Analyses of the ratings - Spotting the issues

[Mercy9545]

@ casusincorrabil Thank you, and it’s nice to see someone spending time and effort on this too.

I mostly agree with you and will reply to the parts of your post where I have commentary.

@casusincorrabil

The question would just be which divisor to chose for the exponential average, as each divisor would give way different results.
As base I would chose either the natural exp or 2. I don’t know which is faster to calc for high exponents for the computer. I think maybe base 2 should be easier to calc - but I read somewhere that they actually use the taylor seris with a table, so this would mean the natural exp should be the way to go, at least if the exponent doesn’t exceed a specific value.

My proposal:

Team elo = ln(avg(exp(ind.elo/500)))*500
This would mean the team elo for a 3000/3000/1000/1000 team would be 2663 opposed to the current 2000.

They should use whatever base is most convenient for them and change the number they divide the individual elo by to compensate. There is actually only one degree of freedom in the exponential average calculation. Since (x^a)^b = x^(a * b), any change in the base could be translated to a change in the exponent and vice versa. For example if I am not mistaken (quick maths), then ln(avg(exp(ind.elo/500))) * 500 is the same as log_2(avg(2^(E * ind.elo/1000)))*(1000/E). (I multiplied the bases with 2/E and did the same with the ‘500’.)

In my first post where I suggested to use the exponential average (Analyses of the ratings - Spotting the issues - #93 by Mercy9545), I chose to put my degree of freedom (and I called it the parameter ∆) in the exponent in a specific form such that it conveys intuitive meaning: ∆ is the rating difference we think you need to have with other people in order for a 2v1 match with them to be fair. If we agree on ∆, then there are no more degrees of freedom.

@casusincorrabil

There is also another method which could possibly be viable. This method would need some calc to do. It would work like this:
If Team A wins against team B the EACH teammember of A) would get elo according to if they would have won against a single player with the Team elo of Team B. And Team B would lose elo individually in the same manner.

This is how the old system worked (only there they would get Elo as if they had beaten the highest rated player on the other team, while at the same time they would get matched based on average Elo, a combination that did not make sense). In this approach, if a group of players play together for a while, their ratings will converge. I don’t like that. It means that if two players with different rating play together, the higher rated player will start to unintentionally smurf and the lower rated player will be unintentionally boosted.
I remember that during the times when the old calculation was still in place, someone told the following story: ‘My lower rated friend and I regularly play together and when we do, we have a 50% winrate. However, whenever my friend plays without me, he almost never wins, causing him to have an abysmal winrate overall. How is this possible? Should the rating system not make sure everyone gets a winrate that is close to 50%?’ I explained how I thought the story he sketched was consistent with a rating system where players who play together converge in rating and ended up advicing him to use a smurf account to play games with his friend in order to result in matches that were paradoxically more fair (!).

@casusincorrabil

I don’t speak about it’s not possible, but the calc would be so complicated that you can’t explain it anymore to anybody, what would cause even more problems if some new shenannegans occur.

This point was not about a specific rating system that I support, but nonetheless I think this is an interesting point: aren’t we making things too complicated for people to follow? I think on the one hand yes: many people will not be able to fully understand our discussion. But on the other hand no, I don’t think it is bad for us to make things complicated. The 1v1 Elo system is already very complicated. Almost no one understands the mathematics and assumptions behind it. Yet, it is not difficult for people to get an intuitive grasp on how it works. People know that if they beat someone stronger than them, they get lots of points, and if they beat someone weaker than them, they get not so many points. How the mathematics ensures this happens does not need to concern them. Similarly, though some people will not be able to follow our discussion on exponential average, they can understand that we want the higher rated players in the team to have a bigger impact on the matchmaking. In fact, if Microsoft were to adapt the ‘exponential average’ formula, they could just write in the patchnotes something like “The higher rated players in a team now have a bigger influence than the lower rated players in determining what other team they will be matched against.” and leave it at that.