect in the 30 degree direction. For other shots, it is difficult to reliably know exactly where the cue ball will go, so it is best to not attempt caroms in these cases unless you have no other options. Like many things in pool, all you can do is practice a bunch and develop intuition for how much the cue ball deflects with various amounts of vertical spin. Also, as described in "90° and 30° Rule Follow-up - Part II: speed effects" (Download) (BD, March, 2005), shot speed also affects the exact cue ball trajectory. However, the 90 and 30 degree directions are still good to know to have some definite points of reference.

Here's a good challenge drill, from Disc V of the Video Encyclopedia of Pool Practice (VEPP), for practicing carom and kiss shots: (external web-link)

Here's a good challenge drill, from Disc V of the Video Encyclopedia of Pool Practice (VEPP), for practicing carom and kiss shots: (external web-link)

For more information, see “VEPP - Part XIII: Safety and Carom Challenge Drills,” (Download) (BD, April, 2013).

One advantage of a tangent line (90 degree) carom or kiss is that the CB path does not depend on the speed of the shot, assuming the CB has stun at impact (which does depend on both speed and tip position). However, most people have a good feel for stun shots (stop shots at an angle) since they are so important in pool and therefore are practiced a lot.

The advantage of a 30-degree carom or kiss is that the natural angle applies fairly closely over a fairly wide range of cut angles, so your aim doesn't need to be perfect. Also, it is very easy to ensure ball roll, by using slow enough speed, or with shot distance, and/or by hitting the cue ball above center. The disadvantage is the CB's path off the OB curves before heading in the natural angle direction, and the amount of shift down the tangent line depends on shot speed (see cue ball path speed effects for more info). This isn't a significant factor at slow speeds, but at faster speeds, the shift is significant.

*What are the advantages and disadvantages of stun vs. roll caroms?*One advantage of a tangent line (90 degree) carom or kiss is that the CB path does not depend on the speed of the shot, assuming the CB has stun at impact (which does depend on both speed and tip position). However, most people have a good feel for stun shots (stop shots at an angle) since they are so important in pool and therefore are practiced a lot.

The advantage of a 30-degree carom or kiss is that the natural angle applies fairly closely over a fairly wide range of cut angles, so your aim doesn't need to be perfect. Also, it is very easy to ensure ball roll, by using slow enough speed, or with shot distance, and/or by hitting the cue ball above center. The disadvantage is the CB's path off the OB curves before heading in the natural angle direction, and the amount of shift down the tangent line depends on shot speed (see cue ball path speed effects for more info). This isn't a significant factor at slow speeds, but at faster speeds, the shift is significant.

*How do ball conditions affect the 90-degree and 30-degree rules?*

Diagram 1 in "90° and 30° Rule Follow-up - Part III: inelasticity and friction effects" (Download) (BD, April, 2005) illustrates the effects of inelasticity (i.e., the coefficient of restitution) and ball friction (i.e., throw) on the 90 degree rule. TP A.5 shows the detailed technical analysis along with example numbers.

Only inelasticity affects the cue ball direction. Friction, from collision-induced throw and/or sidespin, theoretically (and practically) has no affect on the cue ball direction for a stun shot (for which the 90 degree rule applies). Diagram 1 in "90° and 30° Rule Follow-up - Part IV: sidespin effects" (Download) (BD, May, 2005) shows the effects of friction and sidespin on other types of shots. The technical details for that are in TP A.7. (Download)

Experimental verification of the theoretical results in the articles above can be found in the following article: Ball Motion Properties in Stun and Follow Shots (external web-Blog)

For more information on ball elasticity, see the ball elasticity resource page.

*How does the peace-sign technique work?*

See the following videos for complete information and demonstrations:

- NV B.43 - Cue ball position control stun, roll, and draw reference lines
- NV B.44 - Dr. Dave 30-degree-rule peace-sign hand calibration

FYI, "90° and 30° Rule Follow-up - Part V: the final chapter" (Download) (BD, June, 2005) wraps up a series of 12 (a year's worth!) of articles dealing with the 90 and 30 degree rules. Diagram 2 of this article (see below) shows how you should move your hand to adjust for speed. It is fairly self-explanatory, but you can see the article (Download) for more details. The 30 degree rule applies for a wide range of shots. For more info, see when the 30-degree rule applies.

The peace-sign technique can also be applied to draw shots using the trisect system.

See NV B.44.(YouTube) Also, here's a template (Download) useful for learning how to apply the 30-degree rule accurately. The template can be used to help you train and calibrate your hand peace-sign (see "The 30° rule: Part I - the basics" (Download) - BD, April, 2004 and "90° and 30° Rule Follow-up - Part V: the final chapter" (Download) - BD, June, 2005).

