Re:Implementing the Elo Rating System (2020)
by jerf on Friday February 12, 2021 @03:59PM
(#26118475)
"The sentiment you're expressing is the idea that one 2k player is so much better than two 1k rated players that it doesn't make sense to simply sum up each team's rating and keep it even, which is the false assumption that the AoE 2 devs made. Elo is not linear."
It's even better than that. Elo is purely relative. The difference in score between two opponents is what is supposed to predict the likelihood of victory for the two. This means that you can add any constant you like to the entire Elo pool without affecting the Elo rankings at all.
As a matter of aesthetics, when initializing an Elo pool it is nice to try to start with values that will result in nobody having a negative value, because that gives humans the feelbadz, but that's not mathematically necessary; you can run the whole thing deep in the negative billions if that floats your boat.
The Elo math is very much based on two players playing head-to-head. It would be completely broken for almost any other scenario, as multiplayer introduces new degrees of freedom that Elo has nowhere to put. By that I mean that there may be one game for which the team's skill is essentially the max of the members, another for which is it essentially the minimum, and a wide variety of things in between. Elo has nowhere to put that "wide variety", and it was never designed or intended to do so, so that's not a criticism of it. It just isn't what it was for.
It's even better than that. Elo is purely relative. The difference in score between two opponents is what is supposed to predict the likelihood of victory for the two. This means that you can add any constant you like to the entire Elo pool without affecting the Elo rankings at all.
As a matter of aesthetics, when initializing an Elo pool it is nice to try to start with values that will result in nobody having a negative value, because that gives humans the feelbadz, but that's not mathematically necessary; you can run the whole thing deep in the negative billions if that floats your boat.
The Elo math is very much based on two players playing head-to-head. It would be completely broken for almost any other scenario, as multiplayer introduces new degrees of freedom that Elo has nowhere to put. By that I mean that there may be one game for which the team's skill is essentially the max of the members, another for which is it essentially the minimum, and a wide variety of things in between. Elo has nowhere to put that "wide variety", and it was never designed or intended to do so, so that's not a criticism of it. It just isn't what it was for.