This is a sequel to the recent article "Hoopoids". Here a simplified concept is introduced which requires only eight hoopoid balls of which only six stay on court. This is of immediate interest for indoor play where ordinary hoops are not available. No desirable hoopoid attribute is lost in the simplification. At the same time it allows the hoopoid based game to resemble the ordinary game more closely. The previously stated hoopoid laws are updated in the light of this evolution. We also look at historical aspects and remark on the potential benefit to novices and intermediate-level players.
1. The Simplified Concept
The underlying idea remains unchanged -- hoop running as a scoring stroke becomes replaced by an accurate rush as a scoring stroke. To qualify as an accurate rush a suitably placed A-ball needs to be rushed into a suitably placed D-ball. As before, hoopoid balls (A-balls and D-balls) are croquet balls distinguished by colour from the balls in the game. Striped balls or secondary or tertiary colours could be used in this role.
In the simplified concept the hoopoid balls become deployed in a different manner, as follows. At the start of the game an A-ball will have been placed at every hoop position. The only furniture in sight will be the peg and these six A-balls. Picture 1 shows what things would look like near the Hoop 5 position at the moment when a ball (say Blue) arrives at shooting position for Hoopoid 5.
The white ball markers to the right of Blue, also installed before the start of the game, indicate the position of the D-ball for the hoopoid of opposite direction with the same A-ball. So while the top markers apply to Hoopoid 5, the bottom markers apply to Rover. Similar remarks apply at all other hoop positions. For indoor croquet in a carpeted hall the ball markers will be pieces of masking tape which could be removed afterwards without leaving a trace. While not essential, it is nice to use blue markers for Hoopoid 1 and red markers for the rover hoopoid. In a friendly game the D-ball positions could be measured via an appropriate mark on the striker’s mallet as substitute for ball markers.
Picture 2 shows an outcome of a successful scoring attempt by Blue in Picture 1.
In case the scoring attempt fails, the striker’s ball stays where it comes to rest (possibly installed as boundary ball), much the same as in the ordinary game. Similar scenarios arise at all subsequent hoops.
2. Updated Hoopoid Laws
HE. Specifications for Hoopoid Balls
(Instead of a Hoop specification there is a Hoopoid specification, as follows, which should come after the balls in the game have been specified).
HE1 General Hoopoid Balls. There are eight hoopoid balls. They are regular croquet balls but coloured so as to be readily distinguishable from the balls in the game.
HE2 A-balls. At the start of the game one hoopoid ball is placed at every hoop position. Its position is marked with ball markers symmetrically placed east and west of the ball so that these balls can be accurately replaced when knocked out of position during the game. These six hoopoid balls are called A-balls.
HE3 D-balls. Two hoopoid balls, called D-balls, appear on the court only for the duration of a stroke in which a scoring attempt is made. They are placed on the nonplaying side of the hoop position at a predetermined distance directly north or south of the hoop position. That predetermined distance is called the (hoopoid) Length of the game in progress. It is the same for all hoopoids. The spots where D-balls have to be placed are marked with ball markers that stay in place for the duration of the game.
H0. Omnibus Law
For the purpose of playing a game with hoopoids in the role of hoops the Laws of Association Croquet are deemed to be modified by the systematic replacement of "hoopoid" for "hoop" wherever that replacement makes sense.
H1. Scoring a Point with Hoopoids
If, as a consequence of any stroke, a ball B causes the A-ball of the hoopoid-in-order for B to move in such a manner that it collides with the D-ball, when the latter has been placed in its marked position, then the following statements apply.
H1a. B is deemed to have run that hoopoid and the stroke is called a scoring stroke. If B happens to be the striker’s ball, then it is said to have scored the point for itself; otherwise B is said to be peeled.
Comment: The peeled ball B may have been in contact with the A-ball at the start of the stroke.
H1b. Any movement of the D-ball after being hit by the A-ball is deemed to be the movement of B and the usual croquet laws apply to B accordingly. In particular,
H1c. At the end of a scoring stroke, provided that the turn did not end for some reason, the following applies. If the ball B was roqueted in the scoring stroke, the striker should take croquet from B at the spot where it replaced the D-ball. If the scoring stroke was a croquet stroke the striker plays the continuation stroke from where the striker's ball comes to rest. After replacement of the D-ball by B, the D-ball is removed from the court (it may be carried by the striker or trundled along when a break is being played or stored court-side until needed again).