One way to calibrate or check your peace sign at the table is to use your opposite hand index finger as a ruler to measure how much the tips of the "V" fingers should be spread. Using the 30-degree template (Download) or a 30-60-90 drafting triangle (available at office and arts and crafts stores), one can form the peace sign of the correct angles and then place the opposite-hand finger over the finger-tip gap, with the fingertip touching the tip of one of the fingers. Note where the second finger is relative to the other opposite-hand finger (e.g., just below the main knuckle, or at a certain wrinkle). Then (e.g., when you are playing), you can check your peace sign spread by recreating the same finger tip positions on your opposite hand.

If one has a critical shot close to a scratch, requiring precise caroms, needing ball break-up or avoidance, or with tight "traffic" of balls to negotiate, a well-calibrated peace sign can be extremely useful, allowing one to predict with confidence nearly exactly where the cue ball will go. One can adjust the peace sign slightly for the cut angle using the 30-degree rule angle template (external web-link) for help. One can also adjust for speed, as shown in "90° and 30° Rule Follow-up - Part V: the final chapter" (Download) (BD, June, 2005). Well-calibrated fingers can be much more accurate than intuition-based visualization.

*How can you tell if your peace-sign is the correct angle?*See NV B.44.(YouTube) Also, here's a template (Download) useful for learning how to apply the 30-degree rule accurately. The template can be used to help you train and calibrate your hand peace-sign (see "The 30° rule: Part I - the basics" (Download) - BD, April, 2004 and "90° and 30° Rule Follow-up - Part V: the final chapter" (Download) - BD, June, 2005).

One way to calibrate or check your peace sign at the table is to use your opposite hand index finger as a ruler to measure how much the tips of the "V" fingers should be spread. Using the 30-degree template (Download) or a 30-60-90 drafting triangle (available at office and arts and crafts stores), one can form the peace sign of the correct angles and then place the opposite-hand finger over the finger-tip gap, with the fingertip touching the tip of one of the fingers. Note where the second finger is relative to the other opposite-hand finger (e.g., just below the main knuckle, or at a certain wrinkle). Then (e.g., when you are playing), you can check your peace sign spread by recreating the same finger tip positions on your opposite hand.

*Do people really use the 30-degree-rule peace-sign at the table?*If one has a critical shot close to a scratch, requiring precise caroms, needing ball break-up or avoidance, or with tight "traffic" of balls to negotiate, a well-calibrated peace sign can be extremely useful, allowing one to predict with confidence nearly exactly where the cue ball will go. One can adjust the peace sign slightly for the cut angle using the 30-degree rule angle template (external web-link) for help. One can also adjust for speed, as shown in "90° and 30° Rule Follow-up - Part V: the final chapter" (Download) (BD, June, 2005). Well-calibrated fingers can be much more accurate than intuition-based visualization.

*Why is a 1/2-ball hit (30 degree cut angle) so useful?*

Here are some excellent videos Mike Page put together on half-ball hit "gems:"

NV B.6 - Mike Page's half-ball hit gems (part 1) (YouTube)

NV B.6 - Mike Page's half-ball hit gems (part 2) (YouTube)

and here's a good summary article from Bob Jewett (BD, November, 2000). (Download)

The "natural angle" effect associated with a half-ball hit is one of the most important principles in pool and billiards. It has always surprised me how little (if any) coverage is dedicated to these subjects in commercially-available pool and billiards books and videos. These effects have been understood at least as early as 1835 (see Coriolis' book). Maybe if we keep writing articles and posting videos on these topics, maybe they will become more "mainstream."

Gem #4 from the videos is the basis of the 30-degree rule, which states that for a rolling CB, the deflected angle is very close to 30 degrees for all cut angles between 1/4-ball and 3/4-ball hits (not just a 1/2-ball hit). This gem is the single most important and useful principle in pool, especially when used in conjunction with the peace-sign technique.

Gem #4 is an interesting proposition demonstration with the carom shot from the foot rail. NV A.1 (YouTube) shows a similar "sure-thing" proposition. The following article also illustrates and discusses the shot in "The 30° rule: Part III - carom vs. cut" (Download) (BD, June, 2004).

TP A.1 (Download) and TP A.2 (Download) present an error analysis and look at the effects of table size.

Gem #2 is explained and illustrated in detail in "Draw Shot Primer - Part I: physics" (Download) (BD, January, 2006). The concept can also extended into the trisect draw-shot aiming system. This is also a very useful "gem."

Many additional resources, with lots of illustrations, examples, and video links related to these principle, can be found here:

The 1/2-ball hit is a common shot, especially in the game of 9-ball, where you need to move the CB around the table a lot. With a 1/2-ball hit, the CB easily be given enough speed to travel significant distance. The CB's motion can also be killed fairly easily with a 1/2-ball hit. Also, sidespin is very effective off the cushions with a 1/2-ball hit. For thinner hits, the faster ball speed reduces the effect of the sidespin; and for fuller hits and the resulting slower speed of the CB, the spin doesn't grab as well, especially on new cloth.

