# 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.

### 0 Intro

Ratings and grades are updated after each rated tournament. The following is how that updates are done for one tournament (called the tournament or the current tournament)

### 1 Basic formula

To calculate the rating change after a game you normally use this formula

f(pr, or) = 1/(1+10^((or-pr)/400))

where *pr* is the players rating before the game and or is the rating of the opponent after the tournament (also called the final rating of the opponent).

The rating change is then

k(pr) * (result - f(pr, or))

where result is *1* if the player wins, *0* if the player loose and *1/2* if it is a draw and *k(pr)* is from this table:

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

The total rating change for a player in a tournament is the sum of the rating change for each game. When adding up the results from each game the decimals are kept, but when you have the total sum it is rounded to the nearest integer.

**Comments:**

The model that this is based on is that f(pr, or) is the assumed probability that a player with a rating of pr is going to win against a player with a rating of or and the formula is an approximation to a normal distribution

pr is the rating before each game instead of the rating before the tournament. Otherwise you would need to put a limit on how many games there can be in one tournament.

or is the final rating of the opponent instead of before the tournament because that is a better value for the opponents strength in the tournament and the system does not need to make special exceptions for handling tournaments with players who does not have a rating value before the tournament and especially when such a player plays against another one without a prior rating.

A consequence of the rule for or is that you need iterations and calculate the players final rating repeatedly until you get stable values.

### 2 Performance rating

Instead of using the formula from (1) , you use performance rating when

- this tournament is the first tournament a player played in

or

- the total number of games the player has played, including this tournament, is less than 9

or

- all results from prior tournaments are victories

or

- all results from prior tournaments are defeats

When calculating the performance rating all results in the current tournament and all results in prior tournaments are used. Performance rating is the rating a player needs to have before a sequence of results, in order to have the same number afterwards (ignoring the order of the games). In other words the 0-point of the following function:

g(x) = sum (i, 1, n, res(i) - f(x, or(i)))

where *n* is the number of games included in the calculation, *res(i)* is the result in game *i* and *or(i)* is the (post event) rating of the opponent in game *i*.

If all the players results in the current tournament and all prior results are defeats then the performance rating is 1. In the next tournament you will again use performance rating.

If all the players results in the current tournament and all prior results are victories then a dummy draw against the highest rated opponent is added before doing the calculations. In the next tournament you will again use performance rated but without the dummy draw (unless the player also wins all the games in the next tournament).

**Comment:
**To calculate the 0-point of

*g(x)*you will need to use iterations.

### 3 Prior grade

If a player has a prior grade (usually from Japan) then 2 games are added to the players results in the first tournament he participates in. Those two games are one victory and one defeat against the midpoint of the players grade according to the table in (7).

Grades from online sites are not used.

### 4 Lower limit

1 is a hard lower limit. If you after using the calculations in (1) or (2) you end up with a rating less than 1, you use 1 instead.

400 is a soft lower limit. If the opponents rating (or) is less than 400, 400 is used instead.

**Comment:
**Without a soft lower limit you may have beginners who wins one or two games but still ends up with a rating of 1.

### 5 Bonus

If you win against an opponent with a rating that is so high that

*k(pr) * (or – pr)/160* is larger than *k(pr) * (1 – f(pr, or))*

then that value is used instead.

Also

When calculating the rating change for a game using (1) and the players rating is less than 1800 then the player gets a bonus of *(1800 – pr)/200* points per game, but only for 100 games.

**Comments:
**Without a bonus system and the lower limits then the rating changes in a tournament would basically add up to 0. Since most players has a higher rating when they stop playing Shogi than they got when they started, the consequence would be that the “average” rating would over time decrease and after long enough time all players would have a negative rating value. Without a bonus system but with lower limits, then the lower limits would in effect be a (silly) bonus system, the rating values would be “compressed” together and a large part of the players would have a rating below 400.

The normal adjustment system from (1) is rather slow. A bonus system that detects fast improving players gives rating values that better reflects the actual strength of that player (and the players opponents).

The bonus for players below 1800 may result in a rating gain even if the player looses the game. This reflects the idea that beginners often improves significantly by each game they play.

### 6 Which games are rated

The decision to rate a tournament must be done before the tournament starts. Unless stated explicitly before the start, games with a good enough time limit are to be rated. To rate a game the time limit must be at least 30 minutes and 30 seconds byoyomi or at least 20 minutes and 40 seconds byoyomi.

Games not played are not rated.

If a game ends in Sennichite (repetition of moves). The games is rated as a draw. If the game then is replayed and both players have the same time limit and the time limit is good enough then the replay game is also rated. Usually a replay game is played with the remaining time each player has, and such a game is therefore normally not rated.

**Comments:
**If a scheduled game is not played for instance because one of the players do not show up, it is not rated. Whether a players gets a point or not for that game in the tournament is irrelevant for the rating calculations.

Jishogi (entering king) could be a draw with older rules but now is no longer a draw.

### 7 Grade system and promotions

Grades are mainly based on rating and this table is used.

LB MP UB #LB #MP 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* stands for lower bound, *MP* for midpoint, and *UB* for upper bound.

### 7a Rules for all players

When a player plays his first rated tournament, he has no grade. He cannot get a grade until after he has played at least 9 games. When a player has played at least 9 games but less than 18, he gets a grade if his rating reaches the upper bound (UB) of the grade above.

If a player has played at least 18 games there are 3 ways of obtaining a grade.

- his rating reaches the upper bound (UB) of that grade.
- his rating reaches the midpoint (MP) of that grade and stays above that for #MP games.
- his rating reaches the lower bound (LB) of a that grade and stays above that for #LB games and at one point also reaches the midpoint (MP) of that grade.

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 or who the opponent is, the grade is awarded immediately.

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.

The two games added because of a prior grade (3) counts towards the 9 games and 18 games limit.

### 7b Extra rules for promotion to Dan grades

To get a Dan grade you also need to have played some games against the MP of the grade below:

5 Dan: 8 games against 2160 or better 4 Dan: 8 games against 2000 or better 3 Dan: 7 games against 1860 or better 2 Dan: 7 games against 1740 or better 1 Dan: 7 games against 1620 or better

Those 7 or 8 games must have been played against more than 1 opponent.

### 8 Handicap

Games with handicap are also rated if the handicap is one of the following:

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 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 (or). When calculating the rating change for the handicap receiver the handicap rating effect is subtracted from the rating of the opponent (or).

**Asle Olufsen**