It is hard to imagine a contest more individual- istic than a chess game. Yet, the FIDE website presents not only current chess players ratings but also a country rank by average rating of the top 10 players. (Note: FIDE website pages are not dated (!) - I am addressing the data downloaded on March 29, 2005.)

I have a problem with that, I believe countries should be ranked exclusively based on team tournaments performance where countries are represented, like the Chess Olympiad. And when it comes to country rank based on individual results, I can offer several equally doubtful approaches:

Why the average rating of the top 10 players? Just because chess players have ten fingers? Well, most players move chess pieces with three fingers, so, why not average rating of the top 3 players? The top graph on the left, limited to top 20 countries from the FIDE list [NW03], presents how country rank could be dependent on the number of averaged players.

Even if one would accept a country ranking based on one of these averages, it is inherently non-sustainable: the first and twentieth country on the FIDE list are separated by only 6.81% of rating points, the first and hundredth country by only 18.62% of rating points; it means that separation of most countries is well below the standard deviation of the FIDE ranking statistics.

Furthermore, should we make country ranking more ‘country related’ by normalizing the average rating to the country population or country GNP? I know, it sounds ridiculous but I am not the one who advocates country ranking.

The middle graph on the left introduces an additional ranking parameter by assigning non-linear placement points: first country in certain averaging category gets 100 points, second 88, third 78, fourth 70, fifth 64, sixth 60, and every subsequent 2 points less.

Averaging individual ratings does not necessarily lead to a meaningful projection of a particular country strength: in an assumed match of two countries of equal 10 players average rating, on 10 boards, if one player has very high rating then it is likely that more than one of his teammates has to match higher ranked opponent.

The bottom graph deviates from the ‘averaging philosophy’: it is based on country participation in the cumulative ratings. For example, cumulative rating of top100 players is 265,816; among them 22 Russian players are worth 58,802 (22.12%) while 6 Ukrainian players are worth 16,028 (6.03%).

The above graphic presentation is not intended as proof of the superiority of any one way of country ratings. On the contrary, it is just a search for a meaning in any one of them.

On the meaning of averages:

A 60 years old man to his 10 years old grandson: "In average, we are men at our best years!"