FAQFAQThrow in Pool and Billiards

... how to judge and compensate for object ball throw in pool shots with and without english.

Dr. Dave's answers to frequently-asked questions (FAQs), mostly from the AZB discussion forum


for more information, see Sections 4.04, 7.03, and 7.04 in The Illustrated Principles of Pool and Billiards
and Disc IV of the Video Encyclopedia of Pool Shots


answers to questions about CIT, SIT, and OE

How do you know which way the object ball will throw for different types of shots?

For the basics, see the throw section in the online Pool Tutorial.

Throw direction depends on the direction of the relative motion of the surface of the cue ball in contact with the object ball. This direction is affected by both cut angle and spin. "Throw - Part VI: inside/outside english" (BD, January, 2007) and "Throw - Part VII: CIT/SIT combo" (BD, February, 2007) illustrate the different possibilities quite well. Here's a good video demonstration and explanation of both cut-induced throw (CIT) and spin-induced throw (SIT):

See also:

A complete summary of all squirt, swerve, and throw effects can be found here.


Do CIT and SIT add or subtract as independent factors?

Object ball throw depends on cut angle, shot speed, type and amount of english, and the amount of vertical plane spin (draw, follow, stun). The following series of instructional articles elaborate on all of these factors:

"Throw - Part I: introduction" (BD, August, 2006).
"Throw - Part II: results" (BD, September, 2006).
"Throw - Part III: follow and draw effects" (BD, October, 2006).
"Throw - Part IV: spin-induced throw" (BD, November, 2006).
"Throw - Part V: SIT speed effects" (BD, December, 2006).
"Throw - Part VI: inside/outside english" (BD, January, 2007).
"Throw - Part VII: CIT/SIT combo" (BD, February, 2007).
"Throw - Part VIII: spin transfer" (BD, March, 2007).
"Throw - Part IX: spin transfer follow-up" (BD, April, 2007).
"Throw - Part X: the big picture" (BD, May, 2007).
"Throw - Part XI: everything you ever wanted to know about throw" (BD, June, 2007).
"Throw - Part XII: calibration, and hold shots" (BD, July, 2007).
"Throw Follow-up: Part I: Cling" (July, 2014).
"Throw Follow-up: Part II: More Results" (August, 2014).
"Throw Follow-up: Part III: Frozen Throw" (September, 2014).
"Throw Follow-up: Part IV: Follow Cling" (October, 2014).

Collision-induced throw (CIT) and spin-induced throw (SIT) are just different names for throw, depending upon the primary cause of the throw, but the effects don't really combine as separate factors.

Outside english (OE) can diminish, eliminate, or even reverse the direction of throw. But at larger cut angles, a small amount of OE can actually increase the amount of throw (e.g., see Diagram 1 in "Throw - Part VII: CIT/SIT combo" (BD, February, 2007)). Again, the reason has to do with the relative surface speed between the balls. Sliding friction (and therefore throw) is greater at slower relative surface speeds. With larger cut angles, inside english (IE) increases the relative surface speed between the balls and reduces the amount of friction and the amount of throw. For a large cut angle, a small amount of OE can reduce (but not reverse) the surface speed some resulting in more friction and more throw.

With "gearing outside english" (gOE) there is no sideways force whatsoever. That's why there is no throw. The OB heads exactly in the impact-line direction (i.e., in the ghost-ball line-of-centers direction). There can be throw only when there is a sliding force between the CB and OB. With gOE there is no sliding between the balls during contact (see "Throw - Part VI: inside/outside english" - BD, January, 2007). With less-than-gearing OE, throw is in one direction (the CIT direction); and with more-than-gearing OE, throw is in the other direction (the SIT direction). There either is throw or there is not, and it can be in one direction or the other. GOE completely eliminates throw and cling. It's just tough judging the exact "gearing" amount of OE you need for each cut angle.


"cling," "skid," and "kick"

What is "cling," "skid" and "kick?"

