The mean and SD are above. I used a mean of 4000 SR for 20 players in a two-tailed z-test.
For the binomial, 1% of the player base is at GM. I assumed only 20 players over 1000 trials achieved GM again.
In both cases, I used an alpha of 0.05 and Bonferroni adjusted for 20 comparisons.
Conversely you should be asking him to show data for the opposite.
And if you add me on discord, I can show you a player who has thoroughly documented multiple alt accounts he has boosted from bronze to plat/Diamond and higher 
So let’s say 20 GM players did and 20 didn’t. How does that prove your hypothesis?
Because, if it’s random, you’d only expect 0.4 players per 40 to achieve GM again.
If 20 players per 40 achieve GM again, that’s not statistically occurring by chance.
If the game is rigged, you expect 0.4 players. That’s not what happens.
Edit: We don’t prove hypotheses, we reject them. This test rejects the hypothesis that rank is random for GM players.
Ok so ranks are fake. Then ofc you would need some kind of mmr if the ranks are fake. Nothing to really compete for except mmr. It makes laddering a sham. Fun game.
No because you’re not forcing the coin bias (amount of heads or tails) between tosses. You’re not correcting the coin between attempts. In the case of mmr you are forcing those odds, towards 50-50. That kind of forcing is rigging. OW is a game of skill not a game of chance. A fair competition would be demonstrating skill above/below random odds, not forced (adaptive) ones.
Don’t take my word for it, it’s the literal definition of rigging. Sorry the truth hurts. Damage control it all you want. It doesn’t change the fact that 50-50 is a kind of rigging.
LOL that’s literally rigging. They’re trying to set the result before the contest is played. Next?
Random is fairness over the long run. Forced balance match on match is not fair laddering (SR movement). Again, if you’re submitting that SR/ladder ranks are just totally fake, then sure you can rig matches because no one really belongs anywhere.
It sucks to suck. If you’re good, you’ll do well in a random matchmaking system. Rigging the contest odds handicaps good players and buffers bad ones. It attenuates mobility. It’s not at all fair laderring.
You’re not competing naively, randomly, against people in your bracket. And their skill levels are hidden. With mmr rigging, you’re competing under forced outcome attempts. The competition level is fixed ahead of time. In no sport do they change up the teams based on individual performance, and cherry pick the following match based on analytics. They seed you and you progress. Anything else is rigging the natural progression of unadulterated competition.
Is SR my skill level or not? If it is, then MMR has no place. If it isn’t, then there is nothing to accept since no one even knows where they belong.
Rigging matches for 50-50 outcomes around hidden metrics is a fake, rigged, sham competition. It makes no sense for a competitive ladder that already ranks and pays out by SR.
You’re having trouble understanding how the ladder works. Did you even read that post? Adding alts increases disorder, because you are seeded with additional SR (no matter what) that must be absorbed. This creates a lot of collisions and absolutely disrupts rank integrity for several matches.
Show data that the MM tries to preserve a normal pdf, literally mapping people to slots on it no matter what. Also, be sure not to equivocate players with accounts by %. Because with current system - and the data they reported - they are distributing accounts by %, not players by %. So a high % player can place many accounts into a high % rank, disrupting the players % dist, and vice-versa for low ranks.
Please show any source, link, or reference that suggests this so-called “conditioning”. It’s not going to work, because any one can compete more than once. Once you have multiple competes per entrant you’ve already lost distribution integrity because of over sampling.
But it’s ranking accounts. Your analogy fails, because some people get to write the test many times, sometimes tryharding sometimes not. Every alt disrupts ladder integrity, as explained in that thread I linked. Please consult the math there as to by how much (approximately).
No they are not. A full reset is a fresh test with a large degree of simultaneity. A new entrant is taking a test against a ladder with ideal pdf established years ago, while multiple accounts per player have entered and displaced, ruining the SR distribution (and MMR distribution) away from ideal reference configurations. As they enter they disrupt and those disruptions are absorbed. In a reset-to-middle scenario, there is a lot more mobility and the disruption is minimized by for the maximum number of people (as per Virial Theorem which you would be familiar with from thermostats).
I think the author means distribution of % players by skill. Not accounts, not mmr, not sr. That curve is supposed to be normal and basically scale invariant. But current ladder is SR, which is not MMR, based on rigged mmr matches, based on multiple accounts per player, with no data to support restorative or corrective actions in 5+ years.
If you read the thread I linked, even a small % of duplicate entries bork the results because of sampling errors. So even under the ridiculously conservative assumption that only a small % of players have >1 accounts, say k=1.1 accounts on average, you still impart errors.
