However I don't think they'd have fixed it just by averaging the Elo ratings, they must have implemented something more complex, like a proximity based algorithm, otherwise if the teams were the same size you'd hit a similar problem with an average as with a sum. A 2k player + a 0 rated player would sum to 2k and average to 1k. You and your friend would also sum to 2k and average to 1k, again assuming even team sizes.
That said, still very funny!
Also, fun fact: Elo isn't an acronym/initialism, it's someone's name, Arpad Elo (the inventor).
Also also, I don't think Elo is really a good idea for multiplayer (more than 1v1 that is) games generally. Don't know enough to say that authoritatively, but using it for something like AoE 2 is likely prone to all kinds of strange unexpected outcomes.
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.
Overall you can make it somewhat work, but Elo really isn't well suited for anything larger than 1v1
Its similar to how you model situations where multiple latent skills contribute to performance (multidimensional IRT). In practice, it's a way easier though to use simple stuff like averaging / constraining groups so everyone has roughly the same skill level.
At least in comp I don't get rolled too often, so it sort of works.
It would be generally unclear that rankings can be treated linearly. A subtle aspect of Elo is that as the disparity between two players increases, the Elo metric essentially becomes less and less certain that there is any relationship between the skill of the players at all, which is probably a bit deeper way of understanding "why" . Eventually you'll reach a point where if you round to integers, the winner winning will result in an increase of 0 points. (In fact one thing to watch out for is how you round; it's easy to end up with a wandering Elo basis if you truncate both sides rather than rounding properly, for instance.)
It's fairly trivial to show that if you take a pool of the worst players and the best players, Elo will eventually converge to those two pools having about that amount of distance between them, but by inserting a fresh pool of middling players into the pool, the distance between the best & the worst will increase despite their skill not changing. If skill is linearly distributed... assuming you can even define that... Elo ratings might be somewhat reasonably treated linearly, but skill is very unlikely to be linearly distributed.
Basically, I like Elo when used properly and I have used it to good effect a few times myself, but it is a bit dangerous in that it offers a number... but that number lacks many properties we associate with integers. (For instance, in another posting I point out you can shift the entire Elo pool by any constant you like without changing the system. Integers do not have this property.) They have a definite meaning, but it isn't what your intuition might suggest. You really shouldn't do any arithmetic on them. They only make sense in the context of the Elo computation itself.
But honestly, elo is a shit system for fun matchmaking anyhow.
https://en.wikipedia.org/wiki/Elo_rating_system#Practical_is...
Trueskill and many others are often used instead.
https://en.wikipedia.org/wiki/TrueSkill
The biggest issue is fun is not the same fair and its a lot more complicated to tune for fun.
You could, for example, play 100 matches where you were given the closest opponent but at a disadvantage for every single match. There's a lot of other scenarios around how you want to fold in ping based match making and how that smaller pool effects the fairness of the matchhing.
Elo tells you how skilled a player is, how surprising a result (win, loss, draw if applicable) is, and how a player's rating should change based on a result and how surprising the result was. It does NOT tell you who should be matched up against who.
> The biggest issue is fun is not the same fair and its a lot more complicated to tune for fun.
> You could, for example, play 100 matches where you were given the closest opponent but at a disadvantage for every single match. There's a lot of other scenarios around how you want to fold in ping based match making and how that smaller pool effects the fairness of the matchhing.
Elo tells the system that if you play 100 games at a disadvantage, your rating should not go down as much when you lose, and should jump up more on a win. Elo is the math that tells the system that if your skill does not change, your score does not change, regardless of whether you play 100 games at disadvantage and lose most of them, or play 100 games at an advantage and win most of them.
I agree that Elo handles uncertainty poorly; when you're rating a chess player whose career is tracked over the course of decades, this isn't an issue, but online play with transient accounts, players who blip into a game when it's hot and then never play it again, smurfs and account buyers, people who take a break for a while and come back, patches which might radically change the meta, etc, uncertainty should be accounted for. Note that TrueSkill is, for all intents and purposes, just Elo+Bayesian inference. Like Elo, it is a rating system, not a matchmaking system. TrueSkill does not handle the problem of playing 100 games in a row against players who are better than you. TrueSkill, like Elo, just tells you what a result means, not which players should be pitted against each other.
It's open-license, handles complex matchups (e.g. 5 vs. 3 vs. 4), comparable in predictive accuracy, and is up to 20x faster than TrueSkill. The implementation is also much simpler.
> You could, for example, play 100 matches where you were given the closest opponent but at a disadvantage for every single match.
not really, you'd derank aggressively and end up playing people at a lower level and presumably winning comfortably after some time.
It’s also a bad fit for team games. But ranking individual contribution to a team is hard. Even for something like the NBA where there’s obviously a ton of incentive to do this, statistical methods rely on a large sample size and often need to be taken with a grain of salt.
I think I'm missing something. Could you rephrase this?
Players C and D and randos on the internet and solo queue for whatever. Player C has a rating of 1900 and Player D has a rating of 2100.
The matchmaking system tries to find a match for Players A and B to play against. Their Team Rating is 900+1100 = 2000, so it looks for another team rated around 2000 to play against. The matchmaking system finds a team rated 1000, and that's no good, and a team rated 3000, and that's no good either. It can't find a team rated 2000, so it goes to the fallback plan. It just tosses the team into the solo queue and lets the solo queue matchmaking system handle it.
The solo queue matchmaking system has a player with a rating of 1900, a player with a rating of 2100, and a ~~team~~ player with a rating of 2000. Perfect! It matches the ~~team~~ player with a 2000 rating against the 1900 and the 2100, which averages out to 2000.
We would either get paired with another couple 2k players against a full team of 2k (4v4 match) or in the worst case a 2v2 against 2k players.
In the 2v2 case, because of the Elo difference the opposing side was expected to win >99.99% of the time.
A sum might match them up against two players with 1300 skill & 200 skill due to the 1500 sum. OTOH, the average would match them up against... an average of 750, so the same people?
I'm sure I'm just missing something really fundamental about how this all works.
Whenever my friend and I played online together, we would sporadically get absolutely creamed. We started looking up the stats of the others players we were matched with and noticed that on those bad games the average Elo of our opponents would jump to >2k Elo vs our barely 1k.
Both of us being software engineers, eventually the conversation turned to “What the hell do you think is going on here? How does a matchmaking bug like this crop up?”
Eventually we came to the conclusion that they must be summing out Elo for the Elo of our matchmaking party rather than averaging it.
Eventually the issue was patched and our worst suspicions were confirmed that indeed multiplayer party Elos were summed instead of averaged.