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Bob Jewett Thin Hits Learn this to psyche out your opponents. Do you feel good about your thin hits? Would you like to play them better and smarter? If so, read on. If you play any pool game, you will often find yourself in a situation like Diagram 1. The cue ball is a mile from the object ball, and you need to both make a good hit on the object ball and leave no shot. Is a thin hit — just nudging the ball so it moves as little as possible — the right shot for you? In the extreme position shown, you should probably shoot something else if it's available, but let's look at the thin hit a little closer. The goal is to get a hit, come off the far end rail, and bring the cue ball back to its starting point, more or less. There is a problem on each side: If you miss the ball entirely, you foul and give up ball in hand or a point or worse; if you hit too much of the ball, you give up an easy shot to your opponent. The first considerations are the table and the cue ball. If you are familiar with both of them, you know whether to expect roll-off. Some players are able to allow for the "windage" due to table slope, but you might also run into a cue ball that's slightly lop- sided, and might roll left or right unpredictably. I've seen balls that might be off by as much as a tenth of an inch by the time they reached the object ball for the shot in Diagram 1. Diagram 2 shows how accu- rate the hit has to be to control the distance the object ball is driven. The fuller you hit the object ball, the farther it will travel. Along the bottom is how full the ball is struck in inches of overlap. (Think of how much the edge of the cue ball overlaps the edge of the object ball from the tip's-eye view. Overlap of 1.125 inches would be a half-ball hit.) The vertical axis is how far the object ball will roll for a shot that just brings the cue ball 8 diamonds back to the end cushion you start from — use the "Start long" curve for this. For example, if you hit a tenth of an inch of the object ball, it will be driven about 18 inches along the end rail. If the cue ball or table is not quite right, and you get a tenth of an inch of roll-off, you could get no hit at all or the object ball would be driven 35 inches or about 3 diamonds. That would be very bad for your safety, as it would leave the ball in front of the corner pocket. So, how good are your thin hits? In Diagram 3 are a cou- ple drills to test and improve them. Shot A is the same sort of safety as in Diagram 1, but arranged the short way on the table. Play the thin hit to see how little you can move the object ball. Start with the object ball near the side pock- et, and leave it in position for each following shot, but move the cue ball so you will be shooting directly across the table each time. How many times does it take you to get the object ball to the end cushion? On each shot, you have to bring the cue ball back at least close to the side rail you are starting from. When you have mastered the short way for this drill — or at least improved — put the cue ball at C and the object ball at O and try it again, with the requirement that you have to return the cue ball to near the head rail. As you progress, move the cue ball's starting point farther back. To avoid problems from table roll on these drills, be sure to play the shots to both sides. For example, after you have worked the object ball to the left with the drill shown until it is almost to the rail, work it back the other way. Is your table flat? Is your cue ball round? In Shot B of Diagram 3 is a different thin-hit situation. This time you are close to the object ball, so the hit is much 24 BD-JANUARY 2004

Thin Hits - · PDF fileBob Jewett Thin Hits Learn this to psyche out your opponents. Do you feel good about your thin hits? Would you like to play them better and smarter?

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Page 1: Thin Hits -  · PDF fileBob Jewett Thin Hits Learn this to psyche out your opponents. Do you feel good about your thin hits? Would you like to play them better and smarter?

Bob Jewett

Thin HitsLearn this to psyche out your opponents.

Do you feel good about your thin hits?Would you like to play them better andsmarter? If so, read on.

If you play any pool game, you will oftenfind yourself in a situation like Diagram 1.The cue ball is a mile from the object ball,and you need to both make agood hit on the object ball andleave no shot. Is a thin hit —just nudging the ball so itmoves as little as possible —the right shot for you?

In the extreme positionshown, you should probablyshoot something else if it'savailable, but let's look at thethin hit a little closer. The goalis to get a hit, come off the farend rail, and bring the cue ballback to its starting point, moreor less. There is a problem oneach side: If you miss the ballentirely, you foul and give upball in hand or a point orworse; if you hit too much ofthe ball, you give up an easyshot to your opponent.

The first considerations arethe table and the cue ball. Ifyou are familiar with both ofthem, you know whether toexpect roll-off. Some playersare able to allow for the"windage" due to table slope,but you might also run into acue ball that's slightly lop-sided, and might roll left orright unpredictably. I've seenballs that might be off by asmuch as a tenth of an inch bythe time they reached theobject ball for the shot inDiagram 1.

Diagram 2 shows how accu-rate the hit has to be to controlthe distance the object ball isdriven. The fuller you hit theobject ball, the farther it willtravel. Along the bottom ishow full the ball is struck ininches of overlap. (Think ofhow much the edge of the cueball overlaps the edge of theobject ball from the tip's-eyeview. Overlap of 1.125 inches

would be a half-ball hit.)The vertical axis is how far the object ball

will roll for a shot that just brings the cueball 8 diamonds back to the end cushionyou start from — use the "Start long" curvefor this. For example, if you hit a tenth of

an inch of the object ball, it will be drivenabout 18 inches along the end rail. If thecue ball or table is not quite right, and youget a tenth of an inch of roll-off, you couldget no hit at all or the object ball would bedriven 35 inches or about 3 diamonds. That

would be very bad for yoursafety, as it would leave theball in front of the cornerpocket.

So, how good are your thinhits? In Diagram 3 are a cou-ple drills to test and improvethem. Shot A is the same sortof safety as in Diagram 1, butarranged the short way on thetable. Play the thin hit to seehow little you can move theobject ball. Start with theobject ball near the side pock-et, and leave it in position foreach following shot, but movethe cue ball so you will beshooting directly across thetable each time. How manytimes does it take you to getthe object ball to the endcushion? On each shot, youhave to bring the cue ballback at least close to the siderail you are starting from.

When you have masteredthe short way for this drill —or at least improved — put thecue ball at C and the objectball at O and try it again, withthe requirement that you haveto return the cue ball to nearthe head rail. As you progress,move the cue ball's startingpoint farther back. To avoidproblems from table roll onthese drills, be sure to playthe shots to both sides. Forexample, after you haveworked the object ball to theleft with the drill shown untilit is almost to the rail, work itback the other way. Is yourtable flat? Is your cue ballround?

In Shot B of Diagram 3 is adifferent thin-hit situation.This time you are close to theobject ball, so the hit is much

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Bob Jewett

easier, but you still want to drive the cueball eight diamonds for the safety. It turnsout that the object ball is also not drivennearly as far for a given thickness of hit asfor the long safety inDiagram 1. This isbecause it doesn'tlose a lot of energyin the cushion rightafter the ball contact.The thickness/drivecurve for this case isshown in the lowerplot in Diagram 2.Hitting a tenth of aninch of the objectball should be ducksoup from this dis-tance, so the objectball should onlymove 5 inches if youjust barely get to theend cushion.

You can set up a drill based on Shot B;keeping in mind that you should be able tonudge the ball at least six times before itreaches the end rail.

If your thin hits aren't working, or youdon't know how the table is rolling, youneed to have alternatives. In Diagram 1, astandard fuller-hit safety is to hit about halfof the object ball on the right side and use a

speed — this comes through practice — toleave the object ball near O and the cue ballnear C. This may leave a bank for youropponent, but it's not a nice angle, and if

both balls are near the cushions it's tougherstill. A subtle point is that a half-ball hitcauses the cue ball and object ball to movealmost the same distance off the end cush-ion. Fuller, and the object ball moves morethan the cue ball; thinner, and the cue ballmoves more. If they move the sameamount, the balls will be left straight acrossfrom each other, which is a nasty situation

for banking.Thin hits are not just for defense. In

Diagram 4 are two shots useful in one-pocket that require very thin hits. In Shot A

is a common leavewith the object ballon the spot and thecue ball on the badside of the table —your pocket is P. Athin hit can make theball. Do you under-stand why it isalmost impossible toscratch if you makethe object ball fromthe spot? In Shot B,you are banking thespotted ball to pocketP. The cue ball willhit at Bl for its firstcushion, and B4 forits fourth cushion,

and if you are lucky, end up down by theShot A cue ball for the safety. While thereare less aggressive alternatives for both ofthese shots, if you have your thin hits per-fected, these shots can be psychologicallydevastating to your opponent. You'll knowyou've won the mind game when you hearhim muttering, "How can he make thatshot?"

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Bob Jewett

Where's Your Elbow?Do you want to be a piston or a pendulum?

In sports such as golf, swimming, andtrack and field, there is a lot of recentactivity applying new technology to under-standing how the body can achieve maxi-mum performance. When sports scienceappears on TV, you might see a wired-upswimmer in an aquatic treadmill or a golferwith glowing spots taped on each of hisjoints and in front of a computerized cam-era that catches each arc and accelerationand hitch.

I'm sure the funding willsoon start rolling in for suchprojects with billiard players,but in the meantime we haveto study billiard biomechanicsand carom kinesiology withsimpler and cheaper methods.

What is a good stroke? Whatdo you want in a "correct"stance? How does the bodyactually move the stick, andhow can the typical playerimprove the motion? Whatshould you spend your timeworking on, stroke- andstance-wise?

Let's begin by looking at avery simple model of the play-er. We're going to ignore mus-cles and tendons and even thethird dimension for the timebeing. In Diagram 1 is a sideview of our model player.He's simply three dots and two straightlines connecting the dots, plus a pivot pointrepresenting his bridge hand. Call him Ed.Later we'll try to give him more personali-ty-

If Ed has the unfortunate habit of jump-ing up and raising his whole body duringthe shot, just run a long pole through hisshoulder to both walls, so his shoulderdoes not move during the shot. By notmoving the shoulder, I mean the dot whichrepresents the shoulder stays in one place.Maybe the upper arm moves, and thisrequires a rotation at the shoulder joint, butthe shoulder can rotate to move the upperarm without moving itself.

