The Scottish Grading System attempts to give an
accurate measure of a players chess strength, based on games in
tournaments, leagues and clubs throughout Scotland, and on games in
competitions outside Scotland. The Grading System has been tested and
refined over many years and the gradings it gives Scottish chessplayers
are generally respected as according with their own opinions of player
The Chess Scotland Grading System is based on
the ELO International grading system devised by Professor Arpad Elo,
which is also used by FIDE, the World Chess federation, and most national
chess associations around the world. Because a chess game can have only
three clearly defined results - win, lose or draw - any players
performance can be evaluated with great accuracy.
The Elo grading system is based on probability
theory - a stronger (higher-graded) chessplayer should consistently
beat a weaker (lower-graded) opponent. The greater the difference in
strength, the higher the probability of this happening. The more games
that are played, the better the information about a players strength.
When Laszlo Polgar decided to prove that prodigies
are made rather than born, by giving his children intensive coaching
in one chosen speciality, one reason he decided on chess (rather than
music or mathematics) was that the Elo system could measure their record-breaking
progress so efficiently.
Grades in the Scottish system vary from junior
beginners with a minimum level of 100 up to top Grandmaster level of
A list is published in early August each year using
results from July 1 of the previous year up to July 1 of the current
year. Games played in tournaments and leagues in Scotland are automatically
submitted to Chess Scotland for grading by the tournament and league
organisers. Games played in clubs are submitted by club secretaries
directly to Chess Scotland for grading (individuals cannot submit club results ie just their own data, data must come from the organising club). Clubs have to be members of
Chess Scotland before their domestic club games are graded. Games played
outside Scotland are included if the player sends the results personally
to the chief grader - there is now an online form available in which to input results, contact the chief grader for the username and password. Games outside Scotland are only graded for members
of Chess Scotland.
Gradeable games should be played with clocks.
The time limit for inclusion in the Main grading list is no faster than
all moves in one hour (see junior section below). A Chess Scotland Allegro
grading list is produced along with the main list devoted to allegro
tournaments with a speed of play between 15-30 minutes each per player.
Junior Grading: (Revised August 2009). Games played in junior events will only be graded for the Main List when the game is played with clocks and each player has a minimum time of 25 minutes for the whole game.
Games at a faster time control or played without clocks should be submitted for the Allegro List.
Adjudications in junior games: Games will be void for grading purposes when a game played without clocks is adjudicated.
Calculation Steps for Players who already have
An Excel program is available for
which will replicate the exact calculation steps of CS grading. This
user friendly spreadsheet was devised by Alex Clark of Dundee (please
note you must have Microsoft Excel).
To calculate your new grade sum the actual points
scored for all your games during the season. Using Table
1 sum the points you were expected to score for all your games.
Your grade goes up when you score more than expected and down when you
score less than expected.
To obtain the expected score on each game calculate
the gap between your grade and that of your opponent. For example a
player of 1475 plays an opponent of 1660. The grading difference is
185, from table 1 the expected score for the lower graded player is
0.26 and the higher player 0.74. Add up all the expected scores. Take
the total points actually scored and subtract the total you were expected
to score. Put these figures into the following formula.
New Grade = Old Grade + (800 * (Total Actual Points
- Total Expected Points)/Number of Games Played )
For example a player with an old grade of 1770:
plays 84 games, scores 55 points, expected to score 50.338.
New Grade = 1770 + (800 * (55-50.338)/84 )
New Grade = 1814
Junior players and newly graded adults are assumed
to improve their playing strength during the season - established players
are assumed to have stable grades. To compensate the opponents of juniors
and newly graded adults a range of bonus points are added to the junior's
grade before expected scores are calculated. For example you play a
J13 with a published grade of 1200. For your grading calculation the
junior is worth 1200+110=1310. The current range of additions is as
|Junior Age in Grading
|12 or less
March 30 2004: Ages in grading list are ages as at midnight Dec 31 in the middle of that grading season.
June 23 2005 (clarification): Junior additions do not apply to ungraded juniors, only to junior players published in the current rating list.
Maximum Grading Gap and Void Gaps
The maximum gap between players is set at 400.
eg a 1600 plays a 2200. For the 1600 the game is considered as being
against a 2000. For the 2200 the game is considered a game against an
1800. If the grading gap is over 735 points the game is void unless
the higher player fails to win.
Minimum Sample Size
The number of games applied in the grading formula
calculations is the actual number of games played or 30 whichever is
No grade is published below 100.
Adults are delisted after completing a fifth inactive
year. Players who are still junior (J20 or younger) are delisted in
their third inactive year. Players graded 600 and below who are inactive
are delisted immediately.
Adult players are given their old grade if it
appears in the last five grading lists (the current list is one of the
last five). If not in the last five lists then use the last SCA (CS)
published grade minus 10 points for every year inactive, prior to the
last five eg if you were last published six grading books ago take off
10 points etc. (In practice returning players seem to go back to their
previous best strength quite quickly - perhaps they left less enthusiastic
and have refound that enthusiasm). Juniors restart as new players (Tournament
organisers should always be told if you have previously held a grade).