"Cling" (AKA "skid" or "kick") refers to a "bad hit" resulting from an excessive amount of throw, well beyond what is expected for a given shot. When the CB hits an OB with a cut angle or non-gearing spin, there is friction between the CB and OB at the point of contact that resists the relative motion between the balls. This is what causes throw (CIT or SIT), which is normal. A "bad hit" occurs when the amount of friction is greater than normal, usually because there is a chalk mark at the point of contact. In this case, the amount of throw (or ball hop and topspin loss in the case of a nearly straight follow shot) is larger than the typical amount. It is important to note that a "bad hit" has nothing to do with the shooter or the stroke ... it is due solely to excessive friction occurring between the CB and OB at contact. People sometimes mistake a naturally large amount of throw as cling, especially if they are unaware of how throw varies with the type of shot (see throw effects and maximum throw). Again, cling is an amount of throw much greater than should be expected for a given shot and conditions. People also sometimes think that a "bad hit" results from the CB and OB actually clinging or sticking together for a longer time than normal. This is not the case, even though it might seem this way based on the reaction of the balls.

Cling can occur more often with old, beat up (e.g., from phenolic tip damage), scuffed (e.g., from miscues), and dirty balls, where portions of the ball surfaces might create more friction than other portions (especially when the suspect portions collect and hold chalk easily). However, cling also occurs with new, clean, and smooth balls. The primary cause for cling is a chalk mark or smudge (or a significant amount of chalk dust) appearing at the contact point between the CB and OB. Anytime you see chalk smudges on the CB, you should wipe them off (or ask for a referee to wipe them off if you are in the middle of a tournament game). Definitely wipe off the cue ball before each break shot or any time you have ball in hand. We have enough reasons to miss shots as it is without having to worry about excessive and unpredictable throw due to cling caused by chalk smudges.

Some people have suggested that cling can be caused directly by static electricity, but this is highly questionable (per logic, and per the test at the 3:44 point in NV D.16 - Pool ball cut-induced throw and cling/skid/kick experiment). Although, a possible explanation is that static (resulting from the balls sliding across the cloth) could indirectly cause cling by somehow allowing chalk dust to collect on and stick to the balls more easily (but this is also questionable). Throw could also be larger (for all shots) if the balls are "cleaned" or polished with a substance that alters the ball surface (e.g., by leaving a residue behind or by chemically etching or altering the surface), creating more friction. Some polishes/waxes or aggressive chemical cleaners (e.g., acetone) could have these effects. For more info, see ball cleaning and surface treatment. To see the effect (or lack of effect) of the brand of chalk on cling, see the chalk comparison resource page.

Some people have suggested that oils, from human hands, deposited on the balls as they are handled can help minimize the effects of cling (e.g., see englishBilliards.org's "kick" page). This could be the case, especially if the balls were previously "cleaned." However, an excessive amount of oil could make it easier for chalk smudges to remain on the cue ball, which would result in more frequent cling. It has also been suggested that cling can occur more frequently on cloth that is new, thin, and slick because chalk smudges on the CB might tend to wear off less easily under these conditions (although, this is probably a very small effect). Cling might be more noticeable when playing with new and clean balls (e.g., in televised tournament conditions), where the amount of throw is less than with older and dirtier balls. Because the amount of throw can be less with ideal conditions, when cling does occur it can be strikingly noticeable.

George Onoda wrote an article (see pp. 13-14 here) illustrating how cling might be more likely with low-inside and high-outside english shots, where a new chalk mark might be more likely to end up at the ball contact point, but cling is probably more random than this suggests (due to previous chalk marks or smudges on the balls that happen to end up at the ball contact point, on any shot).

Throw, including cling, can be avoided by using a "gearing" amount of outside english. For more info, see: using outside english to limit or prevent throw and cling.

