Page 113 of Lord Tollemache's book says:

"I believe it is the generally accepted idea , that in split-peeling, the pilot ball must always be "pulled" a little. Lots of players even try to allow for this. I should like to take the opportunity of correcting this error. It is absolutely wrong. If the balls are placed correctly, and the angle of the split accurately determined, there is no "pull" whatever. If allowance is made for "pull" by aiming the pilot too much to the left or right, as the case may be, it is obviously an absolute fluke, if you happen to allow exactly the right amount; since it is impossible to tell how much you will "pull" for any given shot. If, on the other hand, you learn to do the shot correctly, you KNOW that the pilot ball will go straight to the point aimed at. I always play this shot myself by using side. I hit the desired point of my own ball with the edge of the mallet nearest to the ball being peeled. If I am going to 2 back myself (peeling Rover), I use the left edge of the mallet, if to 3 back, the right edge of the mallet. In addition to ensuring that the pilot ball goes straight, your own ball is much less likely to stop short of the pilot ball at the next hoop."

He also recommends the use of side in normal split shots where he says, "It is to avoid there being anything in the way of a rebound, that we hit our own ball with that side of the mallet face nearest to which our own ball is going."

Can anyone explain why he used this technique? Why did he get no pull? My experiments show that pull exists whether you hit with the centre of the mallet or side. The book was published in 1914 - so did the mallets or balls have properties that made this technique useful?

I have received a direct E mail suggesting that "side" prevents the mallet/ball contact from being prolonged and could therefore reduce pull. But when I try a split (on a carpet) very very gently, there is pull. The use of "side" seems to make no difference. I can only assume that the milling makes the difference.

The late Ashley Heenan told a lovely story about meeting Lord Tollemache just after the second World War when Ashley was a musical student in London. After the usual introductions and a brief conversation concluded Tollemache said something like, "From New Zealand ahhh? well tell that chap Ross there is no such thing as pull on a croquet ball!" turned on his heal and strode off.

Having played with both Ayres Championship(a few times) and Jaques composition balls in my early days I can confirm that both produced pull. Both brands were milled but the surface of the ball was smooth. Years ago I tried out Tollemache's theory but seem to recall it didn't counteract pull for me. As to the amount of pull to allow? For me it has been practice and more practice we all hit the ball differently and different brands react differently as well.

* The moment imparts rotation to the croqueted ball - it simply rolls around the striker's ball

* The balls slide against each other - possibly more in the wet (though I failed to prove this to myself last season with a bucket of water), certainly less for locked milling

It's worth using the bald spot to eliminate this variable effect

2. The balls, having been compressed together, travel together in line with the mallet before separation occurs, thus appearing to narrow the angle. I think this is the biggest component of pull. The wetter the surface, the further they slide before parting, thus on a wet surface, pull is greater.

3. On wet surfaces and big shots, there is certainly an inwards curve of the croqueted ball, most apparent as it comes to rest (over the last couple of yards). I am not sure if this occurs at other times and is not noticed - the track on a heavy dew gives it away. The cause is even more obscure, I can only think that the rotation about the vertical axis imparted by (1) causes the effect you describe (differential friction on each side of the ball - that which causes spinning balls in the air to curve). Last year, someone dismissed this component, saying it would be completely eliminated by the ball rolling, arguing that in a short time there would be a composite rolling direction and no other component, but if you take a ball and spin it violently on the grass (and you'll achieve nothing like the force a ball experiences from a croquet mallet) it will spin for a while.

There is of course the possibility of a gyroscopic effect - but I think that would work the opposite way.

I guess it's possible for some players in certain conditions for 1 and 2 to appear to cancel each other out in some shots.

A take-off can have many angles, never 90 degrees for a legal one through - it all depends how much you hit into the balls.

If any non-A-class players are still reading, worth practicing: in turn 5 of a (old?) standard opening - the take-off from corner 2 to the tice - you can get a rush to 1 fairly reliably by lining up the take-off as if the ball would go off about a yard and then hitting well into the shot - you also move the other ball out of the corner and into the lawn - get it wrong by being too timid though and you go off!

Peelers should note the first two aspects above since they have different magnitudes depending on the type and angle of the shot and are most obvious when close to a hoop with a wide split angle. In the right conditions, I sometimes visualise the croquet stroke as if it were being played from a point along the line of the stroke several inches in front of where the balls are.

W = KL/M where

W is the number of wires of pull to allow for

L is the distance to the hoop in feet

K is a factor for the shot type, where 0 = straight, 1 is a slight split shot, and up to 4 for a thick take off.

M is a ball factor. I think that it is 3 for Barlow GTs [4 for Jaques Eclipse, and 2 for Dawson]

So for a peel from 3 feet, played with a slight split (1) and with Barlow balls, then you would allow for 3x1/3 = 1 wire of pull.

Note a wire is the width of a hoop upright.

