## International Qualification (Rating) System of R.I.F.

In order to inspire and encourage renjuplayers all over the world to make good results in important Renju tournaments, and in many cases distinguish players for qualification to international tournaments, an international system with internal rankings between renju players from the whole world is introduced.

The following rating rules are effective from August 8, 2021 (R.I.F. General Assembly 2021).

Whole-History Rating (WHR), is an algorithm created by Rémi Coulom in 2008 in his paper, *Whole-History Rating: A Bayesian Rating System for Players of Time-Varying Strength*. In the WHR algorithm, the complete historical game records with time information are used as input, to fit the player ratings at different time slots in their active periods.

**1.** In WHR, each player is assigned a rating as a variable at each time point. These variables are used to construct a probabilistic model, and computed together to get the ratings of all players at all time points, in order to optimize the objective function of the probabilistic model.

**2.** The ratings computed with WHR satisfy a dynamic version of the Bradley-Terry model. For game *g* between player *A* and player *B* at time *t*, assume their ratings are *R _{A}*(

*t*) and

*R*(

_{B}*t*) at time

*t*. According to the Bradley-Terry model, the expectation score player

*A*gets will be:

**3.** The WHR model assumes that a player would have similar scores at adjacent time points. For *R _{A}*(

*t*

_{1}) and

*R*(

_{A}*t*

_{2}), when

*t*

_{2}>

*t*

_{1},

*R*(

_{A}*t*

_{2}) follows a Gaussian distribution with the center point to be

*R*(

_{A}*t*

_{1}):

Here *w* is a hyperparameter showing the changing rate of player ratings.

**4.** Given the above distribution, when the value of *r*_{1}=* R _{A}*(

*t*

_{1}) is fixed, the probability density function of

*R*(

_{A}*t*

_{2}) will be:

Here *σ*=*w*(*t*_{2}–*t*_{1})^{1/2}.

**5.** Following the above assumptions, we have the following probabilities:

- For each game, the probability that the result predicted by the Bradley-Terry model is consistent with the truth. This probability is equal to
*p*=_{A}*E*(_{g}*R*(_{A}*t*),*R*(_{B}*t*)) when*A*wins*B*,*p*=1-_{B}*E*(_{g}*R*(_{A}*t*),*R*(_{B}*t*)) when*B*wins*A*, and (*p*)_{A}p_{B}^{1/2}when there is a draw. - For each player and each pair of adjacent time points
*t*_{1}and*t*_{2}, the probability density*p*(*r*_{2}|*r*_{1}).

**6.** Multiplying the above probabilities, we get a function with the inputs to be the ratings of all players at all valid time points *R _{p}*(

*t*). Assume that

**R**is the set of all these historical ratings, and

*G*is the set of all games. According to the Bayes’ law, given the set of all games

*G*, the probability density of ratings

**R**will be:

Here *p*(*G*) is a constant, *p*(*G*|**R**) is the product of all the elements in (i), and *p*(**R**) is the product of all the elements in (ii).

**7.** In the above equation, the only set of variables are **R**. Thus, as long as we compute the values of **R** which maximize the value of the objective function *p*(**R**|*G*), we get the ratings of all players at all time points in the same time. By iterating with the Newton’s method, we can get the solution to the problem.

**8.** The following are some supplementary details during the rating calculation:

- During the computation of renju rating, the hyperparameter
*w*is set so as to let*w*^{2}=12.9. - For the purpose of regularization, there are 2 virtual games assigned to each player. That is, for each player, on the day of playing his/her first game, 2 virtual draws are assigned to the player, assuming the virtual opponent to be rated 1900.
- The Newton method is run for 100 iterations to get the converged final ratings, starting from the initial ratings of 1900 for all players.
- If not specified, the date of a game is considered as the last day of the tournament during the calculation of the rating.

**9.** Since this rating rule takes effect (August 8, 2021), tournaments that meet the following conditions will be counted in the rating list:

- The tournament needs to be played with one of the R.I.F. certified rules, including the R.I.F. rule, the Yamaguchi rule, the Soosyrv-N rule, the Taraguchi-N rule, the Yamasyrv-N rule, and the Sakata rule.
- The time limit for each player needs to be no less than 30 minutes.
- The complete game records of the tournament need to be input into the database of the R.I.F. website.
- Generally, the tournament needs to be played face-to-face. In special cases, some important online tournaments can be included in the rating list, but all games need to be monitored strictly by video meetings, and there should be referees recognized by RIF or national federations to ensure the fairness of the tournament.

