## What is the average chess grade?

Thanks to the English Chess Federation gradings database we can find out the answer to this and other questions about the statistical distribution of individual chess performance. The average (mean) grade is 134. This applies to all players, adults and juniors, but excludes rapidplay games. The median is 133 and the mode is 128.

The ECF system is different from most of those used elsewhere in the world: for one thing, it is based on 3 digits rather than 4. Recently there was a review of the grades which found that they had been deflating over time – not because players were getting worse but because of the way it is calculated. As a consequence, the ECF grades have been recalibrated upwards. Many people now feel that their grades better reflect their abilities. On the other hand, there are those who fear they will be exposed as over-promoted (a-hem).

## What the grades mean

A formula sums it up:

*E(%score) = 50 + ECF_A – ECF_B*

Or in words, the expected percentage score = 50 plus the difference in grades between players A and B. So if the players had the same grade, then the expected score would be an even 50%. If one player was graded 40 more than the other, then the expected score between them in a ten game match would be 9-1 (because 50%+40%=90%)

The idea behind the ECF grading system is that a player graded 10 points higher than his or her opponent would be expected to score 10% better than evens against them i.e. a 60% chance of winning. Similarly, a grading difference of 20 points implies a 70% of winning by the higher rated player. And so on.

The ECF system is not defined for players that are more than 40 grading points apart. This doesn’t happen very often in competitive play.

## Conversion to ELO grades

Although the statistical assumptions behind the ECF system and the international FIDE system are different, it is possible to make an approximate equivalence. The ECF system has been in use for decades because it is easy to calculate. The FIDE system uses a more sophisticated method devised by Prof. Arpad Elo. The resulting grades are known as ELO grades.

The usual equivalence is:

*ECF x 8 + 650 = ELO*

Let us take an example the average ECF grade for adults of 134.25

This equates to (134.25 × 8) + 650 = 1724 ELO

**Quirky interlude**
The equivalence of 134 ECF and 1724 ELO can be pictured in the following way. The hottest temperature ever recorded in the USA was 134 degrees Fahrenheit at Death Valley.
By a curious coincidence the new-fangled system of temperature measurement was first proposed by Daniel Fahrenheit in 1724.

## Grade distribution

The distribution of grades pretty much fits into the normal distribution.