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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.

opponent's grade	result	points scored	calculation method
165	win	208	opponent
(over 40	draw	158	treated as 40
higher)	loss	108	higher then self
158	win	208
(40 points	draw	158	opponent's
higher)	loss	108	grade plus 50
130	win	180	for a win
(less than	draw	130
40 higher)	loss	80
118	win	168	opponent's
(same	draw	118	grade
grade)	loss	68	for a draw
100	win	150
(less than	draw	100
40 lower)	loss	50	opponent's
78	win	128	grade less 50
(40 points	draw	78	for a loss
lower)	loss	28
70	win	128	opponent
(over 40	draw	78	treated as 40
lower)	loss	28	lower then self

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