Cling is often talked about in relation to excessive throw of the OB with a cut shot, but it can also create a lot of trouble for slow-roll follow shots. The CB won't follow the OB near as much as you would expect when there is cling. This video illustrates the effect:

For more information, see: "Throw Follow-up: Part IV: Follow Cling" (BD, October, 2014).

In the snooker world, the term "kick" is sometimes also used to refer to CB hop and its effect on OB motion. The effects of CB hop, along with video demonstrations, can be found on the ball hop resource page.

Here's an example of purposely creating cling (with a chalk smudge) to help create a reverse bank angle:

HSV A.142 - Vernon Elliott cross-side bank with chalk on the object ball to increase throw and spin transfer

The shot is demonstrated in Shot 731 here:

NV B.92 - "Impossible" cut shots, from VEPS V

Here's a fun proposition shot utilizing chalk-induced cling in a devious manner:

NV B.91 - Frozen-throw-down-rail proposition shot, from VEPS V

Other interesting shots utilizing cling can be found in Bob Jewett's April '09 BD article.


from Dan White (in AZB post):

I have been using Novus 1 for cleaning balls in my ball machine for the last couple of years, based on recommendations I saw in AZB. I came across Dr. Dave's video on throw with various ball cleaners, and it got me to wondering how Novus 1 matched up (Dave didn't test Novus 1). The other cleaner I have is the cream from Aramith, which you would assume is the best thing to use since they make the balls. I never liked using Aramith because it is thick and flaky and seems like it would gum up a ball machine quickly. Also, it is a mess to apply. Novus, on the other hand, can be diluted and easily sprayed on the balls in the machine. After doing this experiment, I am a little up in the air as to what the "right" cleaner is. It would seem that consistency is important, which in my experiment favors Aramith. What cleaners are used in tournaments? Is there a standard? What is used in the 14.1 events, where slipperiness can have a great impact on how well balls open?


Originally, I just wanted to see where Novus fit in compared to Dave's results. However, I began to see something odd, so I decided to take Dave's experiment one step further. For each ball in my experiment, I shot it over and over to see if the amount of throw changed over time. Typically I shot each ball at least 20 times. I did find some interesting changes (summarized below).

First, take a look at Dave's video to see the experimental set up:



For those of you who want the short version, here are my results. Note that I hit the balls a little harder than Dave did so that makes sense that I got slightly less throw with Aramith than Dave did:

1. When I cleaned the balls with Aramith (and buffed them in the ball machine) I found that throw started out at 2 inches, and within 8 to 10 trials, the throw increased to 4 inches, and remained there.

2. When I cleaned the balls with Novus 1 (and buffed them in the ball machine) I found that throw started out at just under 2 inches and took about 20 trials to reach 4 inches of throw. I also found that the amount of throw was inconsistent, as in the throw would go up to 3 or 4 inches, and then come back down to 2.5 inches for several trials, and then go back up to 4 inches.

3. I noted that since my ball cleaner has been using Novus 1 cleaner for a long time, the padding may be impregnated with residual Novus, which could impact the results of the Aramith test (item 1 above). So I cleaned more balls by hand with Aramith and only buffed them until shiny with a cotton cloth. I did not put them in the ball machine. In this case, the throw was consistent at 5 inches the entire time (over 20 tries).


There is a clear difference in throw between using Aramith cleaned by hand and Novus 1 cleaned in a ball machine. The Aramith throws very consistently at 5 inches, even from the very first shot, whereas the Novus 1 throws inconsistently, and changes dramatically after fewer than 10 rolls up and down the table (10 trials). Novus "tops out" at a throw around 4 inches, but is still inconsistent well after 20 tries.

It seems to me that Aramith is the way to go since it provides consistency. I find that when using Novus 1, the balls open up more easily than when using Aramith. I wonder whether this is an "unfair" advantage, akin to spraying silicone on the balls. I would be interested to hear what is being used in tournament play. I believe it is wise to learn how to play under various playing conditions, but knowing how the balls were cleaned can help a player gauge how much the throw conditions are likely to change.


