The Croquet World E-Mail Interview:
Chris Williams, Co-Proprietor,
World Croquet Federation Ranking List
Only the Croquet God knows the true, utterly incontestable ranking
of the world's croquet players. All players, however, whether they admit
it or not, burn to know their place in the
croquet universe. Lacking a clear channel to the divine being's font of
knowledge, we must settle for the WCF World Ranking List produced by
Chris Williams and Stephen Mulliner and distributed to the Nottingham
croquet internet board.
The World Ranking List, sanctioned by the World Croquet
Federation, ranks the top 350 international tournament croquet
players, based on the results of "major" tournaments held around
the world. The list contains players from thirteen countries
(Australia, Canada, Switzerland, England, France, Ireland, Italy,
Jersey, New Zealand, Scotland, South Africa, the USA, and Wales).
The official list appears at the beginning and the end of the
year, with periodic updates appearing on the Nottingham board.
Since 1985, when the list began, 59,000 games have been included
in the database.
The listing itself is not complicated. Click here to see an example of a
recent ranking list. Along with the names of the
players only three numbers appear to the right of each name: the
ranking (a number equal to or greater than 1700), the number of
games played, and the number of games won. For example: "Robert
Fulford 2884 103 86." But to the uninitiated the ranking list is
mysterious. Its surface simplicity deepens the puzzlement players
feel when they scrutinize it.
How is the ranking derived? How are the games chosen for
inclusion? How does a player get included in the list?
For an explanation of the World Ranking List, Croquet World Online
Magazine turned to Chris Williams for enlightenment.
-- Mike Orgill
Croquet World Online Magazine: What is the World Ranking List?
Chris Williams: The World Ranking List is a ranking list of
advanced level singles international rules 26-point croquet games.
An official list is produced twice a year - at the end of March and
the end of October. For a player to be included in the published
list they must have played at least 10 games in the previous 12
months. Intermediate unofficial lists are put onto the net during
the year. The World Ranking List has been officially sanctioned by
the World Croquet Federation (WCF).
CW: How does it relate to other countries' ranking lists?
Chris Williams: The United Kingdom ranking list is the same as the World
Ranking List, but with only the UK based players included. The
Croquet Grading System (CGS), which is the name of the computer
program used to produce the list, started in the UK and has been
expanded to include events played around the world. Other
countries' ranking lists are produced using completely different
methods. Some are computer based, some are 'Grand Prix' based,
i.e., based on how far a player has got in certain key events.
CW: When did the list begin, and who started it?
Chris Williams: The list began in the early 1980s. Initially
Stephen Mulliner did the calculations by hand. A number of people
had input into the early systems. The current system has been
running since 1985 and includes some 59,000 games.
CW: How do you split responsibilities with Stephen Mulliner
for producing the Ranking List?
Chris Williams: Ideally we should both be entering the data
independently and checking that we have the same results. In
practice, I enter the data and Stephen checks it. Ideally, ranking
data and any comments should be sent to both Stephen and myself to
make certain of its receipt, but we keep closely in touch with
each other to reduce the risk of going astray.
CW: What is the purpose of the list? What role does it play in Britain in
selecting players for international teams?
Chris Williams: The list gives an indication of which players
fit into a selection criteria. It is useful for ensuring that no
players fail to be considered for selection.
CW: How does a player get listed if one isn't on the list
Chris Williams: A player can get into the database by playing in
an event which is included in the system. To get into the
published list a player must play at least 10 tournament games in
the relevant year. Usually the lists includes only players with a
minimum grade and up.
CW: Which events are included in the system?
Chris Williams: At first only games played in the UK were
included, but in the late 1980s when the WCF World Championship
started, data from the major non-UK events such as the New Zealand and
Australian Opens were entered. Over the next few years more and more
non-UK data was added, but the problem has been obtaining it, especially for the
minor events. To get as accurate a ranking as
possible we need as much data as possible. For example, every game
played by the leading players in all countries should be in. This
then means that games played by their opponents should be in,
because their grade would then be correct.
CW: How are results collected for input into the system?
Chris Williams: Data is supplied by a number of correspondents
worldwide. It is hoped that, as the Internet grows in size and
more overseas players get on-line, then more and more results will
be sent electronically. I am gradually building up contacts in all
the major countries, but would welcome copies of national Fixture
Lists, so I can tell which events are missing and hence what I
need to chase up. Don Gaunt is currently producing a world-wide
calendar, and this will help us make the list complete.
