THE SCA GRADING SYSTEM

Introduction	Games against ungraded players
Example of a Scottish Grade	Calculation - Previous player
Example Printout for Player X	Ungraded Players
Printout Notes	Worked example - ungraded player
Grading Formula	Can you lose points by winning
Calculation - Graded Player	Time Control
Drift Analysis	Data Input
Minimum Sample Size	Theory

Introduction

To which perhaps we can add the thanks of chess players everywhere for the self-sacrificing efforts of those many nameless individuals all over the world who arrange and organise chess at every level for the rest of us.

Very many thanks to you all

Example of a Scottish Grade

Below is a sample of a player's grade worked out using the Scottish grading system, which is based on the ELO method. It is worth noting that this grading system is a comparative system, and individuals can have widely varying grades in different types of chess because of the pool of opponents they play. No system is perfect.

Example printout Player X

The following games were played in Scottish events:-

Eligible Games in Scottish Events: 9 Points: 6

Explanatory Notes

PUB GRADE

Grade as published in the most recent grading list.

ADJ GRADE

Where published grade is not 0, this is published grade plus any junior or newly graded adult edition applicable.

Where published grade is 0, this is estimated grade for opponent (if possible to estimate).

USED GRADE

This is ADJ GRADE limited to a maximum difference of 400 points from your own PREVIOUS grade.

Grading Formula

A new grade for a previously graded player is given by the following formula:-

New = Old + 800 x (act. - exp.)
n

where:

The resulting new grade for this performance is therefore 2417. (After rounding to nearest 5 the new grade published would be 2415).

Calculation steps for graded players.

To calculate your new grade sum the actual points scored (1, ½, 0) for all your games in the season. Using table 1 (see below) sum the points you were expected to score. Your grade goes up when you score more than expected and down when you score less.

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.

Junior players and newly graded adults are assumed to improve their playing strength faster than established players- To compensate the opponents of juniors and newly graded adults a range of additions are added to the junior or new adult grades. These additions are shown in table 2.

e.g. If you play a junior aged 14 with a published grade of 1500 your expected score is calculated against a player rated 1565.

To check the accuracy of junior additions a program calculates whether established adult players are scoring more than expected or less. If adults are scoring more than expected a small negative adjustment is made to all active players and if less than expected then a positive adjustment is made. This program attempts to achieve stability in grades from year to year.

Maximum 400 Gap

The grading gap between players is always calculated at a maximum of 400 points. A player with a published grade of 1600 plays a player with a published grade of 2200. For the 1600 player the opponent is classed as 2000, for the 2200 player the opponent is classed as 1800.

Minimum sample size/grade

In the general grading formula the number of games is always set at the actual number played or 30 whichever is greater. The minimum published grade is set at 300.

Games against ungraded players

If you play an ungraded player the game may count for your rating. Before the final grading list is calculated all the games of an ungraded player are collated. A temporary rating is calculated for the ungraded player based only on games against graded players. To be eligible for a temporary rating the ungraded player must have played a minimum 5 graded players and scored between 8-92%. The temporary rating is retrospectively slotted into the games records of all the opponents of the ungraded player (both rated and unrated opponents). The temporary rating will be listed in the detailed player print (see above) and will be close in value to the first published rating of the ungraded player. The reason why the temporary rating may be different from the final published rating is that the ungraded player may themselves gain additional games from temporary ratings of ungraded opponents.

This is a major improvement over the previous grading system where temporary grades counted for 1 event only.

Calculations for a previously graded player

A player graded 1770. Actual points 55, expected points 50.338, number of games 84, drift -6.1.

New Grade = 1770 + (800 x (55 - 50.338))/84 - 6.1
= 1810 (rounded to nearest 5 points)

A player graded 2085, actual points 16, expected points 13.307, number of games 21 (set to 30), drift 21/30 x -6.1 = -4.27

Ungraded players

For an ungraded player to achieve a new grade he must play at least 8 gradeable games within 2 seasons. A gradeable game is one against an opponent with a published grade or an ungraded player with a temporary grade.

Worked example of a newly rated player

The published ratings of "0" are unrated players. The adjusted ratings are the published ratings plus any junior additions. The ratings in brackets are temporary ratings.

Can you ever lose points by winning?

The Scottish grading system is an averaging process over an entire season. The arithmetic of the grading formula means that in certain circumstances the marginal effect of winning against a player whom you have a very high expected score might result is a slightly lower positive change in your grade after that particular game than before.

For the above situation to arise both the following circumstances must apply.

1. You must have played at least 3Ogames. (Less than 3Ogames and all wins are positive)
1. You must be going up at least 64 points. (Less than 64 and all wins are positive)

For example,- actual score 40 points, expected score 30 points, 60 games played. The grading change on these figures is +133. You play another opponent against whom your expected score is 0.9 and you win. New figures are 41, 30.9 and 61, grading change is now +132.

However after 30 games have been played the value of any game is affected by the number of games you play. The Scottish grading system should be looked at as your total actual and total expected over the course of a season.

Time Control

The fastest time limit for grading is all moves in one hour each per player. This requirement may be relaxed in junior chess.

Data Input

The accuracy of grades produced is only as accurate as the quality of data input. All tournament organisers and clubs should use the standard grading forms available from the SCA. All events advertised in Scottish Chess will be sent grading forms. Grading forms are available from the chief grader and area graders.

Note that there is no longer any request for alphabetical. order for player names, grading order is just as acceptable.

There are still a number of clubs who do not send their club championships for grading. Make sure your club is a member of the SCA and gets all its internal events graded.

Theoretical Background

The statistical basis for grading is detailed in the book "The Rating of Chessplayers Past and Present" by Arpad E Elo. (Now out of print - Editor)

Note: After the difference in grades between two graded players has been calculated, the expected score of the higher graded player is found in the "+" column; that of the lower graded player in the "–" column.

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