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Technical
The Croquet Ranking System

Chris Williams writes

The ranking system was developed by Stephen Mulliner in the mid 1980s and uses a system similar to the Elo one 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 (eg, 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 used is

formula

where idiff is the difference in the two players indices 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 better player wins and 3.33 if the poorer player wins. Since the changes in the index can be quite volatile we apply a smoothing function to arrive at the grade used for ranking purposes.

The smoothing factor is

formula

a varies from 0.9 to 0.97 depending on the grade of the player.

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.

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., index = 1000 + {internal *10}). Therefore for the new number base of 2000 multiply figures by 10 (ie, Class Factors become 50 and a difference of 150 leads to 16.7 points changing hands.)

Hence a player in the UK with a grade 2100 (New number) will probably have a handicap of about -0.5. Similarly a player of grade 2000 will be a scratch player.

At first only games played in the UK were included, but in the late 80s when the World Championship started, data from the major non UK events such as the NZ and Australian Opens was 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.

When a new player is introduced to the system they are usually given a grade of between 70 and 90 (1700 and 1900).
 

See Notes for details of setting of Class Factor and alpha

Author: Chris Williams
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Updated 28.i.16
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