TP A.1 (Download) and TP A.2 (Download) present an error analysis and look at the effects of table size.

Gem #2 is explained and illustrated in detail in "Draw Shot Primer - Part I: physics" (Download) (BD, January, 2006). The concept can also extended into the trisect draw-shot aiming system. This is also a very useful "gem."

Many additional resources, with lots of illustrations, examples, and video links related to these principle, can be found here:

- 30-degree rule resource page (containing many additional resources and video demonstrations of how and when the rule is useful).
- collection of instructional articles on this topic: (Downloads)
- The 90° rule: Part I - the basics" (BD, January, 2004). "
- "The 90° rule: Part II - breakup and avoidance shots" (BD, February, 2004).
- "The 90° rule: Part III - carom and billiard shots" (BD, March, 2004).
- "90° and 30° rule review" (BD, July, 2004).
- "The 30° rule: Part I - the basics" (BD, April, 2004).

- "The 30° rule: Part II - examples" (BD, May, 2004).
- "The 30° rule: Part III - carom vs. cut" (BD, June, 2004).
- "90° and 30° Rule Follow-up - Part I" (BD, February, 2005).
- "90° and 30° Rule Follow-up - Part II: speed effects" (BD, March, 2005).
- "90° and 30° Rule Follow-up - Part III: inelasticity and friction effects" (BD, April, 2005).
- "90° and 30° Rule Follow-up - Part IV: sidespin effects" (BD, May, 2005).
- "90° and 30° Rule Follow-up - Part V: the final chapter" (BD, June, 2005).
- "Fundamentals - Part V: CB position control" (BD, January, 2009).
- "Fundamentals - Part VI: CB control examples" (BD, February, 2009).

- 30-degree rule and peace-sign technique one-page summary (Download) and the angle template. (Download)

The 1/2-ball hit is a common shot, especially in the game of 9-ball, where you need to move the CB around the table a lot. With a 1/2-ball hit, the CB easily be given enough speed to travel significant distance. The CB's motion can also be killed fairly easily with a 1/2-ball hit. Also, sidespin is very effective off the cushions with a 1/2-ball hit. For thinner hits, the faster ball speed reduces the effect of the sidespin; and for fuller hits and the resulting slower speed of the CB, the spin doesn't grab as well, especially on new cloth.

*Does the cue ball deflect the most for a half-ball hit?*

Close, but not precisely. See the bottom of TP 3.3. (Download) The maximum deflected angle (33.75 degrees) actually occurs at a cut angle of about 28 degrees, which corresponds to a 0.53 ball-hit fraction. These numbers are close to 30 degrees and a 1/2-ball hit, but not exact.

*Are there easy ways to remember the 30 and 90 degree rules?*

Here's some poetry:

30-degree rule:

If you let one finger stay,

The other finger points the way.

Peace.

90-degree rule:

When the ball has stun,

this is something you should not shun:

Point your finger, and the cue ball will follow the thumb.

If you do this, nobody will think you are dumb.

*What resources are available to help me learn how to use the 90-degree and 30-degree rules accurately?*

"90° and 30° Rule Follow-up - Part II: speed effects" (Download) (BD, March, 2005) illustrates and describes how to use the peace-sign technique for the 30-degree rule. Also, "90° and 30° Rule Follow-up - Part V: the final chapter" (Download) (BD, June, 2005) shows how to account for speed effects. These and other issues and effects and principles are summarized in the 30-degree-rule and peace-sign technique document. (Download) Also, a large collection of instructional articles (external web-link) are available that address all of the intricacies of and uses for both the 90-degree and 30-degree rules.

All these and other teaching and learning resources can be found here:

Instructor and Student Resources (external web-link)

*For what kinds of shots can the 30-degree rule be used?*

The 30-degree rule is very useful for:

- scratch avoidance

- carom shot aiming

- cluster busting

- obstacle avoidance

- position play

- etc!

Here are some important things to keep in mind:

- the 30-degree rule applies only for natural roll shots.

- the 30-degree rule applies for the entire range of cut angles between 1/4-ball and 3/4-ball hits. This range includes the 1/2-ball hit (which is at the center of the range).

- the cue ball always leaves initially along the tangent line, which is 90 degrees away from (i.e., perpendicular to) the impact line (AKA object ball direction, line-of-centers, target line, etc.). However, for slow to medium speed natural roll shots, the cue ball deflects to the 30 degree direction almost immediately (i.e., the curve in the trajectory is almost imperceptible). Only at higher speeds does the travel down the tangent line become significant (e.g., see NV 3.8 (YouTube) vs. NV 4.20 ). For more info, see the following demonstration from Disc I of the Video Encyclopedia of Pool Shots: (external web-link)

For more info, visit billiards.colostate.edu