Using the January 2015 rating list as a reference, for each player I noted the federation (aka country) and extracted the federation prefix from the player's FIDE ID. Then I built a table of all combinations of federation and FIDE ID prefix, of which I found 855 pairs. Then I noted which prefix had the highest count for a given federation. That is the prefix shown on my page of federation codes.
After creating the base data, I checked duplicate prefixes. For example, I found that both 'SRB' (Serbia) and 'MNE' (Montenegro) were assigned the prefix '9'. When I looked at all prefixes used in those federations (column 'FedID' in the image on the left), I discovered that MNE had a second frequent prefix ('165'). I assumed that players from MNE were once administered by SRB, but had since been split off. Ditto for 'RSA' (South Africa) and 'LES' (Lesotho).
Another duplicate prefix ('100') is found for 'UGA' (Uganda) and 'TAN' (Tanzania). Here I discovered that UGA has more players than TAN and assumed that UGA is handling the player registrations for both federations, so no change to my table is necessary. I found a similar relationship for 'EGY' (Egypt) and 'GAB' (Gabon), although the political connection is less obvious.
One curious duplicate was 'USA' (United States) and 'CAM' (Cambodia). There is only one rated player listed for CAM, who turns out to be 'Truong, H. Paul', Susan Polgar's husband. Indeed, the Fide.com page, Transfers in 2014, lists '2001390 Truong, H. Paul CAM USA', where USA is the former federation.
After applying these changes plus a few other corrections, I updated my page FIDE Country and Federation Codes (unofficial). For anyone who has managed to read this far, a few other anomalies might be worth mentioning.
Along with the FIDE IDs listed on my 'unofficial' page, there are more than two dozen other prefix codes in use. Most of these are additional codes for a single country, where I imagine the task of assigning new codes has been split geographically within the country. For example, 'IND' (India) has four additional prefixes in use:-
India, 'Prefix', 'No.Players'
IND, 250, 3892
IND, 350, 3329
IND, 450, 1502
IND, 466, 2591
Do old codes also disappear? Going back a few years, when I first looked at the FIDE ID for the January 1999 rating list (see Structure of the FIDE ID), I found 148 different federations. I dragged the file out my archive, recreated the data for the 148 federations, and compared it to the 2015 list. I found prefixes for five federations missing from the 2015 data:-
'Federation', 'Prefix', 'No.Players in 1999'
GUY, 83, 1
MAU, 89, 1
GAM, 95, 2
MLI, 96, 8
SEN, 109, 3
What happened to this data? That question will have to wait for a rainy day.
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