YCA info	Yorkshire Chess Association	Last update: 26/07/00
Grading Matters Contents	The 40 Point Grading Horizon

 

The points scored by a player in the grading of a chess game are dependent on the opponent's grade, but only within limits.

 

The difference between people's grades represents the approximate difference in their expected percentage performance against players of each other's grade (see The Meaning of Grades).  However, simply adding or subtracting 50 grading points for a win or loss is an arithmetical simplification which made life relatively nice and easy when grading was done manually, before computers started being used. 

 

The Problems Causes by Simplification

 

In the language of statistics this percentage interpretation of grades approximates a sigmoid to a straight line, or a standard distribution curve to two straight lines.  In layman's terms it assumes you will always beat a player 50 points weaker than you, which is untrue, and means you will score more than 100% against even weaker players, which is meaningless.  The resultant simplified calculation would mean you'd score only your own grade for beating an opponent graded 50 points lower than yourself, which is not too unreasonable, but would score less than your own grade for beating to a player more than 50 points lower, which would erroneously imply you were playing below your grade.

 

The Simplest Solution

 

It would make more sense to treat the opponent as being 50 points different from ones own.  That way you wouldn't lose grading points for beating much weaker players, nor would you gain grading points for losing to much stronger opponents.  Such a 50-point horizon would still cause problems.  Imagine a group of players all of around 110-grade strength who only got the opportunity to play each other.  If none improved or got worse then they would all tend to get new grades still around 110.  That’s perfectly okay, but what if one player were to improve significantly from year to year, winning all his games?  With opponents all graded around 110, a 50-point horizon would not allow him to rise above 160, even if he were reaching grandmaster strength!

 

A Better Solution

 

By making the grading "horizon" less than 50 points (e.g. 45, 40 or 35) such improving players would not be tied down to some ceiling above the grading level of their opponents.  The other side of the coin is that the grade of the player in the example just given would in time rise beyond his true strength, but this is an artificially extreme example.

 

The grading system is considered to work best with a horizon less than 50.  The limit fixed was 40.  This is a somewhat arbitrary but pragmatic choice.  37 or 42 might be "better" choices but would have made mental arithmetic that bit more taxing and error prone.

 

What This Means in Simple Terms

 

Thus if you have a grade of say 118, then your games will be graded as follows.

 

 

 

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