If the CB and OB don't stay in contact longer when "cling" occurs, what is it that happens instead?

"Cling" in the context of pool doesn't actually mean the balls stick or "cling" together (although, it can seems like this based on the reaction of the balls when "cling" occurs). It just means there is more friction to resist sliding during contact.

The contact time between the balls, which is extremely small, depends only on how the balls compress (in the perpendicular or normal direction) during contact. The amount of sliding or friction between the balls during contact really doesn't affect the contact time. With a cut angle, the CB tends to slide on the OB during contact. At smaller cut angles, the CB and OB slide at first but then "gear" together during contact. This happens sooner with more friction (e.g., with "cling"), but the contact time doesn't change. At larger cut angles, the CB slides during the entire contact time, even with a more-than normal amount of friction.

What changes with increased friction is the amount of loss of relative sliding speed between the balls. With enough friction, the sliding disappears completely resulting in gearing motion. But again, this all happens during the normal ball compression and restitution.

draw and follow effects

Do shots with draw and follow throw as much as shots with stun?

Stun shots exhibit the most cut-induced throw (see "Throw - Part II: results" - BD, September, 2006) and spin-induced throw (see "Throw - Part IV: spin-induced throw" - BD, November, 2006). Draw and follow shots exhibit less throw (see "Throw - Part III: follow and draw effects" - BD, October, 2006); and if they have the same amount of bottom or top spin, the amount of throw is the same (and less than the amount of stun throw). See "Throw - Part III: follow and draw effects" (BD, October, 2006) and Bob Jewett's May '06 article to see how stun, follow, and draw shot throws compare. Because bottom spin wears off due to "drag" action, many draw shots will have less spin, and more throw, than typical follow shots.

Now, object ball (OB) swerve does have a slight effect on throw with follow and draw, but the effect is very small (see the end of TP A.24 for example numbers). Strictly, a follow shot will have slight OB swerve in the throw direction, effectively increasing the effective throw a tiny amount; but for all practical purposes, follow and draw shots with equal amounts of spin throw the same amount. Now, if a draw shot has more backspin than a follow shot has topspin, then the draw shot will definitely have less throw than the follow shot. The closer a shot is to stun, the more throw it will have.


Why do stun, follow, and draw shots create radically different amounts of throw at small to medium cut angles and similar (but smaller) amounts of throw at large cut angles?

The reason why top and bottom spin make less difference at larger cut angles is that sliding motion between the CB and OB is mostly horizontal at the larger angles. Imagine a CB spinning in place with topspin in contact with an OB ball. If the CB is in front of the OB (as with a full-ball hit), the CB is rubbing straight down on the OB. Now, with the CB still spinning, move it around the OB (while keeping the spin direction the same) simulating different cut angles. When the CB is on the side of the OB (as with a 90 degree cut), the spin creates no rub at all at the point of contact between the balls. The amount of downward rub changes gradually with the cut angle. It is larger for a small cut angle, and smaller for a large cut angle.

Now, throw is caused by horizontal rubbing motion between the CB and OB. When a stunned CB hits the OB at an angle, the rubbing motion is completely horizontal, creating maximum throw. When there is topspin or bottom spin, the rubbing motion is less horizontal, creating less horizontal throw. However, as described above, this effect is less at larger cut angles. That is why stun, follow, and draw shots create similar amounts of throw at larger cut angles.


effects summary

What squirt (cue ball deflection), swerve, and throw effects do I need to be aware of?

See effects summary.



What are some example shots where throw and spin transfer can be used or must be accounted for?