As the next simplification, let's assumethat the upper arm doesn't move. We'llrelax this requirement soon, but for now,just the threat of another pole will get Ed tokeep his elbow in one place.

Ed's last joint is his wrist/hand at the gripon the cue. Again, we simplify the situa-tion by assuming that Ed is not into wrist-flipping to get that special action on thecue ball, and that the wrist acts as a simplepivot point.

We're also going to take the rails off thetable so that Ed's stick can be horizontal atthe instant it hits the cue ball. In reality,nearly every shot must be played with sig-

nificant elevation because of the presenceof the rails.

The resulting motion is the classic "pen-dulum" stroke. Ed addresses the ball in theposition shown with the tip close to theball, then swings his hand and the stickback moving just the lower arm and pivot-ing at the elbow. The hand swings forward,following a perfect circular arc, with the

elbow as its center and Ed's forearm as itsradius. The tip contacts the cue ball whenthe stick gets back to its starting point, atwhich time the forearm is straight up anddown and perpendicular to the cue stick.The stick follows through the ball with thehand continuing its circular arc. The elbowhas not moved an iota.

Successive positions of this action areshown in Diagram 2. The main thing to

note here is that the stick doesnot move in a straight lineeither before or after it hits theball. At the end of the back-swing, the butt of the stick hasrisen considerably, and at theend of the follow-through, thebutt has risen again. This is asimple consequence of thependulum motion — a pendu-lum is obviously lowest at thebottom of its swing.

While the stick is wobblingup and down during nearly allof the stroke, it is goingstraight forward at the instantit hits the cue ball. This isillustrated in Diagram 3,which shows the path of justthe tip during the stroke. Asit's drawn back to the bridgehand, it first drops a little asthe back hand rises, then itcomes back to the address-

ing/contact point, then as Ed followsthrough, the tip drops again with the risingof the grip hand.

At the instant of contact, the path of thetip has no up or down component; it istraveling straight forward toward the ball.

What are the advantages of this simpleform of stroke? Just the simplicity isimportant; remember the KISS principle(Keep It Simple, Stupid). The less there is,the less there is to go wrong.

A second advantage is that you will hitthe cue ball exactly where you address it.Is it useful to know where you hit the ball?Many think so.

A minor advantage is that it takes theleast amount of effort to hit the ball thisway — just pull the pendulum back andgravity does the work until the bottom ofthe arc, and then gravity starts slowing thestick. A fairly common principle in

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Bob Jewett

mechanics is that the easiest way to dosomething is often the most accurate.

Now you may jump up and say —remember what we do to people who jumpup — "Wouldn't it be better to have astroke that didn't get the wiggly tip path inDiagram 3, but instead brought the stickstraight back andstraight through?"Diagram 4 showsthe successive posi-tions of Ed's elbowneeded to achievethis motion. Notethat as the stickcomes back, theupper arm mustrotate down, lettingthe elbow drop sothat the stick is notraised at the end of the back stroke. As thestick comes forward, the elbow rises to itspeak position at the instant of contact, andthen must drop again to maintain a straightpath on the follow-through. Of course, youcould also get some of the up-and-downmotion by moving your whole body, butEd can't because of the pole.

This is clearly a more complicatedmotion for the body, but it can be learned.In fact, there are stroke-training devices onthe market that will teach you what might

be called the "perfect piston" motion, withthe stick moving just along its axis withoutany teeter-totter from the pendulum.

My main objection to this motion is thatit requires correct timing of two motions.The elbow's drop-then-rise must be syn-chronized with the forearm's back-and-for-

up.But enough of this arm-chair hypothesiz-

ing; let's do a little lab work. The first partof your homework is to watch players'elbows — be discreet, as elbow oogling isstill illegal in some jurisdictions. First noteif their shoulders are moving during the

shot. If so, watchsomeone else whoseems to have betterbasic form. Note howand when the elbowmoves. Does it moveboth before and afterthe shot? For eachplayer that you watch,be sure that you catchboth fast and slowshots, as some playersseem to have more

than one style of stroke. If you have tapesof professional matches, the pause buttonwill help, but the camera angles are notalways ideal.

The second part of your homework is totry to figure out what your own stroke isdoing. If you don't have a video camera,enlist a friend. You might also need a longpole.

Next time I'll go over my own observa-tions, some of which I'll be making at the2003 Mosconi Cup in Las Vegas.

ward movement. For example, if Ed'selbow has gone up too much at the instantof tip-ball contact, Ed will hit too low onthe cue ball. As drawn in the diagram,which is nearly to scale for a normal play-er, if the elbow is raised by 3 mm, Ed willhit 1 mm lower than intended on the cueball. Is 1 mm important? For most drawshots, it will mean you are about 10 per-cent off on the spin. Is 3 mm a lot of accu-racy to expect in dynamic elbow position?It's the thickness of two pennies stacked

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Bob Jewett

It takes all kinds (of strokes) to make a Mosconi Cup.

Last month, I started a discussion of bil-liard stroke mechanics. My hope is thateventually some serious scientific researchwill be done in the area, but for now wehave to settle for armchair (bar stool?)analysis and table-side observations.

It is interesting to note how instructionhas changed over the years. In Figure 1 isa drawing from Kentfield's 1839 book,"The Game of Billiards," which was print-ed until the 1880s. If anyone wants to tryme some 9-ball with that stance and wear-ing a long coat and tie, they've got the wild8. At least the player is shown holding thecorrect end of the cue, which was a fairlyrecent innovation in those days — 50 yearsbefore, most players shot with the blunt endof the stick, which was called a mace.

Note that the forearm of the player's backarm is vertical at the moment of contactwith the ball, but Kentfield doesn't explic-itly mention this. He does say that the bodyshould not move until the shot is over, sothat only the arm moves, but he doesn'tspecify which part or parts of the arm.

Figure 2 is from a 1948 booklet by theBilliard and Bowling Institute of America,and shows the progress in stance over theintervening century. At least we got rid ofthe long coat. The text recommends that theforearm should "hang almost perpendicu-larly" without really explaining what thatmeans. The player's hand as shown in thepicture will actually be a hand's-width ortwo forward of perpendicular at the instantof impact, which I'd call considerably offperpendicular.

Figure 3 shows a modern stance with thechin nearly on the stick. Almost all topplayers use this stance or one very near iton long shots that require accurate aiming.It is interesting to read even some recentinstructional books that say such a stancecramps the stroke, and then to watch a play-er draw the cue ball a table length and a halfwith chin-to-cue. You can't believe every-thing you read.

But you can believe much of what yousee. Your homework assignment was toobserve what players' arms, including yourown, actually do during the stroke. Whilethis is not guaranteed to tell you the singlebest way to play, if you observe good play-ers and bad, you can probably start to fig-ure out what seems to work well.

I conducted my field work in Decemberat the Mosconi Cup in Las Vegas. This wasthe first time in its 10-year history that itwas held in the U.S., and I'm sorry forthose who weren't there. The format con-sists of six-man teams, the U.S. vs. Europe,with the first to win 11 short matches thevictor. Europe led going into the fourth and

shot. I need to study some slow-motionvideo to be sure, but my suspicion is thatthe drop is a simple mechanical result ofthe forearm closing on the biceps. It seemedto me that most of the strokes in the 9-ballcompetition were in this category.

The second stroke I'll call the "orthodoxsimple stroke." Here, the upper arm moves

final day, but Team USA pulled out the vic-tory. (For more info, see the cover story inlast month's issue or visit the MosconiCup's Web site: www.mosconicup.com.)

It was not so easy for me to watch elbowsduring the matches; I'm programmed topay more attention to the balls and situationon the table than the players' mechanics. Ihope you had an easier time with yourhomework. I did manage to make someuseful observations of four different typesof arm motion.

The first stroke is what I will call the"standard power stroke." The elbow isessentially motionless until the end of theforward stroke when the forearm starts toclose against the biceps, and the upper armdrops about its own width, or roughly fourinches. This is the arm motion you willprobably see in the above-mentioned draw

almost not at all, so the motion is confinedto just the forearm. Even for some playerswho often use the first motion, this simplerstroke is used for soft shots. I'll have to dosome more field work at straight pool andone-pocket events, where a larger fractionof the shots are delicate ones. One playerwho used the orthodox simple stroke even

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Where's Your Elbow Now?

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Bob Jewett

on the faster shots was Tony Robles, who isknown for his straight-pool prowess.

A third type of stroke is the "perfect pis-ton stroke," which I described last time.The elbow goes up and down insuch a way that the stick movesin a perfectly straight line. Whilethis sounds simple, it requires afairly complicated motion fromthe arm. The elbow must drop asthe stick is drawn back, rise asthe stick comes forward to con-tact, and then drop again duringthe follow through. The onlyplayer of the twelve at theMosconi Cup that I saw with thisaction was Jeremy Jones. Theonly other player I've seen usethis stroke is Hall-of-Fame mem-ber Loree Jon Jones. If you noticeany other adherents to thismethod — especially one notnamed Jones — please let meknow.

The fourth and final type ofstroke is the "over drop." In this stroke, theelbow comes down much more than withthe first type, so that the tip of the stickends well above the level of the ball. In theextreme form of this, the stick will actuallyhit the rail, making a clacking sound. Theonly player in Las Vegas that seemed to

have this technique was Nick Van den Bergfrom Holland. I have not yet figured outany possible advantage for this stroke. Itseems to me that it doesn't get any more

power into the ball, since the motion of theupper arm drives the butt down rather thanforward toward the ball, and it would seemto be a disaster for consistency due to thetiming required to get an accurate hit on thecue ball.

