Stroom wrote: ↑22 November 2023, 06:28
Meeplelowda wrote: ↑22 November 2023, 02:09
Using Elo/Glicko-like rating systems for chess and other abstract games is well-established for over-the-board play in those communities. So you would not expect that online versions of them would be any different. BGA decided to take a kinder, gentler approach, regardless of how silly it may seem to some people (myself included) used to Elo/Glicko. Also, Elo/Glicko was not designed for multi-player games, so they are already wedging a square peg into a round hole for that use case anyway.
Elo for multiplayer games is OK as it is. Nothing wrong with it. You calculate individual score diffs per player.
There are 2 ways to calculate it - either the winner just wins against each loser or each player gets a ranking and based on those 1st wins against all of them, 2nd wins against 3rd and 4th, 3rd wins against 4th. BGA uses the second way.
Of course, that's how it's implemented, but it's not what it's designed for. If it were actually designed for multi-player games, it would account for the estimated probability of finishing 2 out 3, or last out of 4, etc. When calculating rating change between 2nd and 3rd place finishers, they use exactly the same formula as if the 2nd and 3rd place player were playing a two-player game, which cannot possibly trend toward an equilibrium that estimates the actual probability of finishing *anywhere* above the 3rd place player, including 1st and 4th, 2nd and 4th, etc.
But it's good enough and better than nothing if you care about those kinds of things.
For the curious, here is a
research paper detailing a proposal for an Elo system actually designed for multi-player contests.
Generalizing the Elo Rating System for Multiplayer Games and Races
Abstract: We introduce a non-standard generalization of the Elo rating system for competitions involving two or more participants. The new system can be understood as an on-line estimation algorithm for the parameters of a Plackett-Luce model which can be used to make probabilistic forecasts for the results of future competitions. ...