Several examples of throw shots are demonstrated in the following video:

And here are some more:

These and other examples are also described and illustrated in the following series of instructional articles:

"Throw - Part I: introduction" (BD, August, 2006).
"Throw - Part II: results" (BD, September, 2006).
"Throw - Part III: follow and draw effects" (BD, October, 2006).
"Throw - Part IV: spin-induced throw" (BD, November, 2006).
"Throw - Part V: SIT speed effects" (BD, December, 2006).
"Throw - Part VI: inside/outside english" (BD, January, 2007).
"Throw - Part VII: CIT/SIT combo" (BD, February, 2007).
"Throw - Part VIII: spin transfer" (BD, March, 2007).
"Throw - Part IX: spin transfer follow-up" (BD, April, 2007).
"Throw - Part X: the big picture" (BD, May, 2007).
"Throw - Part XI: everything you ever wanted to know about throw" (BD, June, 2007).
"Throw - Part XII: calibration, and hold shots" (BD, July, 2007).
"Throw Follow-up: Part I: Cling" (July, 2014).
"Throw Follow-up: Part II: More Results" (August, 2014).
"Throw Follow-up: Part III: Frozen Throw" (September, 2014).
"Throw Follow-up: Part IV: Follow Cling" (October, 2014).

Any time there is throw, there is also spin transfer. Numerous examples of where spin transfer comes into play can be found here: spin transfer examples.

Throw can also be used in "hold" or "kill" shots. Throw is also very important in frozen-ball combination (see frozen-ball throw). And many trick shots also rely on, or are affected by, throw. For examples, see famous trick shots.

With clusters, there is a whole world of possible shots available taking advantage of kiss and carom aiming principles and throw and spin-transfer effects. Many good examples can be found in Mark Finkelstein's collection of cluster shots.


frozen balls

Do frozen balls throw more than non-frozen balls?

In the case of combinations, frozen balls will always throw more than non-frozen balls (especially with a larger gap between the OBs) because the 1st OB will pick up some forward roll, which reduces throw. Also, if faster speed is used to help prevent this, throw will be reduced by the speed.

In the case of a cut shot, the OB can be thrown very nearly as much as with a frozen combo, as long as slow speed and stun are used, where throw is maximum (see maximum throw for more info). One reason some people might think frozen balls throw more than a stun shot is that frozen balls can be hit softly, easily creating maximum throw. With frozen balls, stun is guaranteed. However with a non-frozen cut shot, where there is distance between the CB and OB, it is very difficult to ensure stun with a soft shot. Therefore, it is rare to get maximum throw with a cut shot. Although, if you do hit a true stun shot at soft speed, the OB will throw very close to the same amount as a frozen ball would.

To answer this question more scientifically, I did a careful experiment to attempt to measure the difference between throw with a frozen-combination and throw with a stunned ball at the same speed.

I used two new and clean Aramith measles balls as OBs, and wiped them after every shot, along with the CB which was another Aramith measles ball. I firmly tapped the two OBs into place (frozen, but not leaning against one another) with one OB on the head spot and the other on the head-rail side of the first with the line of centers along the table centerline. I also marked the tapped positions with little white donuts to help further ensure consistent ball placement, shot after shot. I then hit the 1st OB squarely with another CB placed between the balls and the head rail to locate and mark on the far rail the line of centers direction (which was pretty much exactly along the table centerline with every shot). I then tapped and marked the CB position about 6 inches on the head-rail side of the near OB along the center-to-edge line of the frozen-ball combo to ensure a consistent cut angle (with a square hit on the 1st ball) very close to 30 degrees. I then hit this shot (after checking that the OB were in fact frozen) about 20 times at as consistent a speed as I could and marked on the far rail where the thrown OB hit (by placing a piece of chalk on the rail with one edge pointing along the line of the thrown OB). I only checked shots where the CB stopped dead and the 2nd OB bounced off the foot rail and came back to within a 1/2-diamond of the head rail to ensure consistent speed. All of the target-speed shots threw the OB very consistently to the same position on the rail.