Having noticed this anomaly in Nick's

technique, I was fascinated by an on-airinterview with Earl Strickland after hisfourth-day defeat of the Dutch player. Earlcertainly raised some hackles when he said

that his apparent easy win wasnot surprising against someonewho did not know how to play,that he would be surprised ifNick's game held up until hewas as old as Earl is now, andthat if Nick were required to"break from the box" (with thecue ball in the middle of thetable rather than against a siderail) he would probably breakhis hand. I wonder how many inthe audience understood thatEarl was referring to Nick'selbow. I think young Van denBerg would do well to try to getpast the put-down and under-stand Earl's point.

Finally, in Diagram 1 is anillustration of what the elbow isdoing on each of the four kinds

of strokes described above during the finalforward stroke. Along the horizontal axis isthe position of the cue tip; back at thebridge hand, at the cue ball, at the end ofthe follow-through. Along the vertical axisis the up-down motion of the elbow. Whichdo you like? Which is like you?

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Bob Jewett

Not So SimpleLook, Ma! No rails! Jewett plays a little "Run This Rack" of his own.

Everything should be made as simple aspossible, but not simpler.

— Albert Einstein

In last month's column, I urged you tokeep the mechanical part of your game assimple as possible, applying the KISSprinciple — Keep It Simple, Stupid. Manyendeavors are ruined by complication.

I had the pleasure of taking a few lessonsfrom the great player Jimmy Caras. Herecounted the times when he and BabeCranfield — another Hall-of-Famer-to-be— would watch Ralph Greenleaf play14.1. Cranfield had an uncanny knack forpredicting the order that Greenleaf wouldshoot the balls, rack after rack.

In his book "The Straight Pool Bible,"Cranfield reveals the secret to his clairvoy-ance: Greenleaf played every rack as sim-ply as possible. In the book, Cranfieldgives examples of how to simplify yourruns, but he also shows when you mightwant to add some flourishes for straight-pool strategy.

Another author who promotes simplicityis George Fels, inhis "AdvancedPool." Early inthe book, heintroduces nine"whenever possi-ble" principles,such as not usingEnglish, not hit-ting rails, notbumping balls, allwhenever possi-ble, or "WP."

In Diagram 1we have nearly abest-case situa-tion at the start ofa 9-ball game.Your opponenthas scratched,there is no bother-some cluster, andit looks like you can get through the rackwithout touching a cushion. Do you seehow?

There are several advantages of not usingthe cushions during your run. The main isthat the cushions can be surprising: sur-prisingly dead, strangely fast, remarkably

crooked, or sticky beyond belief. If younever visit them, they can't hurt you. Ahidden reason is that if you don't go to arail, there is almost never any reason to usesidespin. (If you're not already convincedthat sidespin has many traps to avoid,there's little I can do to help you.)

Cranfield revealedthe secret to his

clairvoyance: Greenleafplayed every rack assimply as possible.

When I'm playing in tournaments, if Iencounter a table as friendly as the one inDiagram 1, I'll go for the no-bumper solu-tion. Here's how I would approach thisparticular layout, along with alternativeshots.

With ball in hand, you have the luxury of

placing the cue ball at A, with a slight cutto the left on the 1 ball. For position on the2 ball, you want to get close to straight — inalong the dashed line through the 2. Manyplayers overlook the no-rail way, and placethe cue ball at B for the first shot, figuringto spin back from the cushion.

It's best to run slightly past straight — in onthe 2, so that you can stun over to D. Usingrails, you should leave yourself more angleon the 2, so you can go to the rail near Cand bounce over toward the 3. From D, themain objective is to get to the straight — inline on the 4. Note that D gives you a slightangle to get over to that line. If you don'tquite reach the 4-line, it's okay, since youcan draw over for a shot to pocket P withthe 5. If you do get a little past the line,which is best, you can stun the cue ballover to E, leaving a slight cut to the righton the 5. Now for the hardest shot of theseries. You have to play the right amount ofspeed and draw for the angle you've left tobring the cue ball to the line between C andD for the 6. Then, stun over for the 7.

If you get straight — in on the 7, just followforward past B fora draw shot on the8. Note that a farmore commonplay for the 7-8-9sequence, and onethat requires lessprecision withspeed control, isto go abouthalfway from the7 to B, for about ahalf-ball cut onthe 8 ball, with thecue ball comingoff F with a littleleft English tohelp it down to the9.

Similarly, if youend up with a shotfrom C for the 3

ball, you can spin off the cushion above theside with right English to run toward the 4.

Here is a drill you can try, which is amodification of Ron Shepard's "progres-sive 9-ball" drill. Put two balls on the tablerandomly, and see if you can run them inorder without touching a rail. (The harder

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Bob Jewett

form permits no cushion even after thefinal ball.) If you do two, try for three, thenfour, and so on. If you fail to run the tablewith the "use no rail" requirement,decrease the number of balls you're tryingfor. A good way to make sure you get arandom set of ball placements is to breakthe full rack and then remove the lowestballs to leave your current number.

In Diagram 2 is a typicalshot for position to get fromthe 1 to the 2. For the variouscue ball positions shown (Athrough D), which pathwould you use? (If you hadball in hand, I hope youwould be anxious to try theno-cushion option by puttingthe cue ball down by theshort rail.) For the positionsshown, I think A is the sim-plest shot. If you just let thecue ball roll after it strikesthe 1, it will bend forward alittle after the cushion fromthe natural follow, and takethe path along Al. If you usea little outside English, theball will come over to A2. Asthe cue ball gets closer to thecushion at B, C and D, the

one-cushion option becomes much harder,even though it remains the simplest way todo the shot. From C, or even B, many play-ers prefer to use either the follow path withright English, or the draw path with leftEnglish.

If you ever have shot D, you shouldn't bemad for not having perfected your draw-with-English stroke; you should be disap-

pointed that you didn't put the cue ball atA so the shot would be a simple roller.However, if you want your game to becomplete, you need to have all of theseshots in your repertoire.

Do you work to simplify your game? Ifyou need examples, I'll recommend younot study Efren Reyes, but instead checkout Buddy Hall's minimalist techniques.

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Bob Jewett

Short KicksLearn to use the mirror system to makes these shots less tricky.

When you have to play the cue ball tobank off one cushion to hit an object ballseveral feet from the rail, the most you cancount on is to hit the ball, or, with a littleluck, to hit the ball on the correct side. Withtremendous luck, you might actually pock-et the ball.

When the object ball is close to the cush-ion, your odds improve tremendously, tothe point where even beginners can counton making some short shots. With a littlemore experience, you can count on control-ling the cue ball after contact. Let's go oversome systems and practice techniques thatwill help you perfect this part of your game.

In Diagram 1 you'll find a typical situa-tion where the object ball is blocked from adirect shot, but is still eminently makeable.Shown is the path of the cue ball to theobject ball, along with several other cluesfor aiming the shot, including the locationsof the cue ball at the moment it contacts thecushion and when it hits the object ball.The cue ball at the instant it hits the objectball is referred to as the "ghost" or "phan-tom" ball.

In addition, the "mirrored" object ball andghost ball are shown. These are the posi-tions of the two balls as they would appearin a mirror that was held up near the cush-ion. Why is this mirror idea important?Ideally, the cue ball will "reflect" from thecushion making the same outbound angleas the inbound angle. This is the same waythat light behaves when reflecting off a mir-ror — the angle of incidence is equal to theangle of reflection. Let's not worry for nowabout the fact that cushions are not perfectreflectors; let's just see where this ideatakes us.

Also shown is the mirrored path of thecue ball, which is a straight-line extensionof its path into the cushion, and the mir-rored path of the object ball. It turns outthat the center of the mirrored pocket is,amazingly, in the same place as the centerof the real pocket: the center of a ball on thebrink of the pocket.

A major point to note is that the cue ballis not reflected from the nose of the cush-ion, as some authors imply. The ball is real-ly reflected at what I call the "rail groove,"which is the line half a ball from the nose ofthe cushion that often shows wear on oldcloth. It is where the center of the ball is

when it hits the cushion. Mike Hilden, amath professor at the University of Hawaii,recently pointed out to me that the onlygeometrically consistent way to diagram aball's path for cushion contacts and ball-ball contacts is to draw the path for the cen-ter of the ball. Think on this a while, ifyou're not convinced. If you remain uncon-vinced, you should look up Mike Shamos'BD article on accuracy in billiard diagrams.If you see a diagram with ball paths actual-ly touching the noses of the cushions,please realize that the diagram is inaccurateand misleading.

OK, philosophy mode off and practicalmode on. This means that you need to getto a table to study the shot carefully. Butfirst, you need to do a little preparation.Make a round target out of paper 2.25 inch-es in diameter. A small jar lid may be a suit-able template, or go to the the SanFrancisco Billiard Academy Web site

(www.sfbilliards.com), and in the "miscel-laneous files" section, you'll find a file ofball outlines that you can print out andmake targets from. The other item you'llneed is something to precisely position andre-position the object ball. I recommenddonut-shaped self-stick paper hole rein-forcements for binder paper, which you canget at any office supply store.

Place the 1 ball exactly a ball off the cush-ion, on its reinforcement. Place a target onthe cushion even with the 1 ball and alsoeven with the nose of the cushion, as in thediagram. Do you see why the target is thereflected object ball? If you want, alsoplace a second target, at the reflected ghost-ball position, so that you will have a directsight line for the cue ball. There is no rea-son yet to place the 2, 3 and 7 on the table;they just complicate things at the start.

Try the shot with just enough speed to getthe 1 ball to the pocket. If your setup is cor-rect, and your stroke true, you are almostcertain to hit the 1 ball too full, and it will

hit the long rail. The reason for this is thatwhen the cue ball is played softly along thecushion, the angle of reflection is closer tothe rail than expected, due to the follow onthe cue ball. Bud Harris, a former U.S.three-cushion champion, showed this to mea long time ago. Bud pointed out that theangle off the cushion is only about 70 per-cent of the angle expected, and this holdsfairly well for all kinds of side spin. That is,even with reverse side spin on the rollingcue ball, for a very shallow contact with thecushion, you still get about a 30 percentreduction in the outbound angle.

