Your basic premise is wrong. SR is not a zero-sum resource that must be split evenly between all players in a match, or all players in the game. Instead, SR is determined independently for each player trending towards their MMR, which means that it can enter or leave the system every single match.
MMR may or may not be a finite resource - we don’t know exactly how it works. But we do know it’s not affected by decay or the full leaver penalty, which means it does not necessarily trend towards 0.
It seems that people might be overestimating the role of SR and MMR when the matchmaker is trying to form groups, there are a bunch of other variables, an example is:
“The unfortunate truth is that there is not always a “perfect” match for you, especially at very high (and very low!) skill ratings where there’s fewer players of similar skill. Then you throw in the desire to match groups vs. groups, with everybody having low latency, and doing ALL of this as fast as possible even though it’s the 3AM offpeak… it can get tough. We’ve tried different tunings with regards to wait times”
That was from this post, which explains some more of the variables:
Sure, the average SR at the end of the season will likely be lower than the average SR at the when people place, largely because of decay. However, you describe it as a fatal flaw, but it doesn’t really seem to be a fatal problem to me since SR resets each season.
The biggest issue is fairly fundamental, that SR can enter and leave the system at Blizzard’s will, so it is not clear that Blizzard would ever let SR get to zero, even if the seasons were of infinite length. Also, SR doesn’t really act like a currency where the equation balances one person’s loss is equal to another person’s gain. This is most obvious in decay, but it could happen in a more subtle way with performance SR, for example.
This is conspiracy theory talk. The game does not rig matches to favor one team to push players where they belong.
Blizzard doesn’t force the bell curve. It appears naturally because of the ranking system (wins make you go up, losses make you go down) and because people often distribute into bell curves (this depends on how the measurement is made).
Let’s say that during the course of the season, the average SR rose 20 SR because of poor players quiting the game. Everyone could have their SR bumped down 20 SR at the start of the new season. It doesn’t have to be drastic if the drift isn’t drastic.
Win percentage only goes up at really high tiers (like 4200+ or so) and it happens because the game cannot find fair matches for players that are good enough. No manipulation or rigging is required.
Well, we don’t quite know how SR is calculated so we can only make assumptions. However, I think the assumption to treat SR as an economy is flawed for basically one reason:
The amount of total SR is not finite. *
From what we can tell from the scarce data Blizzard has given out, SR is supposed to find your place on a Bell’s curve based on the population of the active players. A good example was Lucio Ball. You could be in silver for the normal competitive but Diamond for competitive Lucio Ball simply because fewer people were playing. The same thing happens with competitive deathmatch or CTF, or any other “minor” season. I am certain we all had our rank being a lot higher or a lot lower in those “minor” seasons. I understand that those are different game modes and therefore someone might actually be a lot better, but the size of the active player base was definitely a factor.
As a thought experiment consider if everyone who is above 1500 SR (silver) stopped playing, and I mean to remove them completely from the season. Then the SR system would distribute the bronze tier across all ranks. The top 500 would still be at 4200+ SR because compared to the new active population they would be better.
From that, it is safe to extrapolate that every time Blizzard has an overwatch sales deal, if a sufficiently large number of high tier players enter the system (smurfs), they will inflate the skill metrics (whichever those metrics are) causing the Bell’s curve to redistribute SR. This will cause platinum players to go back to gold or not climbing despite getting better.
However, as I said we don’t know exactly how the SR is calculated so we can only speculate. That said, it makes more sense to me to design a system that will be invariant of the population size and simply attempt to place everyone on a Bell’s curve, rather than build a system that has to keep track of the total SR and adjust for inflation or recession.
*EDIT: It does not need to enter or exit the system
Take a look at How Competitive Skill Rating Works (Season 13) and the references (most of which are developer statements). From this, you can reject most of what is being said in this thread.
I just want to make the obligatory comment about how (pure) mathematicians ignore application. The mathematics was fine, it just had little relevance to the problem at hand.
Applied mathematics is what we need here. I’m a physicist, so sort of very applied mathematics. We’re kind of the opposite to pure mathematicians. We ignore the mathematics which doesn’t fit our situation where as pure mathematicians ignore the situations which don’t fit their mathematics.
Ok… 1, your example is a bell curve in a non-head to head scenerio… and actually highlights a bell curve that is opposite of the bell curve we see in OW. In OW there is more people on the top tail, then the bottom. After many years, inflation should be pushing everyone closer to the top, not still below the 2500 middle.
2.Bell curves go away when you have a flat win/loss in a head-head scenerio where the extremes of both ends only play each other and are unable to play the bottom
of the tier while also being in a 50% win scenerio.
At that point, the win/loss mechanic is used to spread people apart and differentiate who is better. Think of it like a tournament.
You have 8 people. A-A beats b. c, d
A, c, e, g win
b, d, f, h lose
Then round 2
A, E 2-0
b, c, g, f 1-1
d, h 0-2
round 3
a 3-0
b,e,g 2-1
c,d,f 1-2
h 0-3
Round 4 (rematches are 50%)
a,b,e 3-1
d,g, 2-2
c,f,h 1-3
As you can see… having a 50% win change handicaps and equally spreads people apart, not form a bell curve when you then turn around and have the ends of the bell curve face each other in a 50% chance to win.
