The grading system

The Scottish Grading system is based on the system developed in the 1950s by Professor Arpad Elo, and used by FIDE in its lists.

The Elo system uses probabilities to calculate the value of a result to a player; in simple terms, more credit is given for defeating a much stronger player than a player of around your own strength or below. The other side of the coin is that losing to or drawing with a player significantly lower than yourself will be costly.

A table of values is used which has the expected score for players depending on the difference in grades (download this table»). For example:

• When two players have the same grade, their expected score against each other is - as you would imagine - 0.5.
• If I am playing an opponent 100 points above me, I have an expected score of 0.364, and my opponent an expectation of 0.636

Calculating a grade for the new season

To calculate your new grade: total your points for the season, and then your expected score using the table.

You now have an actual score and an expected score.

You also need a note of the number of games you have played, using a minimum of 30; eg if you have played 42 games, then games = 42; if you have played 12, then games = 30

Your new grade is your old grade +...

(800 * (actual - expected) / games)

A further refinement to the grade is made by Chess Scotland in the form of drift. This is a separate calculation to correct minor anomalies, but typically is only in the region of 2 or 3 points. (see a fuller explanation from Chess Scotland»).

Automatic calculators

Two spreadsheets to do this are:

• One from Alex Clark of Dundee which he devised for Chess Scotland
• One from Dave Bogle of the Selkirk Club

English Chess Federation

ECF equivalent grades can be calculated from Chess Scotland (CS) grades using the following formula:

ECF = (CS / 10) - 18

Chess Scotland website

The definitive introduction to CS gradings is at https://www.chessscotland.com/grading/