**10.** About active and established players:

- A player is an active established player, if there are at least 10 rated games, and the last game was played no more than 5 years ago.
- A player is an inactive established player, if there are at least 10 rated games, and the last game was played more than 5 years ago.
- A player is a provisional player, if there are no more than 9 rated games.

**11.** The rating list is updated automatically every day with the open source code.

### Appendix: Historical Decisions on the General Assembly

#### General Assembly 1995

**#1.** To achieve an estimation of quality of a players momental playing strength a system with individual coefficients (rating) is used, an adapted variant of professor Arpad Elo's system.**#2.** The official international rating coefficients for all renju-players are calculated three times per year - April 30, August 31, and December 31 - by the International Qualification Commission in R.I.F.

The rating is based on results from individual games between players in renju tournaments with direct play, and with a minimum time access of 60 minutes per player and game, and with no time limit to watch before 60 minutes.

Following types of tournaments will entitle to international rating:

- World Championships (WC) finals
- International Qualification Tournaments for WC-finals
- Open International Tournaments in connection with WC
- National qualification tournaments for WC in R.I.F. member countries (though not the countries regional qualifications)
- European Championships
- Other open international renju tournaments, sanctioned by R.I.F. Central Committee.
- National Championships in R.I.F. member countries, final tournaments
- Some other important tournaments of national character, which the R.I.F. CC may decide to sanction, if those tournaments are open for all RIF players.

Requests regarding sanctioning a national tournament must be made to CC, not later then three months ahead of the tournament. International tournaments must be announced in the official journal "Renju World" or in other official R.I.F. periodical, or a special invitation must be sent to all R.I.F. member countries, which is received

by the official R.I.F. predecessors in these countries not later then three months ahead of the tournaments.

**#3.** The qualification commissions in the R.I.F. member countries must send a report, after each concluded tournament in their country (which entitle the players to international rating), to the International Qualification Commission in R.I.F. about the results in tournaments according to #2, which includes complete tables of all individual results in these tournaments. If this will not be done after three months after the tournament the responsible federation have to pay a fee (USD 20).

In December each year, a report is also given about players, who are no longer members in the national renju federations, where after ratings for these players are no longer published by R.I.F.

Players from countries without a national renju federation connected to R.I.F. can get rating from all tournaments in 2nd #7 where they have the right to participate (if not the R.I.F. GA or CC decides else).

**#4.** Only tournaments, which are played according to the International Renjurules of R.I.F., can entitle players to an international rating.

Only results from games played in reality will be counted. A game is counted as "played in reality" and entitles both players to receive rating if somebody won the game or they agreed to make a draw in the game (no "walk over"). If a break is made in a game and one player does not appear when the play is about to continue, the game will be counted as "played in reality" for both players regardless of which the referee's decision about the result in the game will be.

**#5.** In the beginning of a tournament the players have start ratings, which are equal to their the current official rating coefficients. After a tournament, which entitles the players to international rating, all contributions (positive or negative) to a given players start rating coefficient are summed up. All players total rating contributions in tournaments finished latest April 30, August 31, and December 31, are summed and added to their current official rating, which give all players new official rating coefficients on the given dates. (see #8 about how this start rating is calculated for "new" players)

**#6.** The contribution (positive or negative) to a given players start rating coefficient in a tournament is calculated as:

**F = 32 x (Et - Ee)**

where

F is equal to the total contribution (positive or negative) to a players start rating coefficient,

Et is equal to the total number of gained points by the player in games, which entitle to rating in the tournament,

Ee is equal to the expected number of points, which the player must achieve to receive no rating contributions at all in the tournament.

**#7.** To find Ee for a player, a calculation is made:

**Ee = N/(1 + 2 ^{dR/120})**

**dR = (P _{1} x R_{1} + P_{2} x R_{2} + ... + P_{m} x R_{m}) / N - R**

where

dR is equal to the difference between the average start rating coefficients for the opponents and the start rating coefficient for the player,

R is equal to the start rating coefficient for the player, P_{1}, P_{2}, ..., P_{m} is equal to the number of games the player has played against the respective opponents, R_{1}, R_{2},..., R_{m} is equal to the start rating coefficients of the respective opponents,

M is equal to the number of opponents,

N is equal to the total number of games played in the tournament by the player.

