# Ranking

The Ranking System ranks all croquet players in the world, separately for Golf Croquet and Association Croquet.

These rankings are based on results from all tournaments and competitions played world-wide to the internationally recognised rules, including local club ones. Revised rankings are normally calculated at the end of a tournament. Some players are not included in the published lists as they have played only a small number of games. A description of how it works is below.

Although there is a correlation between your Grade in a Ranking System and your Index in the equivalent Automatic Handicap System they are actually independent of each other; apart from anything else they are determined using different sets of games, with the Ranking System being a subset of the Automatic Handicap System.

The systems are provided by the World Croquet Federation, with the Golf Croquet version using results from Level-Play GC games and Association Croquet version using results from Advanced Level-Play AC games.

The performance of players from the UK (plus overseas players who are resident in the UK) can be extracted from the International rankings by selecting the appropriate list.

For more details, including how to submit results see

# A Simple Guide

Stephen Mulliner as the originator of the system wrote the following for the layman a few years ago:

The system recognises that there is more merit in scoring five out of ten against ten very strong players than five out of ten against ten very weak players. That is why a simple ranking system based on the percentage of wins is unsatisfactory.

The system needs a consistent basis for deciding how much more credit to give X for beating a relatively strong player than a relatively weak player and, the other side of the coin, how much less discredit to give for losing to a relatively strong player than a relatively weak player. All mentions of "relative" are to the strength of X.

The basis chosen is a relationship called the Verhulst or logistic distribution which is a close relative of the normal distribution but easier to use in a simple computer (which is all I had in the early 80s). This is in turn based on research done by Arpad E. Elo who created the modern chess ranking system. Elo's central principle is that "the many performances of a player in pairwise competition will be normally distributed [about an average level]". He observed this as a phenomenon and was able to prove that it worked mathematically because his ranking lists agreed with surveys of players' opinion and, more importantly, his rankings had reasonable predictive power. The Normal Distribution is the formal name for the bell-shaped curve that appears to describe many naturally-occurring distributions (heights of children in a class etc.).

After a game has been entered into the system the output from the formula is the "increment" which is added to the winner's index and subtracted from the loser's index to produce the new indices. If the winner had a much higher index than the loser, this implies that he was highly likely to win and the increment will be small, i.e. close to zero. Hence the winner's and loser's indices will be little changed which is consistent with the low degree of "surprise" in the result. If the winner had a much lower index than the winner, this is a surprise result and the increment will be large, tending to a maximum of approximately 19 for very unexpected results.

The current GC ranking system has two features which are designed to make the process more accurate. First, the start grade allocated to a new player can be changed automatically between their 20^{th} and 30^{th} game if their performance in those games suggests that their start grade was not a good indicator of their actual play in their first ranked games. Second, the system detects players who are winning or losing more games than might be expected. Such players are said to be "mobile" and the increment calculation for their subsequent games is based on a higher modulator than the value of 19 mentioned above.

I hope this helps a bit. If you want to understand exactly how it works, the articles already published are the best source. A degree in maths is not necessary but some familiarity with probability theory would help.