A few years ago, I also tended to scoff at Panther using his formula. It was too nerdy for me.

But then I hit a patch where I lost the ability to judge pull and his formula gave me something definite to work from. These days, if I feel like I know what the balls are doing, I go by what seems right, or if I'm feeling unsure of myself, I check whether the balls are lined up roughly in accord with Panther's formula. When what looks right differs much from Panthers formula, I'm sad to say that his formula has often proved the more accurate. Equally sadly, I have the memory of a goldfish and seem to forget the formula details every couple of years...

I feel very vague about the effect of wet conditions on pull, though some people express strong views about it increasing or decreasing the pull. Has anyone reached any objective conclusions?

What I have found, interestingly, is occurrences of "anti-pull". I noticed it for the first time in the season that I started to use the sextuple as a game-winning strategy (around 2000/2001). I am a believer in peeling 1-back before making hoop 1 (played well, you can get the first two peels done either after hoop 1 or after hoop 2), by doing a big pass roll peel at 1-back, going down to the pioneer at hoop 1. Three or four times that season, and probably every season since, I've found that the peelee pulled in the opposite direction to what I expected when doing an big angled pass role peel. At the time, I put it down to a bad contact, an imperfection on the lawn, or plain bad judgement.

However, last season I spent a couple of hours investigating this. It only occurs when:

1. the angle of the peel is around 45% off the direction I want the Strikers Ball to travel (and doesn't happen when its straighter or wider, AND
2. the shot is a pass roll, rather than a roll (i.e. where I want the Strikers Ball to travel up to twice the distance of the peelee).

Under these circumstances only, I found consistent anti-pull. When you attempt a big 1-back pass roll peel with the peelee pointed somewhere near the middle of the West boundary and you're peeling from a couple of yards out, it can be quite an unnerving shot. On occasion, the anti-pull makes the peelee hit the outside wire of 1-back and go off the boundary!

The only explanation I could think of was that the Strikers Ball maintained contact with the peelee for a fraction longer (given that it's a pass roll), and the line (or direction) of the peel moved slightly wider from the intended direction at the time that the two balls parted company. I would maintain that this anti-pull is not evidence of a double-tap, but simply the physics required to perform a pass role, though I'd be interested to hear from others on this point.

Nowadays, if I want to attempt this ambitious peel, I ensure that the shot is not played as a pass roll, but a full-blooded three-quarter drive (or at worst, a full roll). This ensures that anti-pull doesn't occur, though the risk is that the peelee goes sailing through 1-back and off the South boundary. However, at least the estimation of the pull is more accurate.

As an aside, the only analogy I can think of is the discovery of reverse swing in the game of cricket. Until the emergence of reverse swing (attributed, I believe, to a bowler from Pakistan) in the Eighties, a ball was thought to swing in the direction of the rough side of the ball. This was based on the differential of the friction of the wind over the two sides. Reverse swing comes about when one side of the ball becomes heavier than the other, and the swing is in that direction, rather than on the rough side. It was disbelieved at the time, but has been accepted now as a fact. I wonder how (or even if) anti-pull will be perceived?!

I performed the same [anti-pull] test also and attribute the anti-pull to two possible reasons.

1. double tap due to the follow-through, when balls seperate after the initial striker contact and the second contact changes the angle of the peelee.
2. More likely in Reg's case, slippage - This is very exaggerated on a wet lawn or cold weather, during the initial striker contact, especially during a smooth stroke and follow-through, at a 45 degree angle the striker ball may slightly slide off the croqueted ball causing a change of angle.

Suspect Duncan's problem is to do with playing shots close to the tangeant line. This is one of Kevin Brereton's thoeries on which I am completely sold. If you place two balls in contact and imagine a line going through the centre of the strikers ball and the edge of the object ball, this is what Kevin calls the tangeant line. The tangeant line happens to be at 30 degrees. If you play inside that line the shot is going to be characteristic of a drive, outside a take off. If you try and play hitting down the tangeant line, bearing in mind the line is infinitely thin, you will play one or the other but you won't know which until afterwards. The difference between playing at 29 degrees and 31 degrees is much greater with hard balls than soft.

The answer for Duncan (assuming I have correctly diagonosed the problem) is to avoid playing shots down this line. If you are sending a ball to 3 going to a pioneer at 2 and you are considering playing close to the tangeant line, settle for sending the pioneer to a less perfect spot where the angle is slightly different. Occasionally when you don't appear to have a useful rush it can make sense to take it a yard or two in what at first appearance is the wrong direction, because the split shot is then at a less treacherous angle.

Roughly speaking at 31 degrees the striker's ball will start its motion by sliding off the face of the object ball. At 29 degrees the striker's ball will go through the position of the object ball to a much greater extent. Think you could argue that a roll style shot played at 31 degrees is a take off, but thought calling it characteristic of a take off might be more appropriate.

