Introduction:

The Scottish Grading System attempts to give an accurate measure of a player’s 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 ‘strength’.

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 player’s 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 player’s 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 Grading System vary from junior beginners with a minimum level of 100 up to top Grandmaster level of near 2600.

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. 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. 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: Only games played with a clock and a time control of at least thirty minutes per player should be submitted for main list Chess Scotland grading. This is a general guideline and experienced junior organisers may consider there are sufficient extenuating circumstances to mitigate either submission or non-submission of an event for grading.

Calculation Steps for Players who already have a Grade

An Excel program is available for download here 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 = 1815 (rounded to nearest five points)

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 follows:

Junior Age in Grading List	Addition
12 or less	+120
13	+110
14	+100
15	+85
16	+65
17	+45
18	+40
19	+35
20	+20
Age??	+40
New Adult	+25

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 higher.

Minimum Grade

No grade is published below 100.

Delisting Rules

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.

Returning Players

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).

Foreign Players

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 BCF (English) grades. To simplify reporting of outside results the grades to be used are either FIDE or BCF - see discussion on Outside results.

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.

Drift

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.

Calculation Steps

• 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 data.
• 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 records.
• 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 special case).
• 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 System.