I then removed the donut for the lead OB, replaced and carefully tilted the lead OB back toward the CB along the CTE line a very small amount and firmly re-tapped the ball into the cloth until the OB sat about 1mm (a very small gap) away from the 2nd OB. When I was confident with the placement, I put down another donut in the new location and tapped the ball in place even more firmly. I then hit about 20 shots with this new position (resulting in a non-frozen stunned hit of the lead OB into the 2nd), with everything else the same. Again, the direction the ball headed was very consistent for the shots at the target speed.

Here are the results after measuring the distances between the head spot and rail marks carefully and doing the throw angle calculations:

throw angle for frozen balls = 5.16 degrees

throw angle for non-frozen stun shot of same speed and cut angle = 4.95 degrees

Therefore, my experiment suggests frozen balls might throw a very small percentage more (about 4% more) than a stunned ball. However, this difference is not very significant, and could be partly due to experimental error. It could also be due to the fact that when there is a gap between the balls, the 1st OB has full speed before contacting the 2nd OB. This would result is less friction during the initial part of the collision, which could delay gearing (or prevent it from happening). This could explain the difference between frozen and non-frozen throw, especially at different cut angles and shot speeds. It is also possible that with non-frozen balls, the air between the balls being compressed before the collision might help create a slight cushioning effect (especially with higher-speed shots), which could reduce the amount of throw.

The following video documents a more recent experiment that has mixed results, but the conclusion is clear: a frozen combo throws about the same amount as a stun shot of the same speed.


For more information, see "Throw Follow-up: Part II: More Results," (BD, August, 2014), "HAPS - Part V: Combination-Shot Throw" (BD, March, 2015), and combination-shot aiming.


During a frozen-ball combo, does the CB still apply force on the 1st OB while it is in contact with the 2nd OB, and wouldn't this change the amount of throw?

There are delays in the ball interactions due to the time it takes for elastic waves to travel between the contact areas (between the CB and 1st OB, and between the 1st and 2nd OBs), but this happens very quickly. From speed of sound data, the elastic wave speed in pool balls is probably close to 4000 m/s. From Marlow's experiments, ball contact times are probably close to 0.0003 seconds. During that time, the waves have time to travel back and forth across the 1st OB at least 20 times. From these rough calculations, it is clear that forces developed between the CB and 1st OB can certainly have an effect while the 1st OB is interacting with the 2nd OB.

The CB interaction would tend to slow the induced spin that develops in the 1st OB as it interacts with the 2nd OB. This would tend to increase the relative sliding speed between the OBs, which would reduce the dynamic friction COR (since friction is less at faster sliding speeds with pool balls). This would tend to decrease the amount of throw. However, gearing between the 1st OB and the 2nd OB will be hampered some, and more throwing force can develop before the balls gear together, creating more throw. The experiment described above did show a small increase in throw, probably due to this effect.


"hold" or "kill" shot to limit cue ball drift

Can throw be used to "kill" cue ball motion on a cut shot?

When the CB is close to the OB, spin-induced throw (SIT) can most definitely be used to limit how much the CB drifts after the hit. For illustrations and explanations, see "VEEB - Part IV: Throw Hold Shots" (BD, February, 2016) and "Throw - Part XII: calibration, and hold shots" (BD, July, 2007). Here are some example SIT hold shots from from Disc II of the Video Encyclopedia of Eight Ball (VEEB):


Swerve and drag control become bigger factors at larger distances (see the article and below for more info). TP A.29 presents a full analysis for those with math and physics backgrounds.

