But the Euro players play in America and vice versa. Shouldn't all the ratings converge over time when they play each other enough?
So if Ma Jinbao is 2800 in USATT, but some lowly German guys comes to US and beats him, then Ma Jinbao's rating would decline. and vice versa
Yes. Different players from different places do play each other as you correctly wrote.
The thing is where are they playing. If they play a sanctioned USATT match, (in USA) then it is the USATT rating used and updated. If they play sanctioned Germany, (in Germany) TTR system is used. If they play sanctioned Canada, then Canadian rating system is used.
None of these systems are synced nor should they, it would be chaos. Although all those systems are ELO based systems... they just operate differently and have different algorithms used... and have their nuances of have rating adjustments are done.
What you probably looking for is a system called RATINGS CENTRAL. They used to record all the pro events and update rating points. RC is an ELO based system with its own statistical probability model and operation. It is designed to be having less standard deviation with more match data vs know players. Some other countrys' leagues use this ratings system... it is pretty much free to them... and RC gives out some nice league/tourney software.
RC is run by a Boston math dude... it could have/should have become USATT's rating system of record... but there were so many internal politicking actions going on in USATT 20+ years ago (how shocking !!) (our current state is still like that !!) that it did not get adopted as the USATT ratings system of record... still, it has a lot to offer and some clubs/leagues/tourneys take them up on the offer.
You could play at a tourney run with RC provided software... and it reports results to USATT ratings system... and also RC. So... you could have TWO USA ratings.
So RC might be the closest to what you are searching for... but not all the world's matches are reported/recorded... but RC has made the best effort so far to accomplish what you were asking about.
Still... every country or state or league can run stuff their way... and do. If it makes sense to everyone, then everyone would use RC voluntarily... but that is an over-generalization / over-simplification of the situation.
