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I'm trying to compute a global elo rating for a popular eSports title, but the problem is that the teams mostly compete in their own regions. Specifically, there are five major regions, and teams normally only compete against teams in their own region. Twice every year though, the top 3 teams from each region come together and play against one another in a "championship tournament".

My concern with applying the elo algorithm naively is that teams from stronger regions will likely end up with elo similar to teams from weaker regions, because stronger teams mostly only compete against other strong teams and vice versa.

My idea was to use the results from the "championship tournament" to give every top team (i.e. those that competed in the championship tournament) a global elo. Then, I would set the elo of the other teams in the same region to the average elo of the top 3 teams from that region. I would then use the classical elo algorithm to compute elo for matches played in that region.

However, I think my idea is flawed in that I'm giving every team in a region a very high starting elo (i.e. the average elo of the top 3 teams from that region). The truth is there are teams that dominate their own region (e.g. going undefeated) but play very poorly against top teams from other regions, which means that I might still end up giving these teams very high elo ratings even though they are actually not as strong as teams from the stronger regions.

How do I compute global elo ratings when teams mostly play in their own regions?

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Since the question has sit unanswered for years, I'll try to give a probably incomplete answer.

If the pool of players is closed, with naive Elo rating system you are fine in the long run.

Elo rating is a zero sum game where matches don't produce rating points but distribute them among players. At the beginning, top players from the weaker regions will have similar ratings than top players from the stronger regions, but after the inter-regional matches those top players from the weakest region will have lowered their ratings. That is going to affect the other players in their own regions, since nearly top players in that regions will get less points when winning to the top ones and will lose more when losing to them - compared to what they would get or lose if the top player had a higher ratio.

This way, inter-regional matches will be a way to move points between regions, not just between players.

However, there are a couple of caveats:

  • In the long run, we are all dead (J.M. Keynes): The long run could be to away in the future to be actually meaningful. If there are very few inter-regional matches and very few players take part in them, the transfer of Elo points between regions could be very slow.
  • If there are limits on how much rating points can a player lose, or there is a flow of new players in each region, there can be rating inflation, and rating inflation can have an stronger effect than transfer of points between regions.

Both caveats could be worked around, but the solution doesn't seem to be going to be clean nor easy to explain to players.

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