Bob Jewett has a good test to explore the ability to use english to hold the CB. At small distances with slow-speed stun, with about 50% english, the effect of throw is irrefutable and dramatic. In fact, with a small enough cut angle, and the right speed and amount of spin, the CB can actually be made to move in the same direction as the OB (e.g., to the right, with a cut to the right). An example can be viewed in the first shot of the following video:

NV B.21 - Straight shot squirt, swerve, and throw

As pointed out at the bottom of TP A.29, it is theoretically possible (neglecting swerve) to hold the CB and create an OB angle at any CB-OB distance. However, at the table, there is a practical limit to the CB-OB distances over which this can be done. The analysis in TP A.29 ignores the effects of swerve. Swerve changes the effective cut angle of the shot, making it more difficult to hold the CB. And at larger distances, swerve becomes more of a factor. Also, stun (for maximum throw) is more difficult to control at larger distances. Also, it is much more difficult to judge squirt and swerve and be accurate with the hit at larger distances. At larger CB-OB distances, a plain stun shot will be the most effective at holding the CB.

If you want to cheat (e.g., in a proposition shot), add chalk at the OB contact point. This will make larger throw possible (see cling), and you will be able to cut the OB and hold the CB at larger CB-OB distances.


Is inside english a better choice than outside english to limit CB sideways drift on some shots?

See the following two videos that study this effect:


maximum throw

What is the most throw I can get, and how can I achieve maximum throw?

Maximum throw, under typical conditions, is about 1 inch per foot of CB travel, which is about 5 degrees. Although, more throw can result with cling/skid/kick.

Maximum spin-induced throw (SIT) occurs with slow speed, stun, and about 50% english. See "Throw - Part V: SIT speed effects" (BD, December, 2006) for more information. The reason why more spin doesn't give more SIT is: friction is less at faster sliding speeds. With more english, the CB slides along the OB with faster relative speed during contact, producing less throwing force. One possible reason for this is that the air compressed between the balls during contact doesn't get out of the way as easily with a faster relative surface speed. And maybe with faster relative surface speed, the asperities (small but rough features) on the surfaces don't catch and interact as easily. Per Diagram 1 in the SIT article, below about 25% english, speed has no effect on the amount of SIT! For more information on SIT speed effects, see: HSV B.18 - spin-induced throw speed and english effects.

Maximum cut-induced throw (CIT), with no english, occurs with a slow-speed stun shot at about a 1/2-ball hit. See "Throw - Part II: results" (BD, September, 2006) for more information. At larger cut angles, again the friction is less due to the faster relative sliding motion between the balls during contact. Per Diagram 1 in the CIT article, for cut angles below about 20 degrees, speed has no effect on the amount of CIT!

For examples and demonstrations, see the following video:


outside english to prevent throw and cling

Should I use outside english to reduce the effects of throw (i.e., "spin the ball in")? If so, how much?

See outside english to prevent throw and cling.


physics details and results

What are all of the factors that affect how much throw a shot will have?

TP A.14 contains a thorough analysis, and TP A.28 contains graphs for all types of shots. Let me warn you ahead of time: TP A.14 is full of lots of complicated math and physics, so you might not want to look at the whole thing, but the results in TP A.28 might still be of interest. If not, or at least look at some of the conclusions summarized below. Plots in TP A.14 compare well to experimental, theoretical, and qualitative results presented by Marlow, Sheppard, Koehler, and Jewett. The analysis and results cover both cut-induced throw (CIT) and spin-induced throw (SIT). The effects of cut angle, speed, and spin are also considered.

The model of friction I use is more complete and accurate than any other I have seen presented before. First, I include the effect of speed on friction, based on experimental data from Marlow. And more importantly, I correct an error that appears in many analyses of collisions with friction (e.g., in Shepard's work). The error involves not taking into account the potential loss of relative sliding motion between the CB and OB during impact. I have accounted for this effect, and it significantly affects the results.

Here are some of the conclusions resulting from the mathematical analysis (which agree with what most people understand about throw effects)

See also: aim compensation for squirt, swerve, and throw.


spin transfer

Can you prove to me that spin can be transferred from the cue ball to an object ball?

