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Dr Ian Plummer

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Technical
Handicapping in Croquet

"Over a period of time players have learnt that the result of a single game between high bisquers in Short Croquet is largely dependent on who wins the toss. In effect the number of bisques is too high and favours 'last in'. "

To make handicap games less one-sided the number or distribution of the bisques can be changed or extra manoeuvres added to allow each player the opportunity to ‘get in’ and have a chance of winning. This is especially the case in shortened games where each ball makes 6-hoops then pegs out, whether on a full-size or near half-size lawn. Players may have the ability to make 6-hoop breaks but not 12-hoop ones hence the number of bisques needs to be modified for these shortened games to even up the odds.

Firstly to review the various handicapping systems.

Handicap Systems

Currently there are two systems of handicap play (see also pages in the coaching section):

  • Bisque Difference; the handicaps of the players are subtracted and the weaker player (i.e. with the higher handicap) receives that number of bisque turns.
  • Full Bisque; each play receives the number of bisque turns equal to their handicap

There are then additional modifications to accommodate reduced games (e.g. short or 14-points games) or full games where the number of bisques is reduced, generally to prevent one player whitewashing their opponent by using all their bisques to take their balls around in two turns.

Subtractive and Multiplicative Modifications

The two main modifications are multiplicative and subtractive. For example applying a multiplicative factor:

  • Scaling the Bisques by a Factor; in 14-point games the number of bisques (either full or bisque difference) can be derived by taking a proportion of the players’ handicaps. (In the system introduced by Kevin Carter, I think 1/3 was the factor for 14-point games). This makes allowance for the ability of people to say make 6 hoops before they break down as opposed to 12-hoop breaks.

In Full Bisque games there are combinations of subtraction and a factoring:

  • Using a Constant Base; each player's handicap is reduced by a constant number before the calculation of bisques is made.
  • Yorkshire Variable Base System; the handicaps are added then divided by four to give a variable base which is subtracted from both palyers' handicaps.
  • Capped Yorkshire Variable Base System; as above, but a further condition is applied that the minimum base is defined. If the procedure above produces a base that is less than say, 3, the game is played as Bisque Difference. (Introduced by Carter, Plummer & Patel in Florida this year to prevent low bisque players receiving bisques by this method. Were two 2-handicap players to meet under the Yorkshire System, each would receive one bisque).

Examples

Below, a base of 3 is used and a factor of 1/3. The columns show the number of bisques received by 12 and 24-handicap players in a match. If a fraction of a bisque results at the end of the calculation, it is rounded up to the nearest half or full bisque.

 

Bisques Received

Method

24 hcap

12 hcap

Bisque Difference

12

0

(24  - 12), 0

Full Bisque

24

12

24, 12

Constant Base

21

9

(24 - 3), (12 - 3) ; base = 3

Scaled Bisque Difference

4

0

(24  - 12)/3, 0 ; factor = 3 (for small lawn)

Yorkshire Variable Base

15

3

24 - (24 + 12)/4, 12 - (24 + 12)/4 ; base = 9

Capped Yorkshire Variable Base

15

3

As above providing (24 + 12)/4 >=3, otherwise Full Bisque; min. base = 3

Other Manoeuvres

So far the only compulsorily manoeuvre which has been adopted to balance the levels of ability of strong players playing weaker ones is mandatory peels (causing a ball to run its hoop by striking it with another ball) in Short Croquet (a designated form of croquet played on a small lawn). This introduces an extra level of complexity to prevent a good player speeding around. The first challenge however is to find the table of mandatory peels on the CA web site …

Time limits are not advantageous to good players as all of the time in the game is consumed by the high bisquer spending their bisques.

Whilst other tricks can be thought of none have been adopted to date. As a suggestion a system could be based on a staggered start; the weaker player's clips are placed on, for example, hoops 2 & 3 at the start of the game.

Options for Handicapping in Short Croquet

"Rather than play best-of-three, we are going to introduce some version of full-bisque play which is less 'trivial', but still worthwhile on a small lawn. For simplicity, I favour using a fixed base (say 8) for a 26-pt game, with 2 hour limit. We also play 'normal' croquet on full lawns! What would you think is a good system to improve 'short croquet' on using half lawns?

  1. play 26-pt (using either or a different base, say 10)
  2. play 14pt? (modify YVBS in some way)"

You make a number of suggestions for alterations.

Reduced Time Limits

I would be against reducing time limits as this favours the high bisquers. In a normal handicap game, once the high bisquer has used all of their bisque turns and failed to reach the peg, the low bisquer gets their chance to hit in and make hoops. The following scenario is all too common; the 'burning of the bisques' has taken 3 hrs 7 minutes leaving 8 minutes for the better player to get their first ball around and hope for an innings change. Time limits are bad.

Short Croquet has the benefit that there are few hoops to make (its 14-point) and the lawn is small so the route is shorter. To make games take less time consider advancing the clips of the weaker player with a consequent reduction in bisques. Use a variable base system on full size lawns to ensure that "high bisquer - high bisquer" games are well supplied with bisques but "low bisquer - low bisquer" games remain competitive.

Large Lawn verses Short Lawn

For a smaller court the handicaps would need scaling to allow for high bisquers making further progress than they would because of the proximity of the hoops. This may well have been taken into account in the tables which transliterate between normal handicaps and Short Croquet handicaps.

Using a Variable Base System

If the intention is to use a Variable Base System with Short Croquet, a problem arises with the YVBS in that as the handicaps are first scaled for the smaller lawn and then scaled for the variable base, the results are going to be small numbers which will round up to similar numbers.

The YVBS base would be obtained by:

(H1 + H2)/4 * factor for 14-point * factor for small lawn.

There seem to be a number of conflicting or unavailable figures.The Laws have a table for translation between 24-point game handicap and 14-point games which offers a factor of 11/20 (0.55). I feel sure Kevin Carter's factor is smaller (0.33?). Next the factor for the small lawn could be, hopefully, derived from the Short Handicap tables, which are unavailable currently.

For a guess let's use 1/2 for the lawn factor and call the 14-point factor also 1/2; this yields (H1 + H2)/16 for the YVBS. Try some numbers; say a

32 plays a 16 ... base = 3
24 plays a 16 ... base = 2.5
24 plays a 28 ... base = 3.5

This does not look useful.

26-point Game

If the game becomes 26-point then it would no longer be formally Short Croquet, but Association Croquet on a reduced lawn. This would then eliminate mandatory peels, etc. unless you define it otherwise.

Increasing the number of hoops would introduce more changes of innings/bisque consumption. Novices cannot make 12-hoop breaks but could make 4-6 hoop breaks. It is not easy to predict how this would affect the handicaps or vice versa. All I can suggest is a trial.

Suggestions

If you will be using small courts and similar ability players then, to remove the whitewash factor (the winner of the toss winning the game), introduce a moderate fixed base. This will cause the players to have to make hoops without bisques. It has the advantage that it is easy to calculate. If you have a wide range of handicaps then this is unsatifactory.

If you are playing on a full size court then the a Variable Base system will work well. If you want to make the players 'work' by having a lean number of bisques then you could produce the base by dividing by a smaller number than four: e.g. (H1 + H2)/3.

I would not recommend Time Limits, as I do not think that they are fair when a large number of bisques are available. A slow player with a mountain of bisques will deny their opponent the minutes necessary to gain a victory.

The staggered start method has not been tried to my knowledge so there is scope for some thought there.

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Updated 28.i.16
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