Well, how can we compensate for thisfact? The first is to play with a combinationof speed and spin that doesn't require anycompensation for the perfect mirror sys-tem. Ron Shepard has pointed out that ifthe cue ball has no draw or follow when ithits the rail, and just enough side spin toroll rather than rub one way or the other onthe nose of the cushion, then the minor ideahas the best chance to work for a largerange of shots. Try this sort of stroke, espe-cially with no follow or draw. (By this pointin your career, I hope you know that to getthe cue ball to arrive "dead ball" at any dis-tance, you need to start it with at least somedraw.)

Can you get the shot to work withShepard's "dead ball on the cushion" tech-nique? While it can be made to work, it'snot always the best way to play the shot forposition, and you are not always closeenough to the cushion to get stop action justas you hit the rail. Let's try to use Bud'sidea to modify the mirror system for soft,rolling hits. Clearly the target has to be far-ther from the nose of the cushion to landfarther out on the 1 ball. How much?Experiment. Since the target as shown isabout a ball and a half from the mirror (cen-ter of target cut-out to the rail groove dis-tance), try increasing that distance by abouta third, which when decreased by Bud's 70percent factor should be back to the rightpoint on the real object ball.

When you have the target in the rightposition for the shot shown and for a softlyrolling cue ball, try placing the cue ball indifferent locations to see if the same target— which we can call the "reflected ghostball with Harris' compensation" — is stillvalid. I think you will find that for nearly

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any rolling cue ball that comes in more orless along the cushion, your target will stillbe valid.

Now, let's try a different goal. Often youhave to hit a ball as in Diagram 1 withoutany intention of pocketing it, but ratherwith safety in mind. In the position shownfrom a game of 9-ball, it wouldbe a bad idea to pocket the 1ball with the 2 ball so infelici-tously disposed. A very effec-tive solution is to hit the 1 ballnearly full with nice soft draw— but not too hard — and tryto draw back onto the cluster.The 1 ball, if it has a lick ofsense, will scoot up the table toan inaccessible position.

Set up the target again, butthis time you need only thereflected 1 ball and not thereflected ghost ball. Try to aimfull at the target, and move thetarget closer to and farther from the cushionnose until you get a full hit on the 1 whenaiming at the reflected target. Is the targetat the ideal mirror position? Does it workfor different approach angles for the cueball? I'm not going to answer these ques-tions for you; you have to see how the sys-tem works on your table and for yourstroke. Maybe you will need to figure out a

"fiddle factor" like the one-third adjustmentmentioned above for Bud's observation.

In Diagram 2 is a common situation froma game of one-pocket in which you can usethis "reflected target" idea with great effec-tiveness. Your pocket is A, and your oppo-nent has a ball close to his pocket on the

short cushion. The idea is to play the cueball off the side cushion and knock the balltoward your pocket. The delicious secret toplaying this shot is that on many tables, thepocket iron provides a reflected target thatwill land the cue ball on the first ball-widthof the flat part of the end cushion. By this,I mean that the cue ball, when it hits the endcushion, will have its edge near the pocket

just even with the nose of the pocket. Tabledesigns differ, so you will have to experi-ment with exactly where the target is onyour table.

At straight pool, there is a two-cushion-first safety to brush the side of a full rackthat uses the same aiming idea. It was used

by Willie Mosconi, IrvingCrane and Eddie Kelly, buteven you can do the shot if youhave this aiming trick and a lit-tle control of spin and speed.

At one-pocket, the shotshould usually be played at aspeed that returns the cue ballto the head cushion for thesafety. More running Englishor more angle into the firstcushion will generally give theobject ball more speed. As withany shot, you need to practiceit before you need it. When youhave it down, it is easy to make

small changes, for example to hit an objectball that is farther from the pocket.

In a future column, I'll cover more shotsbased on the mirror idea and the requiredcorrections. If you have a favorite shot orsystem that is similarly based, please sendit in. My e-mail address is on the SFBAWeb site, or you can send it addressed tome in care of this magazine.

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More Aiming SystemsHere's how to separate the bogus from the brilliant.

In this column in June of 2000, I lookedat the defects of some common aiming sys-tems, Since then, quite a lot of new mater-ial has come into circulation, so it's time torevisit the topic. It's one of the most com-mon items discussed in the various Internetforums, since every beginner wants a wayto know where to point thecue stick.

There are a lot of bogusideas being passed off as aim-ing systems. It's clear that theproponents of such methodsand the students who seem tofind them useful are not capa-ble of the basic geometry thatreveals the flaws. You mightsay, "If it helps them, whypoint out that their beliefs are blasphe-my, geometrically speaking?" There isthe additional danger that, as with manybeliefs, if the believer thinks you're anon-believer, you may get a violentreaction for your meddling.

While some system-promoters toutfalsehoods, others have the irritatinghabit of ignoring systems that arealready in circulation. In the new litera-ture I surveyed, two different authorsdescribed as "new" a system that waspublished more than 25 years ago and maywell be much older than that. It's hard tobelieve an author who can't do basichomework.

On the other hand, I think any system,method or technique that puts aiming intosome kind of framework and provides away to categorize shots is useful, becauseit allows you to more easily relate the cur-rent shot to shots you've taken before.Most beginners just bang balls aroundwithout the benefit of a method that wouldallow such connections to be built up.

So, if you are going to try to adopt a sug-gestion for improving your aim, first mea-sure its bogosity by looking at the geome-try involved. If it passes, remember thatyou have to practice with it for a long timeand under many conditions before you canreally rely on it. Further, you have to beprepared to be flexible; if, on a particularday or table, the system has you drivingballs into rails rather than pockets, you willhave to modify the system or abandon it.

One of the most interesting new publica-

tions I've seen on aiming is a book called"The Secret of Aiming," self-published byRandy Lee Kukla (P.O. Box 108,Essexville, MI 48732). The main point isto give the shooter specific targets to aimat. Half-ball is an obvious one. A littlemore nebulous is the point where the base

of the ball joins its shadow. I suppose: youneed to practice this with a certain intensi-ty of light on the table.

(I hope you are already thoroughly famil-iar with the fractional ball description ofthe fullness of hits/cuts, such as "half-ball." If not, see any of manypool and billiard books thatcover it, or see page 20 ofthe Basic Clinics Handouton the Web site www.sfbil-liards.com.)

With the full, half-full andthree-quarters-full aimingpoints established, fourmore are set by spotshalfway between those. Sofar, all of the aiming pointsare within the span of thecue ball. Two more areadded by imagining wherethe side of the ferrule is pointed and mak-ing the projected ferrule just touch the out-side of the object ball. That is, if the cueball vanished as you stroked straight for-

ward, the ferrule would just graze the edgeof the object ball, as shown in Diagram 1.A last target is added by having the ferrulemiss the cue ball by "a little bit." Theangles not yet covered on the face of thecue ball are filled in by adding other "littlebits" to the previous aiming targets.

As a practicing geometer,I'm not entirely comfort-able with these construc-tions, but I can see how thenon-geometers among usmight take to them.Personally, I'd like to see atable of targets and angles.Kukla does provide a tableof ball positions and theappropriate target to use.

Kukla mostly leaves uncovered cutangles that require the stick to bepointed outside the object ball. Hedoes offer the thin-cut system shownin Diagram 2. His description may bethe first appearance in print of thissystem, although it was independent-ly discovered and discussed on theInternet discussion forumnews:rec.sport.billiard, and I dis-cussed it here briefly in November1999.

In the diagram, you have a thin cut shoton the ball, and the shot is shown from thetip's-eye view. Note the contact point. Ifyou are trying the shot, use the 1 ball, andturn the numeral so it is vertical and at thecontact point. If you imagine the cue ball

and the object ball as twoequal circles or discs, andthe act of shooting as pro-jecting the cue ball's circleonto that of the object ball,there will be a lens-shapedoverlap that is thinneraccording to the thinness ofthe cut.

The amazing result is thatthe contact point is at thecenter of this lens-shapedarea. Another way to saythe same thing is that iffrom your aiming position,

you see the edge of the object ball stickingout to the side of the contact point by a lit-tle bit, you have to aim so the edge of thecue ball is going that same little bit to the

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other side of the contact point.This thin overlap aiming system is geo-

metrically equivalent to the ghost ball sys-tem, which is the golden standard for sys-tems, if you include the effects of throw. Intheory, it works even for full hits,but usually it's harder to aim withthe edge of the cue ball when it islined up so far from the contactpoint.

Another new vision of how toaim has been developed by RonVitello of New York. I had thepleasure of discussing his methodswith him for most of a day when Ivisited Santa Barbara, Calif.,where he was giving a clinic. Hehas developed a workbook pro-fusely illustrated with pictures ofshot alignments. Diagram 3 is anexample. This shows another wayto use the ferrule to aim. In thiscase, the projection of the stickforward, which is what the pictureshows, has the side of the ferrule againtouching the edge of the object ball, butnow the ferrule is inside the object ball.

Note also that the picture shows reflec-tions of lights visible on the object ball.Vitello goes over situations in which thosereflections — whether on the cue ball orobject ball — can be used for alignment.

Frankly, I thought such "lights on theballs" systems were totally useless untilRon forced me to really think about thegeometry. A warning: The reflections arenot useful on all shots.

Here is a simple example of how to usethe reflections of a light to help you findthe centers of the object and cue balls.