CW: What criteria do you use in including tournament results from
the United States?
Chris Williams: I include all U.S. international rules
tournaments that are submitted. This year the following U.S.
tournaments were included:
CW: How is the World Ranking System calculated?
USCA N.Carolina Championship
USCA N.Carolina Plate
Sonoma Cutrer World Croquet Championship
USCA Delaware Invitational
USCA National Championship
USCA California State Championship
USCA Chattooga Challenge
Chris Williams: The World Ranking system uses a system similar
to the Elo system in chess. A player gains and loses points after
each game depending on who has won and the current indices of the
two players. If a player beats a player on a much higher index
then more points change hands than if the higher ranked player
wins. Each event is given a weighting depending on its importance.
In a top class event (e.g., the World Championship) up to 6 points
can change hands, whilst a lower class event such as a consolation
one only 4 can do. Most events are 5-point events. The formula
where "idiff" is the winner's index minus the looser's index (keeping track of the sign) before
the game and "Class Factor" is 6, 5 or 4 depending on the event.
This means that for a Class Factor 5 game a difference of 15
points in the grades leads to 1.67 points changing hands if the
player with the higher index wins and 3.33 if the player with the lower index wins. Each player
has an "Index" which is changed after every game according to the
result and the current indices of the two players concerned.
The winner adds an amount to his existing "Index", while an equal
amount is subtracted from the loser's "Index". The following
procedures are used to calculate new "Grades" after each game.
CW: Hold on! What's the difference between a "Grade" and an
Chris Williams: The "Grade" is simply a damped value of the
"Index". After each game, the new "Index" often varies enough to move a
player 10 places, and this would result in a very volatile ranking list. The
change in "Index" is therefore converted in a change in
"Grade" by using the damping formula, which is:
New Grade = (0.9 * old Grade) + (0.1 * New Index)
CW: OK, go on. How is the new index calculated?
Chris Williams: First, a new "Index" is calculated for each
player using the formula above. This formula assumes that a
player's index is in the range 0 to about 200, and that each game
has a weighting factor of 4, 5 or 6. In practice, a factor of 6 is
used for major events, such as world championships, international
matches, and some national championships; a factor of 5 for
national and regional championships and some major national
events; and a factor of 4 for other "A" class events that are
The new Indices are used to calculate intermediate grades, using
the damping formula given, after which the intermediate
grade figure is multiplied by 10. The new "Grade" to be used in
ranking each player is then obtained by adding 1000 to this
result. Since the changes in the index can be quite volatile we
apply the smoothing function to arrive at the grade used for
ranking purposes. All this means that the system is objective and
depends on the results achieved by a player and the standard of
opponents. Lots of wins against opponents with low grades will not
give many points.
For an example of the ranking calculation, click here.
CW: How is the initial grade set when a player enters the
Ranking List for the first time?
Chris Williams: When they first enter the system, players are
given an initial grade based on their handicap. Internally the
grades of players vary from about 40 for the worst to 190 for the
best. In the UK we have introduced an Automatic System for
handicaps which uses numbers in the thousands. In order to make
the systems appear similar 100 in the ranking system equates to
2000 in the published rankings. (110 = 2100, 120 = 2200, etc.) A
review of this initial grade is carried out after the first few
game results have been processed for the new player, and if
necessary, the initial grade will be altered and the calculation
re-run to give a result that appears correct. New players are
usually given a grade between 1700 and 1900.
CW: Have any statistical studies been done on the list's utility
in predicting the outcome of matches?
Chris Williams: Yes. The calculations do have a statistical
basis. The CGS is based upon work done in Chess, namely the Elo
Chess ranking system. Players gain points based on the difference
in the grades of the two players. If the player with a higher
grade wins then fewer points change hands than if the lower graded
player wins. As a player's grade rises it gets harder and harder
for them to gain points. If a player only plays 'weak' opponents
then he or she will gain very few points.
CW: Is the list more valid for British players because of the
greater number of matches and tournaments used in the ranking? Are
the rankings of players from other countries less valid for this
Chris Williams: Yes. The more games played the more accurate the
position. Though above a certain number of games there is very
little difference. A reasonably good ranking can be done on as few
as 10 games.
CW: Do you have any data giving the probability of differently
ranked players beating each other?
Chris Williams: In our grading system, a difference of 150
points means there is a two to one probability of the higher-
ranked player winning, that is, the better player should win a
best-of-3 match by 2 games to 1. A difference of 300 points
corresponds to a probability of 4 to 1.