After the calculation, F is rounded to the nearest integer. (see the appendix for a table, which makes it easy to estimate the rating contributions based on results in individual games)

**#8.a.** A "new" player, who has not earlier played in a tournament which, entitles to international rating, must play at least three games in a tournament to be entitled to receive a start rating coefficient in a tournament. If a "new" player has played in such a tournament before, but has not yet received an official international rating

coefficient, his start rating in this tournament is equal to his start rating in the last previous tournament with the achieved rating contributions added.

**#8.b.** The "new" player, will achieve a start rating coefficient (Ro), which is inside the interval 2000 - 2400 at his first appearance in a tournament, which entitles to international rating, if the average rating (Ra) for all is opponents he has played with in the tournament is 2200 or higher. If Ra would be lower then 2200, then Ro is calculated in the interval (Ra - 200)

**#8.c.** Though, a player who gains 0 points in a tournament in all matches against players, who have an official international rating coefficient, will not achieve a start rating in the tournament. No rating contributions, based on results in matches where both players do not have a start rating, will be calculated for either player in such matches.

**#8.d.** The start ratings for the "new" players are calculated after all matches in a tournament are finished, and are based on results in the individual matches.

If one or several "new" players take part in a tournament, start rating coefficients for these players must be calculated first, before the calculations of rating contributions for all players begin.

The "new" players are considered to have the same playing strength in the beginning of the tournament as in the end of the tournament. This means that the rating contribution to a "new" players start rating must be zero as long as the start rating coefficients is higher then the lowest rating in the interval and lower then the highest rating in the interval, according to point b. If the start rating coefficient is set to the minimum level in the interval, the player can get a negative contribution of rating points, and if the start rating coefficient is set to the maximum level of the interval the player can get a positive contribution of rating points.

For the "new" players: **Ee = Et **and

** R _{0} = (P_{1} x R_{1} + P_{2} x R2 + ... + P_{m} x R_{m}) / N - dR**

** dR = 120 x log _{2} (N / Ee - 1)**

Though, R_{0} must be inside the interval, according to point b., and the conditions in point c. must by be paid attention to.

Rating contributions are calculated for all players in a tournament, who are entitled to start ratings, according to the formulas in #6 and #7.

**#9.** A renju player, which due to different reasons has lost his official rating coefficient, can regain his old rating again when his national renju federation approves.

After five years absence of an internationally rated player, from tournaments entitling to international rating (according to #2), official RIF-rating is no longer published. Though, by renewed activity the player regains his old rating.

**APPENDIX**

Table based on the formulas in #6 & #7 for an estimation of rating contributions in individual games.

If a player having the start rating R_{1}, has higher (or same rating) then a player with the start rating R_{2}, the rating contributions in a game rounded to an integer and with different results in the game would be:

Rating difference | R_{1} wins | R_{2} wins | Draw |
---|---|---|---|

0-10 | +16 | +16 | +0 |

11-32 | +15 | +17 | +1 |

33-54 | +14 | +18 | +2 |

55-76 | +13 | +19 | +3 |

77-100 | +12 | +20 | +4 |

101-124 | +11 | +21 | +5 |

125-149 | +10 | +22 | +6 |

150-176 | +9 | +23 | +7 |

177-204 | +8 | +24 | +8 |

205-236 | +7 | +25 | +9 |

237-272 | +6 | +26 | +10 |

273-313 | +5 | +27 | +11 |

314-363 | +4 | +28 | +12 |

364-427 | +3 | +29 | +13 |

428-521 | +2 | +30 | +14 |

522-724 | +1 | +31 | +15 |

725-2000 | +0 | +32 | +16 |

#### General Assembly 1996

Decisions made by the R.I.F. GA in the meeting on May 2, 1996.

**1.)** Calculations are made for a number of old tournaments (see below), from August 1988 to April 1996, and the first Official Rating List will be valid from 1 May 1996. The list of old tournaments for the years 1988 -1996 to be included and counted in the process of the rating calculations is as below:

1988

Stockholm Summer Trophy

Meijin tournament & final

4th Soviet Open team Championship

Swedish CS-final

1989

1st Soviet CS, 1st league

1st Soviet CS-final

Swedish WC Qual. final

Japan WC Qual.

WC-final

WC open tourn.

Meijin tournament & final

Federation Cup in USSR

2nd Soviet CS, 1st league

Swedish CS tournament

1990

Leningrad New Year Prize

Swedish CS tourn.

2nd Soviet CS-final

Open Soviet team CS

Karepa

Swedish Open CS

Meijin tourn. & final

Tokyo Int. Tourn.

3rd Soviet CS, 1st league

1991

Leningrad New Year Prize

3rd Soviet CS-final

Swedish CS tourn.