This is especially useful for players withvision problems who cannot accurately seewhere the center of the cue ball is. Yes,there are a lot of such players, and a symp-tom of their malady is frequent unintendedsidespin.

Find an elevated light easily visible fromthe table. Where I play, there are some tall

windows that are bright during the day.You may have a beer sign or some suchavailable — the light over an adjoiningtable may be too low. Standing by a pock-et, line up the object ball and the cue ballso they are straight towards the light, asshown in Diagram 4.

Now, when you are down on the shot, thepocket, the object ball, the cueball, your stick, and the lightshould all be in a straight line. Youshould be able to see the reflectionof the light on both the cue balland object ball. Because of thesymmetry of the situation, thespots will be very accurately in thecenters of the balls, and any mis-alignment, especially of the stickon the cue ball, will be immediate-ly apparent.

Vitello hasn't published hisworkbook, since it is intendedonly to be used in a hands-on clin-ic, but you can contact him at

[email protected]. Finally, a new bookby Gerry Kanov and Shari Stauch, "PoolPlayer's Edge," has a fairly detailed sectionon various things you can fiddle with toimprove your aiming. I especially like theirfinal item for players with a lot of experi-ence, which is to give up systems and relyon your feel for angles.

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Long KicksAll you'll need for this handy system is a bar stool.

In my May column, I covered some tech-niques for aiming short kick shots, wherethe object ball must be struck after the cueball goes to a cushion, but the distance isshort and the shot is fairly easy. The twomain points to recall are that the mirror-system target is reflected at the rail grooveand that for shallow shots with follow, theball lengthens by about 30 percent regard-less of any running or reverse side spin.

This time the shots are tougher — or atleast longer.

Shown in the right half of Diagram 1 isan ideal case where the object ball is hang-ing in the jaws of a pocket.All you have to do is findwhere on the cushion to hit,and the shot is easy. If thecushion works like a mirror— the angle of incidence isequal to the angle of reflec-tion — the following sys-tem gives the perfectanswer.

Also shown are two propsto help you calculate theangle. Place a "mirroringball" in the jaws of theopposite corner pocket. Ingeneral, it needs to betouching the cushion thecue ball will bank from,and as close to the targetball as possible.(Technically, if you drop aperpendicular from the object ball to themirroring cushion, the mirroring ball willbe at the base of that perpendicular. Notethat for the example shown, the ball isplaced where it would touch the side cush-ion if the cushion were longer.)

Now, you will need a bar stool and one ofthe round paper targets you prepared inMay. If you've lost the targets, use a sodapop can or an object ball, but those are lesslikely to stay on the bar stool. Place themirrored target so it is exactly in line withthe other two balls and so the two distancesare equal, ball-to-ball-to-ball.

Now, no matter where the cue ball is, ifyou are going to bank off the side cushionto sink the object ball, the mirrored targetball gives you the exact target — if the mir-ror system works for kicks. Try it from var-ious angles and at various speeds before

you continue with the rest of this column.Unless you have an amazing stroke and a

strange table, the system did not work formost of your shots. For the angle shown, atslow speed, follow will bend the cue ballafter it leaves the cushion and it will hit atA. Shoot harder or with draw, and the cueball ends at B. You probably found thatwhen the cue ball was near the head cush-ion, the system worked tolerably well, butup there it is easy enough to just guesstimatethe angle.

The problem is that the rail is not a mir-ror. To solve the problem, let's see what it

takes to make it work likeone. This "make it like amirror" system is based on asuggestion by Ron Shepard.

The first thing to note is thatany follow or draw on the cueball when it hits the cushion willmake it curve as it leaves the cush-ion. This bending is easy to see onnew cloth (or with a waxed cue ball),because the slippery cloth lets the actiontake longer in time and over a longer dis-tance. So, shoot the equivalent of a stopshot at the cushion. To see what angle thisgets us to, move the cue ball close to therail and hit the ball right in the center. Youcould shoot from farther back, but then youwould have to judge how much draw to useto have no spin at the rail.

Does angle in now equal angle out?

Probably not, because there is one otherfactor, and that's the cushion rubbing sidespin onto the ball. This will tend to makethe cue ball "go short" and hit at point B.So, we need to apply a final correction, andthat's to put just enough running English onthe ball so that it rolls on the cushion ratherthan rub in either direction. How much sidespin? That's for you to determine withpractice, although Shepard has worked outa formula for it. Fortunately, if you have thebar stool set up with your target, you don'thave to count diamonds with each cue ballposition. Just pick a spot for the cue ball,

and aim at the mirroredtarget. In theory, youshould be able to play theshot at any speed and geta perfect reflection withthis method, once you getthe spin perfected.

In the left half ofDiagram 1 are two shorterkicks using the same cueball but a different objectball (OB2). For each ofthe two cushions thatmight be used, the mirror-ing ball and the mirroredtarget are shown. See ifyou can get a full hit fromeach rail.

In Diagram 2 is anextension to a two-cush-ion kick. Again, we'regoing to assume that therails are perfect and seewhere it leads us. Theproblem is to play the cueball off the end and siderails to get to the objectball. To construct the mir-rored target, place themirroring ball in the cor-

ner where the two banking cushions meet,and then place the target on the straight linethat goes out from the object ball throughthe mirroring ball. Make sure that the twodistances are again equal.

This time, you should use a paper rein-forcement to mark the position of the objectball, so you don't have to remeasure for themirrored target each time.

Can you find a stroke that's most consis-tent over a wide range of angles? Trying to

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apply the idea of "stun shot, roll on thenose" from above is not practical, since weare unlikely to get the perfect spin on bothcushions. I think you'll find that for manycue ball positions,follow and runningside give fairly con-sistent results. Thespin will tend tomake the cue ball hitnear A on the secondcushion, but thesame spin will bringthe cue ball out tothe object ball.Perhaps better is tohave the cue ballarrive at the cushionwith no follow ordraw, but plenty ofside. See what worksbest for you on yourtable.

Also illustrated is a system that gives thesame aiming line but doesn't require a barstool next to the table. To go two cushionsout of the corner to the object ball, first finda point that is half-way between the balls.I've marked that with the "mid-point" ball.Now sight from that point through the mid-dle of the pocket in that corner to a distanttarget. Ideally, the target should be infinite-

ly far away, but 20 feet beyond the tableshould do. Just shoot to the target with thespin you have found that works. Do you seefrom the diagram why that target will give

you close to the same aiming line? Do yousee why a target too near will give thewrong line?

There are two ways to compensate for notplaying in a large enough room to make theangle right. First, you can find the line fromthe mid-point ball to the corner and thenjust shoot parallel to that line. I have a lot oftrouble with this method because my stick

seems never to come over parallel to theoriginal line. I guess it's an optical illusionfor me, but I tend to turn the stick towardthe corner. A second way is to find a rela-

tively near target along the "fartarget" line, and then take a newtarget the same distance to the sideas the cue ball is from the mid-point ball. For example, inDiagram 2, the cue ball line isabout a foot to the left of the mid-point ball. Find your "not so far"target, say the left side of A near-by table. Now take a point, per-

haps in the air, a foot to the leftof that target. A line from

the cue ball to thatnew "offset"

target willbe in thec o r r e c tdirection.

If you'rehaving trou-ble kickingout of

safeties, try these systems. Of course thereare lots of others, and there are many waysto calculate the ideal reflecting line, butthese are easy to use and experiment withand perfect once you have your mirroredtarget set up.

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Shortening BanksBob Jewett wipes the egg off his face.

In my July 2003 column, I covered sever-al loose ends and indicted some commonmyths. I proposed some experiments foryou to try if you happened to still believe inany of the myths. This month I'll report onmy own results from one of those experi-ments — results that were surprising.

The trek from my comfortable armchairto a table was precipitated by the ratherprominent repetition of the myth in ques-tion right here inthese pages. As Clickand Clack, the Tappetbrothers would say, Ihope to distancemyself from that arti-cle.

So, the question tobe answered is: Doesmore speed on a bankshot shorten it, and ifso, under what condi-tions? (Rememberthat a ball is said tobounce "shorter" offa cushion if it comesstraighter off thecushion and "longer"if it goes more paral-lel to the cushion.)

The previous experiments that I had donewere fairly rudimentary, and since thereseemed to be knowledgeable playersweighing in on the side of the myth, I feltthat more care and completeness was calledfor. Many casual experimenters — some-times including me —• will take a couple ofquick shots and be satisfied with thehypothesis. Not this time.

The main problem with testing bank shotsis the difficulty of repeating the shot withsufficient accuracy so that you vary onlythe parts of the shot you want to vary. If youjust shoot a bank shot in a couple of differ-ent ways, it is too easy to subconsciouslyadd a little English or take off a little speedor change the cut a little to get the resultyou expect.

The typical setup is shown in Diagram 1.A line of three object balls is set up alongthe bank angle to be tested. For this experi-ment, that angle was about 40 degrees fromthe cushion. To make sure that the ballswere aligned the same way each time, analuminum L-beam was placed on the table,

and the location of its ends were marked onthe cloth. Then the three balls were placedagainst the beam and moved up to anothermark on the cloth which set the amount oftravel of the banking ball to the cushion.The balls were separated from each otherby a small amount to prevent the possibili-ty of any funny interaction as you some-times see among clusters of frozen balls.The beam was removed, and a cue ball was

shot directly into the combo with no spin.For the position shown, I measured the

landing spot on the second cushion of thebanked ball for two speeds: soft, which isjust hard enough to bank off the secondrail; and hard, with speed at the high end ofnormal bank shots — maybe 12 MPH. Tomeasure the landing spot, I placed anotherobject ball at the expected arrival point, andrepeated the shot until the banked ball con-sistently arrived for a full hit on the extraball. From the distances on the table, it's asimple matter of trigonometry to figure outthe angles into and out of the first rail.