For the non-believers out there, I have several resources available to prove that spin transfer exists. HSV A.66 provides a high-speed video demonstration of the effect ... the spin transfer is clearly visible! For the physics nerds out there, TP A.27 provides a mathematical proof. And for people who need to see shot examples, here's one that relies on both throw and spin transfer:

With shots like the one in the video above, throw and spin transfer are maximum at slower speeds with about 50% english (half maximum). However, at slow speeds, more of the transferred spin will wear off on the way to the rail, so the optimal speed (for the spin-transfer rebound-angle-change effect) will depend on conditions and the distance to the rail.

And here are some others (also see more posted by others below):

Also, HSV A.143-A.146 illustrate spin transfer and "vertical throw" (ball hop) resulting from follow and draw. Notice how the effects are much greater when chalk is added to the object ball surface. Remember: keep those balls clean. Here is another video, with explanations, on the same topic:

HSV B.46 - CB and OB hop and spin transfer during follow shots

Whenever there is throw (SIT or CIT), there is spin transfer (SIS:spin-induced spin or CIS:cut-induced spin); and the more throw you have, the more spin transfer you have. It is a small amount of spin, but it makes a big difference with bank shots (e.g., with an inside cut, the bank is lengthened; and with an outside cut, the bank is shortened). For more info, see bank and kick effects.

For a good example of how throw and spin transfer can affect a bank shot, see "Throw - Part VIII: spin transfer" (BD, March, 2007) and:

Sometimes the phrase "twist the bank in" is used to describe shots like this, where spin transferred to the object ball is used to alter the bank rebound angle. For more info, see bank-shot cut-induced spin effects.

Section 40 (Spin Transfer Shots) in Disc IV of the Video Encyclopedia of Pool Shots presents several types of shots (with many examples) where cut-induced spin (CIS) and spin-induced spin (SIS) are important factors.

Many trick shots also rely on, or are affected by, throw and spin transfer. For examples, see famous trick shots.

Here's an example of spin transfer in reverse, with a stunned ball hitting a stationary spinning ball:


from Bob Jewett (in AZB post):

Here's a simple demo posed as a proposition shot. Under the right conditions, you can add a second blocker ball frozen to the 2 ball so the block is a full two balls wide. People who don't know that you can spin the object ball could lose a lot of money at this proposition.

spin tranfer bank propostiion

from Patrick Johnson:

In both setups (see below) the OB must have spin to go. However, the setup on the right needs CB spin in order to transfer spin to the OB, but the one on the left can transfer spin to the OB without spinning the CB.

spin transfer examples


from JB Cases:

...back in the olden days..., back when balls would actually spot, this here shot (see below) used to come up all the time and we had to know how to make the 8 spin BELOW then nine so that it would be safe. This shot very rarely comes up now.

The cue ball STOPS frozen to the nine or just behind it. The eight goes to the side rail and spins to the left going lower down table than the where the nine is. It was IMPOSSIBLE to hit the 8 ANYWHERE to the right of center or it would make the 9 move as well. So you have hit center ball with low right spin which then transfers left spin to the object ball.

spin transfer example


stop shot with sidespin

How do you account for throw with a stop shot with sidespin?

To stop the cue ball using sidespin, there must be a cut angle. In other words, the cue ball must hit the object ball slightly off center as if you were going to "cheat" the pocket (e.g., see NV 5.7). If you are aiming the shot straight-on, cue ball deflection (squirt) will automatically create the cut angle (see NV 4.13 for a description and illustration of squirt). With a cut angle, if there was no sidespin the object ball would cheat the pocket and the cue ball would drift along the tangent line. With left sidespin, squirt causes the cue ball to deflect to the right, creating a cut angle to the left. However, the object ball would be thrown back to the right (due to the left sidespin) towards the center of the pocket. Because the cue ball throws the object ball right, the object ball pushes back on the cue ball to the left, counteracting the expected tangent line motion to the right. Therefore, the cue ball stops in place. "90° and 30° Rule Follow-up - Part IV: english effects" (BD, May, 2005) doesn't address this issue directly, but the information in the article is relevant.


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