The only way to form a bell curve is NOT to have 50% chance to win matchups… but then you run into the problem of Person “A” running undefeated to infinity because they are the best. It is the same thing you see in sports leagues… where when someone clearly is better… they rise to the top… while an equally sized tail appears on the other side.
However, OW doesn’t have equal tails. The bottom 1500 comprises of 8% of the population… whereas the top 1500 comprises 4% You have an additional 10% in the top 2000 Sr… where you get up to 30% in the bottom 2000. Then 60% in the middle 1000, which over half of those are in the lower 500.
Considering this bell curve is also the same over multiple seasons a good year apart makes it look very contrived and planned out. Especially when you consider that if it was natural, more of the population would trend toward the higher end of the competitive bell curve like you showed in the Marathon. Instead it is the opposite.
Also, notice that the bottom half of the bell curve has INCREASED. This leads credence to the alt accounts being added in and pushing the avg player lower as the new players are added in… The slots in diamond and above are finite by design as a percentage of the player base.
I did not say the matches themselves were rigged. It is also stated by the devs that not all the matches are equal, and that varience in SR gained even in diamond and above are due to variences in the the matchmaker viewing if someone is favored or not. They also said you will get put against tougher and tougher matches.
Now, the conspiracy theorists say that Bliz intentionally sets you up to lose a match. They say that games are unwinnable. That is just not true.
However, what I am saying is that when you win… and the game doesn’t think you belong there, the SR will bring you back down by giving you an adjustment. Favor status can also not be determined by SR… even in gold where pbsr can theoretically put your SR exactly where your MMR… that having a team with a higher SR then the enemy does not put you in the “favored” position all the time.
So there is no way to tell if the devs when they say “harder” opponents intend to say… oh, you climb so obviously they are better. Or, is it that they will test you if you can carry a group of similar people that are inflated against a team with a higher MMR but same SR.
Because everything you posted can be true, and everything that I said can be true, and match everything the devs have said.
Somewhere along the line in both cases, SR has to play a role in the matchmaking, otherwise the number fails to have meaning.
They have to artificially fix the SR number so it is relevant. If the computer thinks you are bad, it WILL make the SR find a way to get to the MMR. It is harder now for the system to do that in 3k, which is what decay is mainly their for… and why once you hit diamond it is more about how much you play until you hit GM.
Even in your 3k analysis, you mentioned a variable that your couldn’t attribute to anything other than the MMR which you separated from Hidden SR.
I think what they did with the non-pbsr 3k+ was to tie MMR closer to the SR… like MMR moved faster with wins over performance like it is at the lower ranks.
But when they did that, they showed how much favored and non-favored status has such little effect on SR in lower ranks. IF that is really what the variable is… We won’t know until they actually show us if we are favored to win or not.
What I DO know… is that based on my data I collected from s12, that SR gains and losses are NOT tied to the displayed team SRs in low gold. There is no correlation at all. This leads me to assume that favored and not favored status also is not accurate at 3k and above.
Want to know the best thing about this thread?
Nobody is being toxic and saying “git gud” because you’ve actually mathematically proved that the SR system is inherently de-ranking everybody, and that those who climb are statistical anomalies.
Nobody can argue with sound mathematics… it is the universal language. I too was a mathematics PhD student (graduated).
The fact that you have outlined a valid proof that Activision’s/Blizzard competitive design has de-ranking in its design makes me warm and fuzzy inside. I think the design choice for this system was purposeful… de-rank everyone (or make it nearly impossible to rank up) until they get fed up and just buy a new account.
What definition are you using for bell curve? If you contrive a strict 50% win percentage for each game (or flip of the coin) you get the binomial distribution:
These details, the ones you spoke of, are absolutely possible. Since we can’t see MMR, we cannot know for sure either way-- its important to note this.
However, let’s assume you’re right. What then? Well… If SR is to follow MMR, then consider how matches are formed: the team with the higher total MMR should be favored to win, probabilisticly, right? Yet, if the two teams SR is relatively equal, then you’re saying that they will receive MORE SR for the win than for a loss? This is ezclap if I’ve ever heard it. The team favored to win will get more for winning, think about this for a second.
This is why I reject this theory. It contradicts what Scott Mercer has said in many Q&As where he said the match maker factors in the probability of a win and uses this to decide what was, or wasn’t, an “upset” victory for the purposes of giving, or taking, SR. It rewards unlikely victories, punishes unlikely defeats. I then assume MMR is used in establishing this probability which seems like a reasonable assumption.
Maybe Blizzard is just saying what, in context, sounds fair, even when they contradict one another. Maybe your ‘SR follows MMR’ theory is right, after all. Or maybe Blizzard is doing neither of these things and simply saying what they think we want to hear. We’ll never fully know.
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.