Once I had measured the angles with theballs starting back some distance from thecushion, I moved them up near the cushionbut not quite touching it, and measured theangles again for hard- and soft-speed shots.Balls for this part of the experiment need tobe fairly close to the cushion, because anyfollow the ball picks up on its travel to therail may have some influence on the angleoff the cushion. The reason to leave a smallgap between the banking ball and the cush-

ion is so the banking ball will be free fromthe ball that hits it in the combination, andthere can be no "funny business" while theball is actually on the cushion.

Similarly, the bank angle is less than 45degrees because that's the angle at whichyou start to risk a double kiss for a combi-nation frozen on the rail. (In a recent col-umn, Willie Jopling showed how not to kissfor a 60-degree angle in a proposition

frozen combo bankshot, but the cueball is not shotalong the line of thecombo.) The objectball will sink intothe cushion for fastshots and tend toavoid the kiss, butfor softer shots, youdon't have as muchmargin on the kiss,so keep the angleunder 45 degrees.

Once I had mea-sured for fast andslow shots with longand short distancesto the rail, I waxedthe banking ball and

remeasured the angles. This is like playingon new cloth without the cost of actuallychanging the cloth. The wax makes theball-cloth friction lower.

Once I had measured all eight cases onthe pool table, I tried the same experimenton a five-by-10-foot carom table and thenon a six-by-12-foot snooker table, giving24 cases in all.

The pool table was a Gold Crown III withmoderately worn Simonis 860 cloth oncushions that had been recently replaced. Ithink it's fair to say this is representative ofthe better tables most players willencounter. Shown in Diagram 2A are theresults for a normal ball compared with theideal perfect reflection angle of 39.4degrees. The five arrows coming out fromthe cushion are the ideal angle and the fourcases of near/far fast/slow. Diagram 2Bshows waxed-ball results.

For each of the two kinds of balls (waxedand unwaxed) only one of the angles reallystands out. That is the soft shot from a dis-tance. It is about 14 degrees "longer" (more

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along the rail) than the other bank anglesfor the normal ball and about 15 degreeslonger for the waxed ball.

There is only a small separationbetween the three other bank angles(slow and near, fast and near, fast andfar) for both the waxed and normal balls.In fact, in Diagram 2, it's hard to tellthem apart. The conclusion is that thebank angle is nearly constant except ifthe ball is allowed to acquire roll beforeit gets to the cushion. Looking moreclosely at the results, it turns out that forthe unwaxed ball starting close to thecushion, the hard shot banks 0.9 degreesshorter than the soft shot. That's about aninch difference in the distance across thetable. However, for the waxed balls, theharder shot actually banked longer by 0.3degrees, exactly contrary to the myth. InDiagram 3, I've put together a table show-ing the numerical results. The shots that arerepresented by larger angles are "shorter,"smaller number mean "longer" reboundangles.

On the carom table, the results were sim-ilar with the three angles clustered closetogether, but for both the normal and waxedballs near the cushion, the hard shot bankedabout 2 degrees shorter than the soft shot.While this is in the direction of the myth, itis a very small effect compared to the 15

degrees you pick up from letting the ballroll with follow into the cushion.

The largest surprise for me was what hap-pened on the snooker table. This was aBritish-style six-by-12-foot table by BCE,with napped cloth and L-profile cushions.Follow on the banking ball caused about as

much lengthening as on the othertables, but for the close ball, shootingsoftly shortened the shot by 3 to 4degrees. This is directly contrary to themyth, and is a very significant changein angle, amounting to nearly three balldiameters in where the ball lands on thesecond cushion for this angle and table.

One explanation for this large changewith speed on the snooker table is thatthe L-profile cushion is thinner than theK66 profile on the pool table. If therubber is compressed so far on a hardshot that it loses its rebound, the speedcoming off the cushion will be reduced,

while the speed along the cushion will notchange as much. This will lead to a longerangle off the rail. Of course, until moreexact measurements are made, perhapswith high-speed cameras and accelerome-ters, this explanation is just speculation.

My conclusion from this experiment isthat on bank shots, speed changes the anglemostly by changing how much follow is puton the banking ball — if the ball is slidinginto the cushion, speed changes the angleonly slightly. Furthermore, with new (ormaybe slippery) cloth, you might see theopposite effect, in which a harder bank shotactually goes longer than a soft shot. WithL-profile rubber, the lengthening of hardshots is very significant.

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Short BanksSink 'em with this target-point system.

In my last article, I showed some resultsfrom an experiment that studied how speedcauses banked balls to go "shorter," or moreperpendicular to the cushion they strike. Amajor point to note from the measurementsis that the banking angle for a ball withoutspin was nearly independent of speed. Thissuggests the following system.

In the ideal mirror banking system, one ofthe very useful and amaz-ing features is that thereflected pocket is alwaysin the same place. If youhave set up a marker at thatplace — which is out inspace — you are notrequired to count diamondsor construct crossingisosceles parallelograms ordrop mutually orthogonalperpendiculars. You justshoot toward the target.

The problem with theideal mirror system is thatit usually doesn't work. Asshown by the measure-ments last month, the actu-al angle is usually eithermore or less than the idealreflection angle, dependingon the shot's roll and dis-tance from the cushion.

Now suppose that there isa similar target for banksfor sliding balls. If such atarget existed, it would have all the benefitsof the mirror target with the added bigadvantage of working for a large class ofshots. Where might such a target be? Howcould we find it?

In Diagram 1 is an outline of how to findthe target, if it exists. Shown are three shots— A, B and C — all to the side pocket. Theaiming lines are extended off the table, andthey are shown all meeting in a point, moreor less. This suggests a way of finding thatpoint: just shoot bank shots from theselocations until you find the correct aimingline for each starting position. Then drawthe lines, maybe by placing cue sticks onbar stools, and see where they intersect.

There is a faster way if you use a trick.Imagine that the side pocket P is not thereon the first rail, so that if the object ballwere on the centerline C/L, you would bank

it straight back along the centerline. Thismeans that if the magic point exists, it is onthe centerline. Now you only have to findthe aiming line for one shot, for example A,to find the target point for all the cross-sidebanks.

When shooting the shots, it's important toremember that the object ball must be slid-ing when it hits the cushion. If the ball

starts very close to the cushion, the speed isnot important, but if the ball starts fartheraway from the cushion, say two diamonds,you have to use enough speed to make surethat the ball doesn't pick up much followbefore it hits the rail.

If you do use the fast one-shot method offinding the target point, it's important totest the point with the other shots. Note thatthe bank shots from the other half of thetable, such as AA, have the same targetpoint. Everything is nicely symmetrical.

The target point can be given by a singledistance: how far the target is from the noseof the banking cushion, shown as X inDiagram 1. On the two 4.5- by 9-foot tablesI tested, that distance is close to 35.5 inch-es. This is just a little less than three dia-monds and close to 70 percent of the widthof the table. And on the tested tables, there

is a single target point for all cross-sidebanks.

If you are familiar with "spot on the wall"systems, this is similar. The big differenceis that the spot for this system is at a pre-cise, fixed location close to the table. I'veseen an instructor try to use a spot on thewall for this kind of bank that was 10 feetback from the table. While that might work

for a couple of shots thatare close to the correctline to that far point, it isguaranteed to fail formost cross-side banks.The main point to learnhere is that not all systemconcepts apply to all situ-ations, and a deeperunderstanding is oftenneeded to see the limita-tions and extensions of asystem or concept.

Because any systemrequires practice before itcan be added to yourarsenal, here are somedrills. At first, shoot theshots with the target on abar stool at the correctdistance for your tablethat you found earlier. Fora variety of shots close tothe cushion, like the onesshown, see how manyyou can make in a row,

starting close to the side pocket. As we willsee below, you need to be very carefulabout keeping sidespin off the cue ball, hit-ting straight along the aiming line, andmaking sure that the object ball is slidingwhen it hits the cushion.

Next, try banking without the target pre-sent. You can find the line by using yourcue stick. For my stick, if I place the tipagainst the side-pocket iron pointed straightat the side pocket I'm banking to, the butt-side of the joint is exactly the right distanceout in space. Looking back at the cue andobject ball, I can get a feeling for the line ofthe bank.

In Diagram 2 are some extensions of thesystem. You will still need the target on thebar stool for the setups. In Shot 1, the ideais that the angle is off for the simple bank,and you need to do something special to

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move the angle back to the side pocket. Asshown, the normal angle would go wide ofthe side pocket, and just cutting the ball tothe right is dangerous because of the kiss. Alittle "hold up" English, in this case left,will change the angle back in two ways.First, throw will move the object ball to theright, but more signifi-cantly, the spin transferredto the object ball will takeon the cushion and bringthe ball off straighter.

Try Shot 1 with theangle set up wrong in bothdirections, and see howmuch you can correct theangle with sidespin.Alternatively, place thetwo balls lined up straighttoward the target, and seehow far to either side ofthe pocket you can takethe object ball but stillhave a full hit on it.

Another kind of throwon bank shots is shown inShot 2. First, set up the two object ballsstraight toward the target, and place the cueball at A, also on that line. Hit the shotstraight-on and firmly to make sure thebank goes into the side. Now set the ballsup again in precisely the same spots. If you

used donut-shaped reinforcements before,this will be easy. Shoot from B directly atthe front object ball. Where does the secondball bank to? Try the same shot from C.What I think you will observe is that a shotfrom B will bank short (landing on yourside of the side pocket), while a shot from

C will bank long. I think you'll be surprisedby the size of the effect.

In Shot 3 is an extension of the system forcross-corner shots. Do you see immediate-ly where the target should be to get to pock-et P?

A final extension is Shot 4 to pocket R. Ididn't have particularly good luck with thisone, probably because the shot is muchharder, but a first guess for the location ofthe target is 70 percent of the length of thetable away and along the line of the sidecushion.