H1d. If a double tap occurs during a stroke in which the striker’s ball scores a point for itself, that double tap is not a fault.
Comment: This exemption is similar to the exemption of a double tap that occurs in a roquet attempt. In both cases the striker’s ball becomes a ball in hand, so the double tap cannot be to the advantage of the striker.
H1e. If a ball in the game occupies a position that blocks the direct path of the A-ball to any part of the D-ball so as to prevent scoring, then that blocking ball is temporarily removed until after the scoring attempt, when it is replaced in the position it had before.
H2. Moved Hoopoid Balls
H2a. If, as consequence of any stroke an A-ball becomes moved away from its marked position, then the following applies. The A-ball becomes replaced in its marked position before a further stroke is played. If another ball is in the way of such replacement then that occupying ball is moved away in the direction that requires the shortest movement so as to make room for the A-ball; thus the A-ball will be left in contact with the occupying ball upon replacement. If the occupying ball is exactly at the marked position of the A-ball then the latter is replaced in its marked position and the occupying ball is left in contact with it in a direction chosen by the striker.
H2b. If, as consequence of a non-scoring stroke, an A-ball becomes moved away from its marked position, then the following applies. If the moving A-ball has collided with a stationary ball C in the game, then C becomes replaced in the position it had before the collision; if it has collided with a moving ball C, then C stays where it comes to rest.
H3. Ball in Contact with an A-ball
H3a. If at the start of a stroke the striker’s ball is in contact with the A-ball of its hoopoid-in-order then the striker may hit his ball in any direction. If that stroke causes the A-ball to hit the D-ball, then a point is scored for the striker’s ball in accordance with H1a.
H3b. If at the start of a stroke the striker’s ball is in contact with an A-ball which is not of the striker’s hoopoid-in-order then the striker must hit away from that A-ball without shaking it; otherwise the striker’s ball will be replaced where it was and the turn ends.
Comment: This corresponds to the situation of a striker’s ball in contact with a hoop, which must be hit away from the hoop to avoid a crush. There is another reason to prohibit movement of the contacting A-ball, namely to avoid its use in scattering other balls, the equivalent of which does not exist in the ordinary game.
The stated laws are of course not the only possible ones. Further evolution is possible.
3. Historical Note
In D.M.C. Prichard’s book "The History of Croquet" one reads (in Chapter 18 under the heading Hoops):
Today, more than a hundred years later, it is still the case that the need of elite players is putting pressure on ordinary players and beginners to play with hoops more challenging than they might prefer or should ideally be using. It is not surprising that the geometric clearance of 1/8-inch has shrunk to 1/32 and even 1/64 over a hundred years. It is not hard to think that top players today are better than they were a century ago. But what reason is there to believe that novices today are better than they were then? Happiness at grass roots level is important for every sport.
There is of course the practical obstacle that croquet clubs can hardly be expected to acquire and maintain a large collection of hoops of different sizes. However, by using hoopoids in the role of hoops, players get instant access to a large range of challenges. For novices the Length could be very short. For intermediate players it could gradually increase as skill increases. For elite players it will likely be upward of 100 cm (I gather this from positive feedback received privately from world class players). It can quickly be adapted in accordance with lawn speed, made longer on easy paced lawns, shorter on very fast lawns.
4. Comparison of Hoopoids with Hoops
Let us consider more systematically how playing with (simplified) hoopoids differs from the ordinary game.
As the two players walk onto the hoopoid-installed court the view before them is very similar to the ordinary view: they just see A-balls where ordinarily they would see hoops. So there is not much practical difference in the amount of furniture that has to be avoided. Should a player find himself wired from a connecting roquet by an A-ball where he would have been wired by a hoop it would generally be easier to jump over that A-ball than to jump the hoop. But that kind of thing rarely happens. The blue crown of hoop 1 and the red crown could be reflected in the colour of the ball markers.
