Thank you for the reply. That's my bad only using mu, I'm still getting my grasps on this and my memories of my statistics course has been lost with time.

What kind of data would you need? I have records of tournaments played with games, sets, points and placement for all teams in the tournament if that helps. Up to 17 teams in a tournament with two players per team.

Any games where player weights make sense. Small sample sizes are usually not good enough as only a small subset of them end up relevant to the benchmarks. For example datasets please take a look here. Ideally the data should contain timestamps, ranks, abilities and so on. Something one can use as weights.

In this case it's not weight on the player, but on the match itself. The importance of the match is lower and should have a smaller effect on the ranking.

If we consider a tournament between players only, the following happens to the 3rd and 4th place ranks.

I have put the ordinal below the player in the image.

diagram2

1st Player5 5.045
2nd Player1 3.159
3rd Player8 3.288
4th Player4 -0.479

The player that finished 2nd has a value lower than the player that got 3rd place. This is the problem I am looking for a solution for.

I think you're misunderstanding what a rating system is for. It's not meant to create leaderboards for tournaments. It meant to assess and matchup players without having to go through every permutation. In a tournament, you already know wins against who and how to give out ranks. But in online MOBA games or chess, having every player play against each other would take a long time and the players will just keep getting randomly matched with weaker players more often. You can think of the rating a player has as a cutoff point for certain titles (Grandmaster, master etc) so that these titles play each other. There is no advantage for a high ranked player to play a low ranked player since it's a waste of time for the high ranked player. If you want to use tournaments to rank players, a round robin is more effective for a rating system that just throwing random strangers into a tournament. Most tournaments like FIDE will using special pairing algorithms or assignment algorithms like Swiss-style pairings or the Hungarian algorithm.