I’m not sure what you are saying we “can’t know”. The devs have talked about the bonuses to SR for performance or divergence from MMR, and they are readily observable in game. Kaawumba has a amazingly well sourced thread explaining all the details of matchmaking we know, with citations to all the dev statements. I believe he linked it in this thread somewhere? If you need I can go hunt down the link for you.
You are mixing up two different effects here. It sounds like you think matchmaking is done by SR? Let’s be clear: SR is not used in matchmaking at all. This has been repeatedly stated by official sources (here is just one example https://twitter.com/playoverwatch/status/850435344457543680?lang=en).
If teams aren’t perfectly balanced and one has higher MMR, they will have an advantage and thus gain less MMR for a win, just like any other MMR/Elo system. If, for some reason, every member of that team had an SR meaningfully lower than their MMR, they would also gain bonus SR. But in your example, the “advantaged” team has an SR below the other team, so it should be obvious this bonus is working to fix the improper rank.
Nothing I’ve said contradicts this. Mercer is just describing how any MMR/Elo system works. If you understand those systems, then realize Overwatch uses a hidden MMR (Like most games: League, CS:GO, etc). It’s the hidden MMR that is the games understanding of how good you are, and what it uses to make matches.
SR, just like the tier icons, is just a shiny badge to reward players. It mostly equivalent to your MMR, but not always so (decay being the most obvious example of when they diverge).
If MMR is stored digitally and is a number, then we know it’s finite. This is because there’s only a finite number of bits in the world to store the MMR data, and as we know 2^K<infinity when K is finite.
But, if MMR is not affected by decay and leaver penalties, then yes the total MMR in the system likely does not trend to 0 but rather oscillates about a increasing function modeling the total number of OW players in the system. i.e. if the total MMR in the system is K at time t with C(t) total OW players, then with probability 1, it will again be K/C(t) * C(t+s) at time t+s, where s is finite.
Again though, I was modeling SR, not MMR. It helps me little to know that my MMR is not tending to 0 if my SR (the only number I see) tends to 0. I am still an upset player in this case – though your point is well received in any case.
It has been stated by Blizzard, (I’ll have to find the link) that MMR is a floating point number generally (not exclusively) between -3 and +3 and is measured in Standard Deviations. This means that there is no bound to either end of MMR, just that being at either end is by definition extremely improbable.
A Mathematical Proof
old thread, I wonder if someone explained to him how to give a mathematical proof. I also don’t even see a real hypothesis. Still not a bad thread.
SR is not a currency. It’s placement on a bell curve. Your performance vs avg performance at your rank = sr gained/lost. This repeated = stagnation/climbing/dropping.
There is the fact however, that as the devs have said, matchmaking is done by mmr and not sr and matches will not be made if the teams aggregated chance to win is lower than 40% or higher than 60%. This causes problems when you have high mmr for your rank. But usually high mmr with low rank = high sr gains so you’ll be good.
