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Technical
Comparative Croquet Handicaps

Ian Plummer - January 2002; Readers should consult "Toward universally comparable handicaps" 2004 which builds on, and greatly extends these observations

This document discusses relative croquet handicaps around the world. There are two points of contact between players in different countries; those few players who hold (different) handicaps in different countries and, more removed, the World Rankings based on advanced play.

Introduction

I was asked in November 2001 to assist the Croquet Association's Handicap Committee by using electronic resources to gather data on handicaps and gradings around the World. I have collected handicaps of 5662 players and presented that data to the Committee for their analysis. In this paper I make one easy comparison; mapping the grades of players to their national handicap range.

Within the data there are only a handful of people with multiple handicaps. Where different handicaps are reported it could just be that the lists are out of date. Consequently I have based my analysis on the assumption that the ability of a player under advanced play reflects their ability under handicap play. Hence the World Rankings, under this assumption, allows players of similar ability to be identified and then mapped back to a handicap.

The weakness of this assumption is readily shown in the following graph. I have taken only the English players with rankings and plotted their Handicap vs. Grade:

UK Handicap vs Grade

All these people subscribe to the same handicapping system, yet there is a huge scatter in the data. Could you predict the grade of a handicap 4 player for instance? I have added a second order polynomial fit to the data. My analysis has only gone as far as people with grades, I leave further analysis of the data to others.

The data comes from a number of countries and they can be split into three categories

  • Countries which follow the CA scheme, (i.e. the automatic handicap system)
  • Countries which derive handicaps from World Rankings
  • Countries which use their own system

The CA automatically handicapping scheme is self consistent within handicap play and has the extension that a player's advanced play performance can affect it - there could be considered to be a weak link to the World Ranking Grade. Note there is no feedback from a World Ranking Grade to a player's handicap.

Hcap
Index
  Hcap
Index
  Hcap
Index
  Hcap
Index
-2
2600
 
1850
  5
1500
  12
1150
-1½
2400
  2
1800
  6
1450
  14
1100
-1
2250
 
1750
  7
1400
  16
1050
2100
  3
1700
  8
1350
  18
1000
0
2000
 
1650
  9
1300
  20
950
½
1950
  4
1600
  10
1250
  22
900
1
1900
 
1550
  11
1200
  24
850
Table used under Advanced Play to adjust a player' s Handicap Index under the CA Automatic System

A number of countries, generally with a small croquet population, use the World Ranking Grade to derive a player's handicap. They use the table used in the CA's domain (above) for mapping handicap index to handicap value. They substitute the World Ranking Grade as the handicap index and look up the corresponding handicap. There is no logical connection between the World Ranking Grade and the Handicap Index, but by happy coincidence they are similar.

Countries such as Australia and New Zealand have their own systems which bear little numerical correlation to the CA's system.

Data Analysis

The data set was gathered in December 2001 from a number of sources which are credited below. Some countries are well represented with a full data sets, others are sparse. This makes it difficult making reliable comparisons. As an introduction to one analysis method I have chosen to plot the Handicap versus Grade for each country and fit a second order polynomial to each. This allows a national handicap to be derived from a World Ranking Grade or vice versa. The polynomials are only proven within the range of the data they were taken from. The maximum handicap is limited by the extent of the World Rankings.

Handicaps versus World Ranking Grade

Australia - handicap vs grade

Australia

Switzerland - handicap vs grade

Switzerland

NZ  - handicap vs grade

New Zealand

England  - handicap vs grade

England

USA  - handicap vs grade

USA

Results from Polynomial Analysis

Australia y = -5*10-7 * x2 - 0.0068 * x + 18.852
Switzerland y =  1*10-5 * x2 - 0.0522 * x + 57.932
New Zealand y =  1*10-6 * x2 - 0.0119 * x + 17.429
England y =  5*10-6 * x2 - 0.0286 * x + 36.666
USA y =  7*10-6 * x2 - 0.0322 * x + 38.264
  y = a * x2 + b* x + c2

The handicap in the country is given by 'y' and the World Ranking Grade is 'x'. Similarly the quadratic can be solved to yield x from y.

formula - solution to a quadratic

where c = c2 - y

Comments on Handicapping Schemes and Data

I have merged the data from the various sources and attempted to eliminate duplicates (both automatically and by tedious inspection) without losing data. I have had some data which has arrived as Mr and Mrs A.B. Somebody with a pair of handicaps.  Where it was obvious that these were two entities I have left the same name in twice. Where duplicate names were found with very close handicaps I have eliminated one of the entries. This I have taken to reflect lists of different ages.

Some correspondents gave an outline of how their Handicapping Schemes work.

Australia

Peter Tavender

As background, each State still does their own thing for the bulk of players although I am hopeful that next year we will be able to get agreement for them to all use a single method (the trials of Federation!!). The ACA decided a few years ago that it would use the world ranking and incorporate handicaps. Below is listed the trigger points which are now used. They were not set with any mathematical precision or basis, primarily to avoid making any significant alterations with the change from the earlier (Stan Hall) system.

We used to handicap down to 10 which was the cut off point for entry for the National Championships, but we have recently decided to stop providing national handicaps at 1650 (H'cap of 6). The reason for this is that many players with handicaps 6 - 10 only play a limited number of their games which are recorded for the world ranking but the rest are recorded by the States and also given a State Handicap.

