We have a scoring system for an existing "real-life" game (sailing races) which is well-established: first position gets 1 point, second position gets 2 points, etc. If someone is absent, then he gets N+1 points for that race. You add up the points of all the races and the one with the lowest score wins.
However, we would like to try an alternative ranking system based on skill, and where absences have a lower impact. Something like ELO rating, where if you make a race where you win opponents with a higher skill than you, then you are rewarded more points, and they are substracted some.
I've researched a bit, but only found ranking systems like this for 1v1 games or team games, but there's very little information on scoring systems for "everyone vs everyone" games.
I've tried composing a 1v1 into "everyone vs everyone" by updating the score individually: After a race, I would update the score of the player at position 1 as if it individually won a match vs every other opponent and adding all of the points won individually, for the position 2 as if it lost to the 1st, but won to all of the others, etc. but somehow that doesn't feel fair.
There's a small but noticeable amount of luck on sailing races, and it could happen that the one with the highest skill could have a bad race (or it could be disqualified for one of the rules). In that case, they get slashed a lot of points because they lost to everyone, including those with a score much lower than them, and they take a lot of time to recover.
It's also very hard to balance the participation reward or absence penalty. We need some sort of score decay if someone is not participating to the races. If it's too much, then people who participate a lot might have a higher score than those who maybe miss some races but have more skill. If it's too less, it could incentivise people to not participate to avoid losing points in case the race doesn't go well.
It feels like this should be a solved problem. Is there any rating system based on skill for these kind of games?
Or is there any way of composing a 1v1 rating system into this that isn't as naively as just calculating the individual effects and adding them up?
