I've thought about ranking systems quite a bit and I think it's best to create a new ranking system whenever you have a new project since every time you'll have different parameters and requirements. You could adjust for example parameters of the elo ranking etc. but this will always result in a half-hearted solution. Most game companies create their own rankings & matchmakings for every game.
Of course the already existing rankings are not bad by any means but usually they try to generalize a given scenario which only gives a rough trend. Looking at how other ranking systems work is a good basis for your own ranking but usually creating a ranking system is a complex process which even after implementation requires a lot of tweaking. Thousands or millions of dummy scenarios are required in order to evaluate the quality of a ranking system and often the math behind it is not that simple.
Writing down how the ranking is supposed to work is one of the first steps at creating one, although this might sound simple it is a lot more complex than you might think.
Users who don't play often should not score higher than users who play every day.
This sounds obvious but on the other hand, how do you quantify often? Is someone who only played one time (scored high points) supposed to have a higher ranking who has mid scores but plays every day? You would have to define a mathematical relation between amount of games/days played with the amount of points. How does this relation look like? Is it supposed to be linear, logarithmic, exponential etc. How will this effect the strategy of the players (will they play less put try to play well in order to get higher points)? Will this behavior have an impact on other aspects of the game (less trained players per user?)?
Every requirement will affect the ranking and thus you have to analyse how they will effect each other (maybe give some higher priorities than others or even ignore certain requirements in some cases). Every ranking system is comparable to a dissertation (depending on how detailed you want to make it)
I'm not sure whether I understood your request correctly but to me it sounds like you want to create a ranking for every user based on the success of every player a user has.
My first idea would be to create a ranking for every game (chess, go etc.). Rank every player who plays this game in it and then calculate the overall ranking based on these rankings for every user. Of course this would be very complex since you would have to create a ranking for every game BUT there are lot's of decent rankings for every game. This way the only thing you would have to think about (given you found a ranking for every game) is in which way you want to calculate the overall ranking based on the rankings of every game (still not easy but way easier than creating only one ranking containing all information of every game).
This is what I would recommend to someone who doesn't want to spend too much time with the math behind it, which is still a lot.
The advantage of a ranking for every game would be that you could use this ranking for your matchmaking process, but this is another topic.