Japanese WC Qual.

Swedish WC Qual.

WC-final

WC open tourn.

Baltic Cup in Riga

Meijin tourn. & final

Tokyo Int. Tourn.

4th Soviet CS, 1st league

Linkoping Open tourn.

Tallin Int. tourn.

1992

S:t Peterburg New Year Prize

Latvia CS-final

Swedish CS tourn.

4th Soviet CS final

Swedish Open in Arjeplog

Karepa

Meijin tourn. & final

Riga Independence Cup (Latvia Open)

Tokyo Int. tourn.

1st Russian CS, 1st league

S:t Peterburg New Year Prize

1993

1st Russian CS-final

Latvia CS final

Latvia WC Qual.

Armenia CS final

Swedish CS tourn.

Estonia WC Qual.

Karepa

Japanese WC Qual.

Swedish WQ Qual.

Int. WC Qual. tourn.

WC-final

WC open tourn.

Meijin tourn. & final

2nd Russian CS, 1st league

Tallin New Year Prize

1994

2nd Russian CS final

Swedish CS tourn.

European Team CS

Latvia CS final

Karepa

Kyoto Memorial Int. tourn.

Armenia CS final

Meijin tourn. & final

3rd Russian CS, 1 st league

1st European CS in Tallin

1995

3rd Russian CS final

Swedish CS tourn.

Latvia CS finals

Baltic league

Japanese WC Qual.

Swedish WC Qual.

Latvian WC Qual.

Int. WC Qual. tourn.

WC-final

WC open tourn.

Armenia CS final

Meijin tourn. & final

4th Russian CS, 1st league

2nd European CS in S:t Peterburg

1996

4th Russian CS final

Latvia CS finals

Swedish CS final

("CS" means Championships, "WC" is World Championships)

**2.)** In a few tournaments results are still not gathered (or incomplete) by QC.

If it is impossible to get complete results from these tournaments before the end of May 1996, these tournaments will be excluded from the rating calculations.

**3.)**The rule in #8c. will not be used when calculating rating contributions in tournaments played earlier then 1996. Also, the minimum time access in games played in tournaments before 1996 is only 45 minutes / player.

**4.)** Such national tournaments as the yearly first league of Russia, the Baltic league and qualification tournaments ahead of Meijin tournament may be such tournaments to be sactioned by RIF CC.

RIF GA in S:t Petersburg

May 2, 1996

#### General Assembly 1997

**3.** New ratings will be calculated after each tournament (or event) and, normally, in chronological order by their ending dates. The ratings produced by each event are used for calculation in next event, and so forth. Results from tournaments, which are played during a longer time must be reported after each separate stage of the tournament. If a separate stage of a tournament also is played during a longer time results can (and are encouraged to) be reported after each playing event to RIF QC. However the dates of reports must be annouced in advance to QC.

**5.** Players with official ratings (and published) are called "established". Players with eastalished ratings are those who after an event have played at least 10 games with other established players AND earned no less then 3 points totally in these games (win=1 point, draw=0.5 points). Players who have played less then 10 games with established players OR earned less then 3 points in these games are called "provisional". Provisional rating are not published.

**6.** For established players ratings are only calculated in games with other established players.

**7.** Provisional ratings is calculated as

**Rp = Ra + (400 (W - L)) / N**

Rp - the performance rating (i.e. the new rating)

Ra - the average rating with established opponents

W - the number of wins

L - the number of losses

N - the number of games

Provisional ratings are much less reliable than established ratings. Rp is maximized to Ra+300.

**8**. For established players ratings are calculated as before, but only calculating each game separately:

**Rc = 32 (W - We)**

Rc - the rating change from one game.

W - result of a game in points (win=1 point, draw=0.5 points, loss=0 points)

We - expected score (Win Expectancy) from following formula:

**We = 1/(1 + 2 ^{(dR/120)})**

dR - difference in ratings between the players

The established players changes of ratings can also be approximated from a table as before. The rating changes Rc added up from each game are added after the event and rounded.

**9.** A players who is provisional at the start of an event stays provisional through the whole event until a new ratings are calculated. If the provisional player during a tournament has fulfilled the conditions to become an established rating his provisional rating will turn into established after the event.

#### General Assembly 2021

According to the Decision 12. a) of the General Assembly 2021, R.I.F. has decided to migrate the rating system from Elo to WHR (whole-history rating).

Using the WHR system, with “recalculating all history” over and over again, will enhance the ratings concerning players who are mainly playing local tournaments. WHR was approved by the meeting.