To give you an idea of games included in the world ranking, the following guidelines now apply:

"All events (total event such as State or Regional Open, or American block of other competitions) should be included if there are any participants in the world top 200.

Other events should be included where there are no participants in the World top 200, but at least 2 players in the top 400.

Where a decision has been made to include particular event or blocks, all results must be forwarded, not just those involving the listed players."

The next question is do you still want a list of players or will these ranking trigger points be enough for your purposes? We just extract all the [A] names out of the world ranking when we issue our own list of senior players.

As I mentioned, each State does their own handicapping so there is no overall list of members. I should be able to get John Hanscomb to let you have a copy of the NSW players if that is any use as he is the record keeper, but the other States may take a little time.

Peter adds

Just a little more background.

A number of years ago we tried to get rid of the minus handicaps and using the Stan Hall score based system we then started with the best player on 2 to allow for downward creep and trying to avoid the problem of fixing our top player as an immoveable base point. As you can see there has only been a half point creep to date which does make us look at odds with UK and NZ.

The trigger points are the world grades rather than world index to avoid very frequent fluctuations. The top players play very little handicap games and apart from our National Handicap Tournament (which is still designed for higher h'cappers) the few games they play are still in 'divisions' i.e. h'cap range say 0 - 5 or 7. We tried to abolish divisions to encourage more play between wider handicap ranges but all the State still insist on keep play within the 4 basic divisions.

I would be very interested to seeing the results of your work as I am always being asked about the difference when people are going overseas.

Ray Howell, Chairman SACA Handicap Committee, April 2003, adds:

... each state uses their own method.

  • SA uses the English AHS system and have been since 1997 although we use a different hcap range 2600 = 1 as the starting point then it corresponds to the AHS in the trigger point steps.
  • Vic have been using the AHS for a couple of years
  • Qld [been using the AHS] for a year but also use doubles results
  • WA have I think used the AHS as a base but set in some of their own parameters
  • Tas use Maurice Woodmansees Merit point system.

I have observed fluctuations in SA State Index and WRank grade (as more game results are used by the state than are sent for Wranking) and have found that there is little variance in the state index and AHS grade for the majority of players. There is a move toward developing a standard national system using the AHS.

Stephen Meatheringham, July 2008 notes:

The information at in this article regarding the Australian AC Handicapping system is rather out of date. We have used the AHS since 2004.

England

The standard CA handicapping system is used. Data provided by the CA Office

New Zealand

Croquet NZ

Attached is the data file for the NZCC's membership for all 20 associations. Obviously I would not like you to distribute this resource electronically or otherwise - it is sent for the express purpose of assisting you to attempt to find a correlation between the various systems of handicapping in overseas countries.

Matthew Brown adds

No what I sent you was one of our twenty associations memberships. I could send you all NZ Assns but is this what you want? There are almost 4000. The top players you mention are all over the country.

Regards, Matthew
Executive Director
Croquet New Zealand

Scotland

David McLaughlin

>A). Does the SCA use the CA's handicapping system?

Almost.

>B). If not could you give details of what it does?

The only difference, AIUI, is that handicaps may be changed under the automatic system at the end of each day's play, rather than waiting until the end of a competition.

>C). Is it possible to get a listing of all SCA members and their handicaps? (including people without handicaps)

The definitive list will be in the SCA handbook, likely to be issued early in the new year. I'm copying this to the editor, David Appleton, who may be able to provide a reasonably up-to-date list. I've left the list below unsnipped for David's benefit.

{enc Scottish Handicaps}

South Africa

Carole Knox

The answer to your question is a difficult one as we are all on the automatic handicap system and there is no-one that has all the current Club handicaps. I can give you the Clubs in the Western Cape and one or two people outside of that but not all the Clubs in South Africa. SACA are not as on the ball as they are UK CA

{enc spreadsheet}

Switzerland

Ian Sexton

I have listed the current handicaps of most of our players: <data>. We have a lot more players with handicaps from 18 to 24 that I haven't bothered mentioning.

If you require the index's let me know and I will produce the figures. I have attached our handicap system so you can see the slight differences between our system and the CA's.

Swiss - handicap system

USA

Erv Peterson -together with the download from the USCA web page.

In regard to Association Croquet handicaps for USCA players; our committee was originally established because the USCA had no system for assigning "International Rules" handicaps to its playing members. We used the CA's system as a model -- learning what we could from its experiences (via Bill Lamb and others), also we felt more US players would most likely be playing in the UK rather than NZ or Australia. Several of us had CA handicaps and world rankings, so we started with those and then evaluated US players. Initially we had a pretty small list of players who played Association Croquet (AC) - 60 or so.

As there has been a growing number of US players taking up AC and more tournaments being played, we are relying primarily on the world ranking system and the CA formula for determining handicaps with some subjective input on rapidly improving players and those who are not included on the world ranking list. Our range covers the CA model.

Until recently we had only updated the list semi-annually, but we have reached a critical mass in needing to update it more often - bimonthly at the minimum - monthly likely during the spring and summer.

Our committee feels that our accuracy is somewhat subjective since we don't have handicapped tournaments to get additional input on players. Plus we still have too few games played - one of our great needs - more tournaments and more games by each player. Many in the US see our list as a ranking list.

I hope this helps. We would love to see a world handicap system which is automatic.

Erv

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Updated 10.iv.16
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