This system is so simpleand so much more accu-rate than the standard mir-ror system that I would besurprised if it hadn't beendiscovered before, so Iwill hold off on claimingits invention.

On another note of dis-covery, it turns out that the"lens-shaped overlap"aiming system that I cred-ited to Randy Kukla in myJune column had been pre-viously described in thesevery pages by RobertByrne in December 1989,at which time he gavecredit to Paul Hahn, who

had sent it to him. That column is availablein Byrne's "Wonderful World of Pool andBilliards." My oversight would have beenless embarrassing if I hadn't chided aim-ing-system authors for not doing theirhomework.

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Useful StrokesAdd these to your arsenal.

H o w m a n y different shots do youknow? Technically, even a simple straight-in shot has an infinite number of variationsif you include speed and spin, but psycho-logically I think the number is much small-er. It seems to be a natural human tenden-cy to categorize similar things and putthem into pigeonholes. When I wasstarting to learn to play, I had namesfor shots like "a little off straight in"and "a little backwards cut" and"real thin near the pocket" and"pretty close to a spot shot."

Putting shots into named groupshelps the player to recognize theshots when they come up and toremember how to play them. Atfirst, you may have only a few"plays," but with more experienceyou might add such techniques as"thud the cue ball sideways," "runaround the corner with spin and fol-low," "slow kill on the rail," "softdraw for no scratch," and "impossi-ble cut."

Authors often mirror this naturallearning method by giving us lists ofshots we should know. The mostrecent is Robert Byrne's "CompleteBook of Pool Shots," with 350items. Twenty-seven years ago, RayMartin wrote "The 99 Critical Shotsin Pool," and 63 years ago WillieHoppe gave us "Billiards As ItShould Be Played," which includedseveral dozen "key shots," as Hoppecalled them, as easy examples ofclasses of shots to try. Some authorsgo on to link multiple "plays"together to solve whole-table prob-lems (like the new "Run This Rack"feature on page 22), but for nowlet's just consider individual shots.

A century ago, prolific British bil-liard author Wallace Ritchie wrote abook called "Useful Strokes forBilliard Players." He thought that 50shots would be sufficient for the purpose ofinstructing most players. In his introduc-tion, after lamenting that only 1 percent ofthe players of his time had ever read a bookon billiards, he stated his hope for his listof shots:

"For the remaining 99 per cent, theoreti-cal dissertations on their favourite pastime

have no attraction whatever; but while thisis perfectly true I can say unhesitatinglythat in all my long experience I have nevermet a solitary player who was not alwaysdeeply enough interested in having anyspecially useful stroke explained to him. Ithas occurred to me, therefore, that a col-

lection of such useful strokes, with a clearthough by no means deeply theoreticaldescription of how they are to be made,will be welcomed by a very large propor-tion of those hundreds of thousands ofplayers who do not appreciate the study ofthe more intricate treatises on the game."

Keep it short, keep it simple, keep their

attention and get their money. A good ideastill.

Diagram 1 is from his book, and showsone of his shots that you may have seenbefore. In the game Ritchie is describing,it's good to scratch, so the not-so-obviousplay is to hit the black ball full, which

clears out the other ball, and allowsthe cue ball to follow forward intothe pocket. Such clearance shots arestandard these days for trick-shotshooters, and can be useful at 9-ball— imagine the 9 is by the sidepocket — or for safety play —imagine that the cue ball will followthrough to a spot where your oppo-nent will be very uncomfortable.

(A brief aside: You may havenoticed that Ritchie's balls are toobig to fit into the corner pockets.The pockets are drawn the correctsize for a 6-by-12 table, but the ballshave been magnified to allow thereader to better see how full the shotis and what side spin is used. Amuch better way to do this is seen inEddie Robin's books, where a mag-nified inset shows tip placement,elevation and fullness of hit.)

In the case of this clearance shot,the problem during play is often justto recognize the possibility to playit. If you have "two ball clearancewith a full hit and follow" in yourrepertoire, maybe you'll rememberit the next time it comes up beforeyou settle for something worse. Or,that notion might even trigger anextension with the cue ball follow-ing at a slight angle and with spin tocome off the cushion to a reallynasty safety position.

Not all of Ritchie's shots are souseful. In his day, it was OK to jumpover a ball by scooping under thecue ball. He recommends againstthe standard suggestion of that time

to elevate the butt and "aim at the cloth aninch in front of the ball," and instead pro-poses to lay the stick flat on the table andjust slide it along under the cue ball. Well,maybe the shot is useful. Suppose youneed to play safe at one-pocket and theonly shot available is to jump softly topocket a hanger in your opponent's pocket.

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Is there any rule to keep you from usingRitchie's method, given that you are readyto take a foul for strategic purposes?Should there be such a rule?

One piece of his advice I do object to ishis bogus recommendation, still parrotedby modern authors who should know bet-ter, to pocket an object ball frozen on thecushion by hitting the ball and cushionsimultaneously. If that idea is in your ownpersonal list of shots, erase it immediately!

A very useful shot — sometimes I over-look it myself — is the kiss-back. Whenthe object ball is on the cushion, can youcontrol where the cue ball will kiss to ifyou hit it full enough for a double kiss?Ritchie shows several variations, includingstraight back, nearly straight back, and 45-degree angles. I think this shot is worth tenminutes of your next practice session. Seeif side spin changes the result.

For draw shots, he shows about threekinds: right-angle draw for a half-ball hit,straight back draw for a completely full hit,and something in between. I suppose youdon't want to clutter up a beginner's brainwith complications, or as Ritchie might putit "theoretical dissertations," but there is ageneral system to find the cue ball anglefor draw shots, and once the system isunderstood, all draw shots fit into a singlecategory. That system is shown in

Diagram 2.Look at the shot along the path of the

object ball, for example to the pocket,directly in the line of the object ball and

the ghost ball (cue ball at instant of con-tact). The cue ball starts out from some dis-tance "X" to one side of that line. It willdraw back somewhere to the other side ofthat line. The splendidly simple system isthat it will come back twice as far to theother side of that line, shown as "2X" inthe diagram. For nearly full shots, thismeans that the angle the cue ball is deflect-ed to the side from its original path is threetimes the cut angle of the object ball, andsometimes angles are easier to think aboutthan distances. But this "X/2X" systemworks for all fullnesses of hit, providedthat you have lively draw on the cue ball. Ifyou only have middling draw for the speedof the shot, the number 2 is bigger. Howmuch bigger is up to your stroke.

Is this universal system better than know-ing three — or four or six — different drawshots? Being a geometrical sort of person,I think it is. For Richie's hypotheticalantitheoretical player, who may berepulsed by even the simplest analysis,maybe it isn't. Which way of organizingyour shot concepts do you prefer?

If you like to think in systems rather thanunique shots, go back to your double-kiss-back practice and see if you can come upwith some sort of rule that governs a widerange of angles. If you do, let me know andI'll present it in a future column.

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Stroke StraighteningWould it do you good to iron out your swing?

Is it good to have a straight stroke? By"straight," I mean that the back of the stickmay go up and down some, but there is nomovement side-to-side.

There are lots of great players to point outas contrary examples. Old-time caromplayers were particularly flamboyant.Willie Hoppe had a side-arm stroke fromlearning to play when small, and BillHawkins, who held the U.S. high-runrecord for years, swerved to the outside onevery side-spin shot.

But if you look at most of today's topplayers at carom, pool, and espe-cially snooker, you will see sticksconfined to a very narrow, verticalplane during the final forwardstroke.

How is your stroke? It is not soeasy for a player to tell on his own.For many years, I had a very pro-nounced and unintended left-to-right swerve in my stroke. I sus-pect it developed because I had mydominant eye in the wrong place,so I simply did not see the centerof the ball correctly — by up to awhole tip. Through long hours ofpractice, my arm learned to get thetip to the center of the ball whenneeded, even though I had noawareness that my arm had taken over con-trol of the stroke.

The most standard practice to test yourstroke is the "over the spots" drill. Place thecue ball on the head spot, and shoot overthe foot spot, hoping to return the cue ballto your tip. Here are some variations on thisold standby to make it more effective.

Use a striped ball as the cue ball. Place itso that the stripe will roll like a tire withcolored tread and a white hub. If you putany sidespin on the shot, it will be immedi-ately obvious as a wobble in the stripe. Usea dark color, so that you can see where thetip hit the ball — there will be a small chalkspot on the ball. The special cue ball thatcomes with the Elephant Practice Balls setholds this mark better because it is madefrom a more porous material than high-quality object balls. (It also has a bull's-eyefor centering.)

The stripe also allows you to see whetheryour tip is centered on the "cue" ball. Ifyour set is the kind that has the "eye" for

the number in the stripe, turn that towardyou so that your tip is centered on the eye.

Instead of watching the ball or the farcushion when you shoot, try watching yourferrule. Does it come straight back and fol-low straight through? To help with this, youcan use self-stick paper hole reinforce-ments. Place one for the ball to start in, andplace a second straight up the table at thelength of your normal follow-through. Ifyour stroke is straight, the tip should endcentered on the farther white donut.

If you can make the ball return to your tip

The StrokeTrainer's aim is a perfect pendulum swing.

for a shot just hard enough to get back (sixdiamonds up and six diamonds back),crank up the speed. Can you make the cueball hit the center of the far cushion twice?Can you make it hit the center of the cush-ion you are standing by twice? Even as youincrease the speed, monitor the stripe wob-ble and/or the finish by the donuts.

Once you are satisfied that you are hittingthe cue ball in the center even at pretty highspeeds, here is a final test that's deceptive-ly difficult: Play the shot just hard enoughto get back to your tip, but play it with yourbest (lowest) draw. Do you know why it isso much harder to get the cue ball to comestraight back with this shot? Think on it fora while.

