# simple point ranking scheme

__Keywords__: Tournament

This scheme is derived from Point Ranking Scheme At Tokyo Go clubs and has elements of kadoban.

The difference is that there is no predefined lookup table to decide on handicaps, no komi, and no mapping to kyu/dan ranks.

# The basic ideas

- arithmetic rather than table lookup
- winning three games in a row gives an extra handicap to fight against (a 3-game kadoban)
- unstable ratings do not impact stable ones. a stable rating has roughly as much wins as losses; an unstable rating is still climbing or descending to its actual value, as long as a game does not break (reverses) the progression, the opponents should not be impacted.
- no komi
- players manage their own simple A6-sized grid that records played games and the rating history.

# the grid

The grid is an A6 that records game information on the opponent, the outcome, and the updated player rating.

The A6 front is used for 9x9, back for 13x13. This means that players have separate 9x9 and 13x13 ratings.

name: Jim | 9x9 | ||||

date | opponent | opp. rating | H | res. | your new rating |
---|---|---|---|---|---|

121111 | John | 80 | 0 | W+20 | 85 |

121112 | Joe | 95- | 2 | B-10 | 84 |

121115 | Jane | 80+ | 1 | W-10 | = |

# stability (reliability)

This is an optional feature of the scheme.

Stability is an indication of the ratio of won or lost games over a sliding window of N=6 *rate-changing games* (ie games for which there was an update in the rating, so where there is no '-'). Excessive amounts of wins/losses indicate that the player's rating might not represent his/her true rating. In such cases, the rating of an unstable player is suffixed with a '+' or '-' to indicate that most games were won or lost in a window of N last games. in the example, Joe has lost many recent games, and Jane has been winning a lot.

Why N=6? There is no mathematical or empirical foundation for this value; it was chosen because it is small and seems to be relevant in following reasoning: when winning 3 out of 6 games, a player is "super stable". 4 out of 6 wins/losses still feels acceptable; 5, and certainly 6 out of 6 wins/losses smells like a player that is under/overrated.

# new player

When a new layer enters the system, a seasoned player assigns a rating. Rating chosen is left to the feeling of the seasoned player, possibly after playing a few games to see which handicap suits the new player. As this process can give a wrong result, the stability mechanism initially protect other players from a wrong rating.

The seasoned player could be chosen as reference in the point system and start with 100.

The game could already be recorded on the grid - this is valuable information.

# new game

- announce your rating (and stability, if in effect) to your opponent. your rating is the last non-dashed value (84 in the example)
- record opponent data
- determine handicap
- play; record game result (your colour + outcome)
- update rating if applicable
- determine stability if rating changed

## how handicap is determined

The handicap is the difference in ratings between W and B, divided by 6, then truncated (ignore the fraction), plus 1.

Examples:

- 85 - 60 = 25; 25/6 = 4.166; H = 4 + 1 = 5
- 110 - 98 = 12; 12/6 = 2; H = 2 + 1 = 3
- 107 - 90 = 17; 17/6 = 2.833; H = 2 + 1 = 3

Notes

- H = 1 means Black begins
- nigiri in case of identical rating

## how the rating is updated

General rule: to update your rating, add 1 if won; deduce 1 if lost; keep the rating if jigo; special rules apply in case of instability (see further).

Note that this stability concept is not necessary to apply the scheme, so it can be thrown overboard.

Detailed rules: Update your rating if either

- you are unstable
- the opponent is stable
- the opponent is unstable and reversed his/her progression (ie was X+ and lost the game, or X- and won the game)(as in the game against Joe in the example)

Otherwise, put a dash ('-') for your rating instead of the value (as in the game against Jane), because this game will not count for your rating.

## how stability is determined

- Count back to the 6th updated rating (ie ignore those games that have a '-')
- Compute the difference between your rating in the 6th updated game and your last updated rating
- If the difference is more than 4 in absolute value, you are unstable. Suffix a '+' to your new rating if the difference is positive (ie your rating is climbing), '-' if negative.
- if less than 6 updated games, you are ... stable.

Games marked with an outcome '-' do not count, because they were played against an unstable opponent and the outcome confirmed the opponent's progression: the opponent's rating (X) was climbing (X+) and (s)he won the game, or descending (X-) and the opponent lost the game. The '-' is a visual aid to skip games that did not change the rating.

# Remarks

- The scheme might have issues, but it has worked for a while at my (former) company for 9x9 (and even 13x13) boards with around 5-10 players estimated 25k-10k.
- there is an oddity when having less than 6 games, as almost per definition you cannot be stable yet
- other win/loss ratios might be better
- When a player keeps winning, that does not mean that his/her rating is wrong, maybe the opponent's might be.
- komi could/should be introduced to refine the points scheme. however, as there is no agreed komi for 9x9, and because this is a rather informal scheme, especially in DDK situations, komi can be excluded (see also Handicap For Smaller Board Sizes).
- the Points Rating System suggests to stick to one change per opponent per day