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What is average anyway? YTRREFS

The term 'average chess player' comes up every now and again. But what does that even mean? I am sure that every person who has ever used that kind of term will have different interpretations of what it means. So I figured I would take a look at some statistics from the official FIDE rating list.

The official rating lists can be downloaded from the FIDE website. One problem, however, is that there are almost 350,000 players on the rating list, which makes the files so big that they are rather difficult to handle. But with some spreadsheet magic, I was able to extract the information.

The diagram below shows the rating distribution of all players on the official rating list. The diagram simply shows the number of players with a certain rating. I have used a quite wide range (100 points) for each category, so the numbers will indicate the number of players with a rating between the indicated number and 100 points higher. For instance, the number at the peak (rating = 1700) is approximately 35,000. This means that about 35,000 players have a rating between 1700 and 1800.

Distribution of all FIDE rated players

One thing that strikes me as a bit odd is the lack of symmetry in the diagram. I had expected something that more closely resembles the symmetrical bell curve that represents a normal distribution. The deviation is more or less completely concentrated in below a 1400 rating. I am not really sure how to interpret this, but one possible explanation could be that there are a lot of beginners who have not yet reached their full potential, and therefore have a rating below 1400. Please feel free to provide your own interpretation of this result. (Edit: The results differs quite a bit from a similar analysis from a few years ago. Makes me think there could be something wrong with the data.)

The vertical lines in the diagram indicate the approximate rating levels that divide the population in quarters (quartiles). Approximately 25% of the players have ratings between each vertical line. The line in the middle thereby indicates the median, which means that 50% of the players have a lower rating, and 50% have a higher rating. This is quite close to the average rating, which indicates that the distribution is quite symmetrical after all. The following statistics describe the distribution quite well.

Average rating	1670
Median rating	1680
Variance (estimated)	250

This means that an average player is someone with a rating just below 1700. And if you have a rating that is above 2000, you can proudly announce that you have a higher rating than about 75% of all players. That's quite an achievement. If you want to take a closer look at the grandmaster level (2500+), this is a quite exclusive group with a mere 0.3% of the players. The table below provides some more details.

Rating	Number of players	Percentage
1000	17401	5%
1100	21902	6%
1200	23876	7%
1300	25723	7%
1400	28172	8%
1500	30958	9%
1600	33330	10%
1700	34483	10%
1800	33743	10%
1900	30758	9%
2000	28394	8%
2100	20109	6%
2200	12202	3%
2300	5564	2%
2400	2201	1%
2500	703	0.2%
2600	227	0.1%
2700	35	0.01%
2800	4	0.001%

This table illustrates clearly what an incredible achievement it really is to become a grandmaster. Despite the awesomeness that this implies, it is not always enough to make a living from chess. Furthermore, the chess celebreties that we see in top tournament (2700+) are only about 1 in 10,000. Talk about exclusive!

Another conclusion that I draw from this analysis is that it provides some kind of confirmation of my notion that an average clubplayer (patzer) is someone in the 1400-2000 rating range. Below 1400 is probably a good indication of the 'beginner' level, and 2000+ is elite. The master level is something else altogether.
I hope you enjoyed this little statistics exposé. At least, the next time someone talks about an 'average' player, you will know exactly what that means.

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