If you play a non Scottish opponent the order
of priority for which grade is used is 1) Scottish 2) FIDE 3) National.
Scottish players resident outside Scotland will be listed provided they
play regularly in Scotland - they are delisted as per the rules in the
previous paragraphs. Foreign players not resident in Scotland are classed
as visitors and are not retained in the grading system unless they play
a minimum of two weekend tournaments within a grading season. If a foreign
player plays two tournaments the Chess Scotland grading system will
allocate them a Chess Scotland grade based on the previous foreign grade
calculated against their Scottish results. The foreign player will be
given the club code NR to indicate their status as a non-resident foreigner.
NR players stay in the Chess Scotland system until they are inactive
when they are delisted immediately.
NB: National grades effectively means ECF (English)
grades. To simplify reporting of outside results the grades to be used
are either FIDE or ECF - see discussion on Outside
Games against Ungraded Players
Most games against ungraded players count for your rating. Before the final grading run all the games of an ungraded player are collated. A temporary grading is calculated for the ungraded player based only on games against published graded players and the new grades of previously ungraded players who have achieved a new grade in the season. To be eligible for a temp rating the ungraded player must have played a minimum 5 games against players with such grades and scored in the range greater than 0 and less than 100%. This temporary rating is retrospectively used as the ungraded players grade in the games records of all the opponents of the ungraded player. Temp ratings are listed in italics on the grading website. The temp rating will be very close in value to the initial new grade of the unrated player. The reason why it may be different is because the unrated player may gain additional games from temporary ratings of ungraded opponents. (April 2005)
200 Up Rule
Fast improving players can quickly find that their
published grade is out of date and understates their current strength.
Opponents of the improving player are victimised because expected scores
are calculated against a published grade which has proved to be inaccurate.
To quickly boost improving players to a more appropriate level and avoid
their opponents unjustly losing grading credit the 200 up rule was invented.
(Modification July 2001) If a grade goes up by 200 points on the first of the (Nov 2006) final
grading runs it will be set to zero and recalculated as if the player
was an unrated player. The temporary ratings thus calculated will replace
the old published grade. Grades will then be recalculated and opponents
will get credit for the temporary rating rather than the old published
grade. (The junior addition is deducted from the temporary grade before
it is slotted into the 200 up player's record - since opponents will
get the temp rating plus any addition when the grades are recalculated.)
NB Before July 2001 the 200 Up players were made
unrated which had negative implications for players who needed a game
against a graded player.
(Nov 2006) Since opponents of the 200 up players get extra grading credit for these games it is possible a player could be over 200 up by the end of the calculation process but not themselves have been a 200 up player.
(Nov 2006:) Players who are 200 up on Main List will use the 200 up Main List estimate as their allegro start grade, even if already allegro graded.
To assist in achieving grading stability the program
calculates a performance of all established adults comparing what they
scored and what they were expected to score. If the adults score less
than expected then a small addition is made to all active grades - if
more than expected then a small deduction is made.
Calculation Steps for an Ungraded Player
To get a new Chess Scotland Grade an ungraded
player must play a minimum of 8 gradeable games in two seasons. A gradeable
game is one against a published or temporary grade.
- 1: Average Score = Total Points divided by
Total Games Played.
- 2: Average Opposition = Sum of Opponent's
Grades divided by Total Games Played.
- 3: The Average Score is converted to a Grading
Difference using Table 1.
- 4: An initial estimate is made using the above
- 5: All the opponent's grades are compared
to the initial estimate and adjusted to be no more than 400 points
different from the initial estimate. (This adjustment is necessary
since a player could get a distorted first grading by playing 7 very
high opponents and 1 game versus a very weak player thereby getting
a distorted average opposition). This adjustment will change the Average
Opposition from Step 2 above.
- 6: The Grading Difference (from step 3) positive
or negative is added to the Average Opposition. The Temporary Grade
thus calculated is the value all your opponents get in their player
- 7: If the ungraded player has played any ungraded
players who gained a temporary grade from step 6 then these temp grades
will be added to their player record.
- 7a) If any ungraded player had less than 5 results v graded AND 8 or more
results v graded or temps then make another calculation. That calculation
will be to create an estimate for this specific group by taking all their
games v graded and temps and making a TEMP1A estimate (new name for this
- 7b) Slot the TEMP1A estimates into all the opponent's records.
- 8: Using all the games against published and
temp grades calculate new Average Scores and new Average Opposition.
- 9: Repeat the 400 adjustment as per step 5.
- 10:Calculate new grade with grading difference
added/subtracted from step 9.
We welcome comments from anyone, especially those
with a stats background, on the methodology involved in the Chess Scotland