Now I'm trying to find a matchmaking system that suits our fun party game. The basic feature I want would be a fair system with few limitations.
As a result, I started my research.
1. ELO
https://www.youtube.com/watch?v=AsYfbmp0To0
the centre of the curve could be seen as average, the centre line is the average
the logistic curve
the more this curve is to the right of 0, the more likely that the player wins
ELO system: if one player is 400 more points than another player, they are 10 times more likely to win
The Winning Probability Equation:
Because B wins = (1-P(A wins)), so
Write this equation in another way, so
If the result is 1, then you must win; if the result is 0, then you must lose
When a player performs better than expected, his points will increase; the more incredible the victory (small P value), the more points he will get; the more incredible the loss (high P value), the more points he will lose
The Elo Points After the Game Equation:
When Player A = 1656; Player B = 1763
Pb’s Elo=Pb’s previous Elo +key factor(1-Pb’s winning probability)
Therefore, there is no advantage in scoring between strong players and weak players
After a long time, the ELO value of this player is very close to his real level
Pros:
widely used & well understood
Cons:
only works for 1v1 or team vs team but only based on the whole team’s point, not the individual's point
new players will take a long time to converge to their skill rating (long time)
2. ELO- MMR
Aram Ebtekar and Paul Liu. 2021. Elo-MMR: A Rating System for Massive Multiplayer Competitions. In Proceedings of the Web Conference 2021 (WWW '21). Association for Computing Machinery, New York, NY, USA, 1772–1784. https://doi.org/10.1145/3442381.3450091
’“MMR” stands for “Massive”, “Monotonic”, and “Robust”
“Massive”
it supports any number of players with a runtime that scales linearly
“monotonic”
a synonym for incentive-compatible, ensuring that a rating-maximizing player always wants to perform well
“robust”
rating changes are bounded, with the bound being smaller for more consistent players than for volatile players
Classically, rating systems were designed for two-player games. The famous Elo system, as well as its Bayesian successors Glicko and Glicko-2, have been widely applied to games such as Chess and Go
Pros:
Massively Multiplayer: the algorithm is fast and numerically stable, even with thousands or millions of individually ranked contestants
Incentive-Compatible: the better you do in competitions, the higher your rating will be
Robust Response: one very bad (or very good) event cannot change your rating too much
Cons:
new players will take a long time to converge to their skill rating (long time)
3. Trueskill
Example: Halo 2 online
improves upon ELO
Eric is experienced, so his area is tall & thin
When Natalia wins, his value will grow taller & thinner (average skill+, uncertainty-)
Eric has a low average skill (25), as a result, he will not lose much value on that
Pros:
Flexible and can be applied to many different kinds of competitive games
quickly converges to the player's true skill (only a few games)
easier to model new players (with the initial rating of 0 and uncertainty)
Cons:
calculations are very complex, players may feel confused and "unfair"
it is proprietary and may need a license (the alternative is the Glicko system - limited to 1v1)
Conclusion:
I found that a lot of the matchmaking and ranking methods are all based on the classic ELO system. As the ELO system was originally designed to support the 1 vs. 1 chess game and our game is a multiplayer party game, we need a matching system that: supports the multiplayer function, can be an incentive - Compatible and a single event may not influence the player’s overall score. At the same time, we would like our players to feel “fair”. As a result, the ELO- MMR can satisfy our needs.
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