The first really significant difference occurs when a scoring attempt is to be made. Let us look again at Picture 1. Clearly, for any given hoop in place of the A-ball the required cut rush could be more difficult than the corresponding hoop shot (when the Length is large enough) or it could be easier (when Length is small enough). In either case the cut rush requires aiming at an appropriate spot and then hitting there accurately. The corresponding hoop running stroke likewise requires aiming at an appropriate spot and then hitting there accurately. The aiming in both cases requires skill developed through practice. In both cases it has to be determined whether the stroke achieves a predetermined direction within a predetermined tolerance. The hoop specifies that tolerance through the requirement that the ball pass between the two uprights. The hoopoid specifies it through the requirement that the A-ball hits the D-ball. Effectively, both hoop and hoopoid have to conduct an examination which the striker will pass or fail.
The difficulty of running a hoop is largely determined by the firmness of the soil, rather than by the clearance it is set for. By clearance we mean (gap between uprights at height of a ball radius) – (ball diameter). Associated with every clearance there is a clearance determined angle i.e. the least upper bound of all approach angles that allow the ball to run the hoop without touching wire. A clearance of 1/16 inches gives a clearance determined angle of 10 degrees. This can be verified by taking a plank whose width is that of a ball and holding it in the hoop at the height of a ball radius and noting how much it can rotate out of the perpendicular 0 degrees position. If the upright diameters were to increase, the clearance determined angle will decrease. If the clearance were to decrease (like from 1/16 to 1/32) then this angle would also decrease.
In their recent preliminary report the CA committee studying hoop behaviour reported (see http://www.oxfordcroquet.com/tech/hoops/index.asp for details) that typical soil conditions allow hoops set with clearance 1/16 to be run with approach angles around 45 degrees. These maximum run angles are way above 10 degrees, so their results demonstrate the extent to which the ball can be forced (in typical soil conditions) through the hoop beyond what the clearance by itself permits. While some flexing of the uprights will also play a role, the soil firmness is the dominant impedance.
If rain causes softness of the soil, the desired hoop running difficulty may be unattainable. Setting a very small clearance (e.g. 1/64) increases the risk of balls jamming because one never has perfect uniformity of ball diameters. Furthermore, a clearance of 1/64 in the morning may no longer be there by the end of the day because all the bombardment will pry the hoops loose. In dry firm soil the difficulty could become too much; then we have disgruntled players and Walter Peel turning over in his grave … All told, hoops do not allow good difficulty control.
People have been searching for better hoop designs for more than a hundred years. See the picture with the caption "Some ingenious designs all of which had disadvantages in practice" on page 178 of "The History of Croquet".
Hoopoid difficulty is directly controlled by the hoopoid Length. This does not depend on soil conditions, remains constant as it is set, is not sensitive to non-uniform ball diameters and can quickly be adjusted at short notice. If rain has made the lawn easier to play on then hoopoid Length can readily be increased to maintain a similar overall difficulty to what a dry lawn would have had. With experience it could become known what combinations of lawn speed Plummers and hoopoid Lengths give a satisfactory overall challenge.
A further bad side effect of hoops is the rash of hampered shots causing refereeing problems. Picture 3 should make it clear that as soon as the Length is larger than about 50 cm it is impossible for a hampered continuation stroke to arise. And even for smaller Length the hampering will be less severe than they are with hoops.
Peeling remains possible with hoopoids, as described in the hoopoid laws. But it is impossible to jaws a ball because hoopoids have no jaws; an Irish peel is also impossible. Is that to be lamented? Not if it is born in mind that hoop based play has become problematic for the very reason that clinical games with very few turns occur too frequently among elite players. With hoopoid play a triple peel could become a more prestigious achievement.
Hoopoids provide the possibility of handicap play without extra turns for the weaker player. The latter simply gets to use a shorter Length and the stronger player a longer one, with two sets of colour coded ball markers. If these Lengths could be chosen so that each player has 70% probability of running a complete all round break, it should result in a game with roughly 50% win probability for each player, which is the purpose of handicap play. By dropping the 70% to a smaller percentage, longer games will result; by increasing it, shorter games. Some experimentation is needed.
When croquet first evolved long ago, the scoring examination device could just as well have been the hoopoid rather than the hoop. Indeed, balls were as readily available as bent iron rods. It is just an accident of history that nobody thought about hoopoids at the time. If that did happen, it would have been more difficult today to revert to hoops than it is the other way around … Who would want to change from a mechanism that gives easy difficulty control to one for which this is as problematic as it is with hoops? However, the way history unfolded means that for the time being the good attributes of hoopoids will be enjoyed only in friendly games by players who choose to use them.
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