There are some other easy drills for strokemeasuring and straightening. Just practicestroking with the stick up on the rail, align-ing the cue with the line between the railcloth and the rail cap. (Or, you could drawa line on the table or use tape, as Bob Byrnesuggests in his "Power Pool Workout"

video.) The eye picks up small side-to-sidemovements fairly easily in this setup. Oryou could use lined note paper — lots oflines parallel to the direction you want thestick to move.

If you set up a shot so that the stick pass-es over the rail and your hand almost reach-es the rail at the end of the follow-through,you can put a piece of chalk on the cushionon each side of the stick with just a littleclearance at the end of the stroke. If thechalk moves, your stroke is crooked. Out inthe open table, tubes on end — empty toi-

let paper rolls? — could definelimits for your stroke.

I think the stroke drills thatallow you to actually shoot ashot and make a ball are themost useful. Being able tostroke the stick in a perfectlystraight line on your diningroom table does you littlegood if your arm (like mine)takes over control when it'stime to put a real ball in a realpocket for glory and honorand maybe a little real cash. Ithink your practice has to beas close as possible to the finalcompetitive situation for thatpractice to hold up under pres-

sure. Which of the above suggestions canbe cast into a game-like setting?

One of the problems with all of the drillsabove is that they don't provide much feed-back during the stroke itself. There is a newproduct on the market called theStrokeTrainer, shown in the photo here, thattries to fix this. It has two major parts. Avertical board is positioned where your griphand swings. This gives you immediatefeedback: Your hand moves away from orruns into the board if your hand wobbles orswerves side-to-side. The second part con-sists of two vertical rods which form a nar-row goal for your shaft to pass through.This gives you mostly visual feedback onthe front end. The construction is quitesolid, which means that it will stay in posi-tion well in spite of your hand bumpinginto it, but repositioning is more effort.

Note that since the front-end alignment isset by vertical rods, your stroke is allowedto be like a pendulum rather than like a pis-ton. (See my March 2004 column for why

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you might refer to the latter as a "Jonesstroke.") If you really wanted to do the pis-ton thing, the rods should be replaced by aring.

Is it worth the cost? There have beenunsolicited testimonials by long-timecrooked-stroke sufferers who swear by itshealing powers. It's clear to me that forsome players it's a major help. While it'ssimple enough that you could build oneyourself, some of us tend to produce nomore than sawdust when we get near powertools. I think the best customers for theStrokeTrainer are instructors and poolhalls, where many end-users can effective-ly share the cost.

As an engineer, it's hard for me not tomake suggestions when I see a new techno-toy. While the hand is prevented from mov-ing to one side or the other by the singlevertical board, why not have boards oneach side? Maybe bumping knuckles orfriction would be a problem, but a lightglove or padded sides might fix that. I thinkthe additional restriction might also reduceany tendency toward rotating the stick dur-ing the shot.

I saw a higher-tech version of theStrokeTrainer about 10 years ago when Ivisited Terry Baker, who did some of thetechnical drawings for Eddie Robin'sinstructional books. He had built a "cue on

tracks" which allowed the stick to moveonly in a straight line. The construction pre-vented it from being placed on the table.The idea is interesting, though: Force thearm to move with a particular motion, andthen when the restriction is removed, the

Do you have a good wayto develop true cueing?Let me know about itso I can blab it to the

world in a future column.

improved motion will be retained. Myquestion about this — Where is a sportspsychologist when you need one? — iswhether forcing perfect motion is a moreeffective training method than providingmistake feedback, as with theStrokeTrainer.

If any disciples of the New YankeeWorkshop are out there, here is my sugges-tion for the "stroke forcer" device that I'veenvisioned. Make a cue stick with a narrowslot cut through its center over a large partof the middle of the length. This will beeasier with a one-piece, but I suppose itcould work with just a butt on a jointedstick. Make a thin plate several inches longthat will just fit through the slot and attachit to a base so it will stand vertically on thetable. Slide the slot in the stick down on thevertical plate. If you now try stroking, theplate will restrict your motion in two ways.First, only straight forward and back will beallowed, as long as the base doesn't move.Second, you cannot twist the stick whileyou stroke, or the slot will jam against theplate. If anyone does make such a device,please let know how it comes out.

I hear from a correspondent that an evenhigher-tech tool is in the works. It will keeptrack of your alignment electronically, andgive audible feedback if you go off-line.Providing that the inventor figures out howto make this work for the majority of shotsituations, while pocketing real balls, Ithink this might be much better than thecurrent tools for stroke straightening.

Do you have a good way to develop truecueing? Let me know about it so I can blabit to the world in a future column.

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Help With AimingSome devices of the past still prove useful.

Did you do your homework from lastmonth? If so, your stroke is perfectlystraight now. With that foundation, let'smove on to a few devices that will help youperfect your aiming.

Perhaps the most remarkable device evermade to assist in lining up shots is shown inDiagram 1. It is the "Pointer" developedby Colonel C. M. Western, and isdescribed in a 154-page book pub-lished in 1911. The list price for thisWonder of Victorian Science wasunder two dollars. For any cut shot onthe table, you set up the "No. 1" arm(marked O-R) along the line of thepath of the object ball and the No. 2.arm (S-A) along the line of the cueball. This will make the slider E movealong O-R and indicate how full youneed to hit the object ball. Note themarks along the O-R arm which arelabelled in eighths of fullness of hit,although there are sub-marks down to32nds of fullness. Point O is at thecenter of the object ball and P is thecenter of the cue ball at impact. In aseparate table, Col. Western shows allthe cut angles so the student will beaware that a 17/32 hit will give anobject ball cut angle of 32 and 1/12degrees. (Western lists thinness ratherthan fullness of hit, which is morenatural geometrically, but the rest ofthe world does it the other way.)

But even more useful is the otherarm of the Pointer. If you know whatsort of draw or follow you are goingto have on the cue ballwhen it gets to the objectball, the numbers alongthe right arm give thedirection of the cue ball asit comes off the objectball after its curve finish-es. For example, if youhave #36 follow on thecue ball, which happensto be normal rolling, thecue ball will follow astring stretched frompoint P past the number36 on the right verticalarm. Western providedtwo 8-foot silk cords forthis purpose which were

colored alternately red and white in eachfoot. The Colonel was very thorough.

For draw shots, there is a simple calibra-tion for you to do with a half-ball shot thatmight produce a number like 85. With thissingle number, you can find the draw anglefor any fullness you set up simply by run-ning the cord from P to 85, assuming a sim-

ilar quality of draw.You may note that the device is patented,

but if you're handy with sheet metal youhave my permission to make a Pointer, pro-vided that you send me a copy. Rememberto number both sides so that it will workfor both left and right cut shots.

Shown in Diagram 2 is a somewhat sim-pler device called "The Arrow"from "The Straight Pool Bible" byHall-of-Famer Babe Cranfield withco-author Larry Moy. It looks prettysimple, especially compared toWestern's opus, but Cranfield says,"I seriously considered focusing thisentire book on aiming with theArrow. It can teach new players, andremind experienced ones, how toaim the cue ball. I have never founda device or system that works betterfor me or my students."

I can safely say that Cranfield ranover 200 balls more times than youand I together will ever run 100, soyou might want to consider hisadvice.

To use the Arrow, place the forkedpart under the object ball so that theArrow points away from the pocket(or other target) and the "interiorpoint" is right under the edge of theobject ball. The tip of the Arrow willthen be where the base of the cue ballmust be when it contacts the objectball, and you simply aim at the tip ofthe Arrow. Cranfield also shows howto use the Arrow to aim dead-ball

caroms in the book.The device is remark-

ably simple, but it gets thejob done. I hope you'renot put off by the lack oflevers, pivots, pulleys andsilk cords. If you makeyour own, don't bother tosend me a copy, as Ialready have one.

The final device for thismonth is shown inDiagram 3. It shows thecut angle for a half-ballhit, which is when thecue stick is directedthrough the center of thecue ball at the edge of the

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object ball. It is made from paper or poster-board in two parts: the circle and the trian-gle. For the 2.25-inch circle, any drawingprogram should let you print one the rightsize, or you can print out the example fromthe www.sfbilliards.com "miscellaneousfiles" page. The triangle is tougher, as youneed a littletrigonometry. Ihave it dimen-sioned for cuttingout of 8.5-by-ll-inch paper. If youuse 11 inches asone side of the tri-angle, and the otherside is 6.3508 inch-es, then the anglewill be 30 degrees.

I find that this is alittle small foraccurate sighting,so you might wantto make your angleindicator out of alarger piece ofpaper, say with thelonger side 24inches long.

You could use thesame proportions

given above or a table of tangents, but thereis an easier way. Go to the www.google.comsearch engine on the Internet and type in"tan(30 degrees) * 24" as the thing to searchfor, and Google will figure out that you aretrying to do trigonometry and will tell youthai the other side of the triangle needs to be

13.86 inches long.Using this aid is as simple as it is single-

minded. Place the circle where the ghost ballwill be to pocket the object ball, and makeone side of the triangle point straighttowards the pocket. The cue ball must bealong the other side of the triangle, as shown

in Diagram 4. Unlike thefirst two devices, thisworks only for one angle,but I think that angle isimportant enough to haveits own special tool.

Here are two more exer-cises. Using the half-balltool, find out where onyour table you shouldplace the cue ball to have ahalf-ball spot shot. A half-ball hit will have abouttwo degrees of "collision-induced" throw.

On a spot shot, theobject ball travels 35inches to the pocket.How much error at thepocket will that resultin? Hint: ask googleabout tan(2 degrees)*35.

Is that much throw sig-nificant?

BD -DECEMBER 2004 33