Ranking system for a cooperative game

Question

A cooperative game in which two players share a final score on each match.

I would like to have an individual ranking for each player in the system considering all matches between all players ever played.

A typical score varies from 500 to 7000 (in theory, from 0 to 10000+).

My first thought is to use the score as the ranking itself as follows:

• Player-A with NA matches (ever played) and ranking RA plays with Player-B with NB matches and ranking RB.
• The expected score is (RA+RB)/2 (this is an assumption that is probably close to reality, but I don't have enough data).
• The actual score was RX, which is distant D = RX-(RA+RB)/2 from the expectation.
• The new ranking for Player-A is RA+D/NA and NA is incremented.
• The new ranking for Player-B is RB+D/NB and NB is incremented.
• A new player enters the system with 1 match and ranking 0.

My specific questions:

• Is there an existing ranking system designed for games like this?
• If my assumption is correct, is the proposed system good?
• If my assumption is not entirely correct, what should be changed? It is guaranteed, at least, that RX is between RA and RB.

Answer 1

I would use the Elo Rating system. It’s what is used for chess and a variant of it is used for CSGO.

https://en.m.wikipedia.org/wiki/Elo_rating_system