This theory seems to me to gel with what I'd expect from considering the interactions of the stroke, and also from what I've seen.

Hence, potentially, people with newer Pidcock mallets (sorry Alan, just an example), particularly using Dawson balls (or Jacques) would notice it a lot more than people with wooden endfaces and using Barlows. (wet hard shiny endfaces seem like a potentially greater risk of this squeezing effect too - perhaps you could experiment Duncan?)

The solution, I guess is to setup for a narrower croquet stroke, and hope that there is a little squeezing to make up for the fact that you're aiming the two balls a bit narrower than you'd ideally like them to go.

Potentially also hitting down a bit more on the striker's ball might make it keep it's line better, but there one might be getting into a rather dubious region of push strokes.

I call the "antipull" effect "push" because I think it's caused by the striker ball pushing the croqueted ball wide through prolonged contact or slippage (not illegally long contact, although the same effect can be got from this, or from having the balls not in contact).

I used regularly to reach situations where wide split drives (or rolls) seemed to be the shot to play, and this accounts for a fair proportion of the time that I ended up ten yards away from where I expected to be. My break control has improved a bit, but I hadn't worked out where exactly this dividing line between drive and take-off was. I'll definitely investigate this tangent line area when the season starts.

If you look at the video clip www.croquet.org.uk/tech/exp/sm/sm_half_roll.wmv and www.croquet.org.uk/tech/exp/sm/sm_half_roll_cu.wmv it appears to me that the strikers ball is pushed down into the surface about 5mm. If the strikers ball is aimed off to the left at 30 degrees, I would think that the point of action on the peelee would be down and to the left of the original contact point. (the peelee tends to rise off the surface) such that the peelee tends more to the right and the strikers ball has now passed that critical 30 degree angle to more like 34 degrees.

The peelee will start moving off at 4 degrees right of its' intended path. The strikers ball is squeezed out to the left.

Martin Murray is correct in seeing the use of the my term <tangent line> for defining strokes that earlier literature called <split shots> and <take-offs>. In researching the Coaching Handbook in 1990 I came across a number of cases where these terms, and some for positional plays, were used without finding any useful ways of identifying them for beginners.

The <tangent> becomes the only easily perceived direction apart from one straight ahead and one at right angles to the line ahead. Together with the added terms quarter and half-tangents it provides a reliable map by which players can repeat the angle of striking with confidence. Observing the outcomes of repeated strokes is the basis of empiracal learning to build a repertoire of reliable croquet strokes.

Many other factors such as a player's mallet, their technique, their somato type, the surface and the composition of the balls etc, influence the result of a croquet stroke. It can be quite bewildering to players to discover strange results from following the patterns advocated and argued about by many books and coaches. The <halve the angle> or <divide the destinations> being some of the most inaccurate and misleading.

Although the concept started as a teaching device it proves equally useful in applying Newtonian physics and Statics to describe and demonstrate the differences of playing down a line of force both inside and outside this constant angle. In regard to <pull> the only knowable factor amonst the many that influences <pull> can also be assisted by considering the resolution of forces. Like any other aspect of two-ball strokes the mastery will depend on the accurate repetition and observation that a player brings to their empirical learning practice.

Clearly this effect increases as the croquet angle increase from a straight drive to a fine take off. There is a critical point where the effect changes - the tangent line.

At the angle Rob mentions, using two smooth spheres, the croquet ball would only rotate and would not be pushed away in the stroke. Milling on balls and possibly other surface binding effects make a difference from the idealised sphere behaviour.

Now to the experiment - go to the pub and purchase two halves, a couple of shorts or just two of anything that comes in a glass with straight sides. Place the glasses together on the table top and look down - you have a plan view of a croquet stroke waiting to happen. Play about with pushing one glass slowly using only your finger tip - in the direction a mallet would push it in a croquet stroke and observe (in "slow motion") how the balls (glasses) behave. You'll find that at the critical angle, the croqueted glass no longer moves in the "right" direction but simply rotates a bit and leaves the striker's glass alone to go in a strange direction.

If it doesn't work, just buy more beer and try again.

There is an interesting paper on the Mechanics of the Game of Croquet at [the Oxford Croquet website]. Fig 13 shows that;

for a Stop shot, the angle the two balls diverge in a croquet stroke rapidly increases to 90 degrees as the angle of aim increases from about 18 degrees,

for a drive shot, the angle the two balls diverge in a croquet stroke rapidly increases to 90 degrees as the angle of aim increases from about 37 degrees,

and for a Roll shot, the angle the two balls diverge in a croquet stroke rapidly increases to 90 degrees as the angle of aim increases from about 43 degrees,

As the critical angle for the particular stroke is approached, the outcome is more difficult to control.

The Tangent angle we have been considering is 30 degrees and hence a critical angle somewhere between a Stop and Drive croquet stroke.