Top Nations Rankings by Typical Player Strength: 1.CUB, 2.SRB, 3.BIH, 4.MNE, 5.NED

In a few recent posts, we have explored different ways of measuring how strong nations are in chess. First, the criterium was the number of all FIDE rated players per capita (in its database, FIDE maintains players with the 1000+ rating).

Then, we saw the top countries ranked by the five criteria that took into consideration not only the average rating of country's top ten players — the way FIDE ranks the member federations on her site — but also the size of country and the "density" of all titled players.

The latest classification, as proposed by Richard James @falseknight showed how chess nations compare among themselves in terms of the number of all players FIDE 2000+ (pretty much all titled players CM and on), as well as all "strong players" defined as FIDE 1500+.

Today, we are going to use the average, or typical player's strength per country from the FIDE database (players 1000+) to stack up chess nations. For the first time we use actual ratings of players, not just the numbers of players in absolute or relative (per capita) terms. This was suggested by @fanxiong

Although average is a commonly used and well understood statistic, median is also a common measure used to express a “middle” value of the set of numbers, or the so called central tendency. The average and median are usually different values. But how is the median different from the average?

The median doesn't require a formula. It is determined by ranking the data from largest to smallest, and then identifying the middle, so that there are an equal number of data values larger and smaller than the middle is. While the average and median can be the same or nearly the same, they are different if more of the data values are clustered toward one end of their range and/or if there are a few extreme values. In statistical terminology, this is called skewness. In this way, the average can be substantially influenced by the few values, making it not very representative of the majority of the values in the data set. Under these circumstances, median gives a better representation of central tendency than average. For example, with a rating of 2862, Magnus Carlsen tops the list of the best players of Norway. Aryan Tari is next with 2618. Had Norway more Carlsens, its average rating would be somewhat higher than the median value.

Here are the results showing how nations compare by the median player strength (added are just a few average ratings to see how they differ from the median),

Table 1. Typical Nations Player's Rating (FIDE DB, Dec 2020, both M/F incl. Inactive)

Quite unexpectedly, Cuba came in first! The country wasn't seen perform near the top of rankings in any of the previous contests (check Table 2 below). Yet, the country has created and maintained a high chess culture ever since the time of her great son Capablanca. 

Serbia is again ranked very high, in the second place. The country also has a great chess culture and, interestingly, has performed very well by all criteria so far and found her consistently among the top contenders (the only criterium by which Serbia didn't show a stellar performance was the country's top ten players' rating). 

Bosnia and Herzegovina and Montenegro came in third and fourth. Russia somewhere in the middle, India trailing.

One interesting fact. Azerbaijan is at the bottom of the list with the average strength of 1430. On the other hand, its median GM rating of 2527.5, the second best among all nations! (after China, 2560.5, and Ukraine 2529).

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Table 2.

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Thanks for reading.

A happy and healthy New Year!

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