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Last updated

21 Feb 2017
3:03 pm

Elo system

On January 2000 the European rating list and the American rating list were converted and united. New rules about what rating you need to get a certain grade were created. As a concequence some players got an automatic promotion on 2000-01-01. The sourcode for the ratingprogram can be found here.


Here is a short description of the rules of the new elo-system. Some prior knowlegde of ELO rating is an advantage:

  1. The basic formula when updating the rating values for a person is:
    d = k * (res - 1/(1+10^((or - tr)/400))) where
    d is the change (rounded to the nearest integer)
    k is a coefficient
    res is the result (1 for victory, 0 for defeat, ½ for draw)
    or is the rating for the opponent, except that if it is less than 400 then 400 is used instead
    tr is the target rating (the rating for the player that is updated)

    The coefficient k could be written k(tr) as it is based on the
    rating to be updated according to this table:

    2240 <= tr         16
    1920 <= tr < 2240  20
    1560 <= tr < 1920  24
    1280 <= tr < 1560  28
    1040 <= tr < 1280  32
     720 <= tr < 1040  36
            tr < 720   40

    In some cases this formula is used instead: d' = k * (or - tr)/160 and the cases are when the result is 1 (a victory for the player that is updated) and d' > d.

  2. Included into the rating system is also a grade system. Promotions are based on rating and the requirements for promotions and the basic correspondence between grades and rating are summarized in this table:

             LB   MP   UB    #LB  #MP
     6 Dan  2440 2540 2640     
     5 Dan  2240 2340 2440         10
     4 Dan  2080 2160 2240    16    8
     3 Dan  1920 2000 2080    16    8
     2 Dan  1800 1860 1920    14    7
     1 Dan  1680 1740 1800    14    7
     1 Kyu  1560 1620 1680    14    7
     2 Kyu  1460 1510 1560    12    6
     3 Kyu  1360 1410 1460    12    6
     4 Kyu  1280 1320 1360    12    6
     5 Kyu  1200 1240 1280    10    5
     6 Kyu  1120 1160 1200    10    5
     7 Kyu  1040 1080 1120    10    5
     8 Kyu   960 1000 1040     8    4
     9 Kyu   880  920  960     8    4
    10 Kyu   800  840  880     8    4
    11 Kyu   720  760  800     8    4
    12 Kyu   640  680  720     6    3
    13 Kyu   560  600  640     6    3
    14 Kyu   480  520  560     6    3
    15 Kyu   400  440  480     6    3
    16 Kyu   320  360  400     6    3
    17 Kyu   240  280  320     6    3
    18 Kyu   160  200  240     6    3
    19 Kyu    80  120  160     6    3
    20 Kyu     1   40   80     6    3

    LB means lower bound, MP means midpoint, and UB means upper bound.
    #LB and #MP are explained in (10).

  3. The players are divided into three categories when rating a tournament:
    - unrated players
    - players with provisional rating
    - established players

    Players whose prior results only include victories or only defeats (including players with no prior results) AND players with less than 9 rated games are unrated players.

    A player who is not an unrated player and whose number of rated games is less than 18 is given a provisional rating. Else a player is considered to be an established player.

    When counting for 9 or 18 games the games in the tournament currently being rated are included.

  4. Games not played are not rated. So if a player gets a walk-over or a scheduled game is not played for instance because one of the players do not show up, that result has no effect whatsoever when calculating the rating changes.

    Games replayed because of sennichite or jishogi are rated as a draw.

  5. Performance rating of a set of results for a player is the perfect performance rating rounded off to the closest integer. If you rate each of the games in the set using (1) with the perfect performance rating as tr and the opponents (post event) rating at the time as or, then the sum of the different d's is zero. Performance rating is not defined if the outcome of all the games is 100% victory or 100% defeat.

  6. Unrated players get their rating by calculating their performance rating for all prior recorded results and all played games in the current tournament. When recording a result the rating is the post-event rating for the opponent. That is the opponents rating after the current tournament. If the score is 0% the rating is set to 1. If the score is 100% a temporary draw result against the highest rated opponent is inserted. This dummy draw is not recorded afterwards, it's just used during the performance rating calculation and the result is used when rating the players opponent in that tournament.

  7. A newcomer with a prior grade is rated as an unrated player but starts with a prior result of 2 games consisting of one victory and one defeat against a dummy player with a rating equal to the MP of the players grade (2). This prior grade is assumed to be some kind of official grade based on actual results achieved. An evaluation performed by a professional or others based on the subjective feel of the quality of some games played does not give a newcomer a prior grade.

    A prior grade is not a FESA/USSF grade and is recorded separately from the FESA/USSF grade.

  8. When rating an established player the formula in (1) is used where tr is the players rating modified with the +/- results of the earlier rounds in the tournament and or is the opponents post-event rating.

  9. Players with provisional or established rating which is below 1800 gets a bonus of (1800 - tr)/200 points per game but only for 100 games.

  10. Promotions:

    The table from (2) is used.

    An established player has 3 ways of achieving a grade
    - reach the UB of a grade
    - stay above the MP for #MP consecutive games
    - stay above the LB for #LB consecutive games including 1 game above MP

    If a player does not have the required number of games above a limit to get a grade, but is bound to get it if he plays some more games no matter the outcome, the grade is awarded immediately. The calculations are based on the fact that the maximum number of elo-points a player can lose in a single game is the players coefficient (1).

    When counting the number of games above a limit, the total rating change for a tournament is divided equally on all games played in this tournament. The actual sequence of the games is of no significance.

    Provisional players can only achieve a grade by reaching the UB of the next grade above.

    Unrated players can not get a grade, but keep any prior grade.

    5 Dan and 6 Dan is not awarded without the approval of Nihon Shogi Renmei.

  11. In the above, when the word tournament is used, it would be a little more precise to say that the "basic unit of rating" is the table. A players rating is updated after each rated table.

    If at the end of a tournament there is some kind of play-off, for instance as a tie breaker for the first place instead of using "quality" points, and the play-off is done at the "same time" as the main tournament, then all the results should be entered into the same table. If a play-off is set as a separate event at a later stage it should be in a separate table.

  12. Most games played with a handicap are also rated. The handicap effect is defined as

    Sente (instead of furigoma)             0.2
    Lance (left)                            0.6
    Bishop                                  1.5
    Rook                                    2.1
    Rook and Lance (left Lance)             2.7
    2 pieces (Rook and Bishop)              3.6
    4 pieces (2 pieces plus both lances)    5.0
    5 pieces (4 pieces plus right knight)   6.5
    6 pieces (4 pieces plus both knights)   8.0

    The value is comparable to a number of grades.

    When calculating the handicap rating effect you start with the rating of the handicap giver and translate it into a fractional grade number based on the LB values (2) of the different grades. Then the handicap effect from the table gets subtracted. This value is then translated back into a rating number. The difference between this number and the initial rating is the handicap rating effect. When calculating the rating change for the handicap giver the handicap rating effect is added to the rating of the opponent. When calculating the rating change for the handicap receiver the handicap rating effect is subtracted from the rating of the opponent.

Asle Olufsen


[Last edited: 2016-02-04]