LOL no. Look at the growth rates. They shift higher order moments as well. It only takes a few % of the players to occupy more than one position on the ladder to increase the entropy geometrically, forcing tons of extra matches before the curve reaches new equilibrium. And this equilibrium is almost surely positively skewed version of prior distribution, because when we think of “mains vs. alts”, alts are more numerous and lower rank than their corresponding mains.
So please tell us how the ladder corrects for alt accounts, maps people to a fixed curve based on player % mmr not accounts % sr, allows fair ladder progression, and does not gain entropy and integrity deterioration from initial ideal pdf, despite having literally 0 maintenance in 5+ years.
What you are suggesting is this ladder is the literal holy grail of ranking systems.
Oof what is this bad math I’m reading. A “rigged” matchmaker arrests ladder mobility, it does not vastly alter the statistical count of final destinations at asymptotic playouts. It’s a 1st and 2nd order percolation tax. You have not computed the length of their trajectory - how many games they have to play in a naive matchmaking system vs. a rigged one. You would be better with math from queueing and percolation theory than lol z-tests that my students do in 8th grade.
Again, “rigging” affects your stochastic trajectory, not necessarily your final rank (for sufficiently long stopping times).
Do you still not grasp what we mean by match rigging vs. fair laddering? It’s about the signal/noise ratio and effort to overcome. The “hypothesis” you want to test is how many GMs make it back to GM after so many games played. And that Receipts guy already showed us some .py simulations to compare mobility in naive mm vs. rigged one.
The result was, you get some streaks and stomps with naive matchmaking, but the final destination (50% winrate convergence at their hidden rank) is achieved faster and more efficiently with naive matchmaking then if it’s rigged.
Nothing to hold people back when MMR is cancelled. But I guess that’s not engaging and retaining enough and you never need to buy multiple accounts.
Conclusion through observation is actually very scientific.
Not to mention having climbed at least 5 or 6 accounts to GM/T500 and never having slowed in progression until at least high Diamond to low masters is proof enough that individual contribution can determine the outcome of a game.
Any GM player can take losses in this process but still be propelled upwards purely by performance alone. If you’re losing less SR when you lose and gaining more SR when you win, you’re mathematically being forced upward.
How are ranks fake? It’s a clear and numerical representation of your position on the ladder. It’s use in match making is to clearly define boundaries high/low for skill matching.
You should provide your reference for literal definition rather than providing abstract context. In that regard you’ll at least establish a baseline for him to prove/disprove.
How many different technical words are you going to string together to deviate from the fact that you’re just not meant to be successful in Overwatch?
That isn’t an argument for/against rigging though. I have many accounts and as soon as I go into climbing mode, the sweat level always comes to me faster than 100s of SR worth of skill. My progression goes from 56% to 51% say, for 2000sr worth of the ladder climb. That’s with reverse boosting, a term from CoD and other SBMM games, where you deliberately trysoft to win, shedding a disproportionate amount of mmr for that slight sr gain. This cools off your matchmaking so you get some easier games on the climb, as not being knapsacked into “fair” match where you are always the expected carry.
Also extremal examples “as a GM i can climb really fast and easy” aren’t a great illustration. They don’t make much of a case, because your signal is so pronounced over the noise it hardly sets you back. The rigging is really obvious for people only 1000sr below where they belong, where there are plenty of smurfs with equivalent mmr to matchmake you against at the wrong sr.
Wasn’t arguing about rigging here homie. You’re out of context a little.
violence have you ever been to mid or low gold? silver?
I’ve been playing since beta…up until 2 seasons after shield nerfs ive been comfortably gold. Now, my games are way harder than any time i can remember in gold at low silver…every game is literally a pull a rabbit out of the bag game. you lose SR faster than you can gain it…you get stuck in an endless loop at the same SR…games are harder in silver and bronze than they are at mid gold and above.
anecdotal evidence…all the players on my friends list…their ranks are getting worse and worse with each season. and all of them were in gold as i was…heck even in low plat…and now they are mid to low silver.
the game is completely opposite at high gold and up vs low gold and down. And, unranked to gm games ( i watch a lot of ml7) start at mid to high gold…
edit: come 2 seasons from now and i wont be suprised if low rank meta as pertains to support will be mercy/zen/bap…becuase bap is broken…and becuase zen mercy are the only 2 hero’s that can boost dmg.
What role do you (Dove) play?
Is it possible that you and your friends list haven’t spent the required time to improve as players?
Up until recently it was tank…at gold. I play the same way at support and for the life of me I cant climb…I play zen and routinely out dps our “dps”. I kill the df, the tracer, the pharah…all the snipers…*the dps our dps seem to avoid, the supports. I heal the tanks but primarily try to keep orbs on dps, save my ults for the big enemy plays or if the whole team just chomps up a metric ton of dmg. I try to build ult as fast as possible, seeing as many hero’s build their ult far faster than zen or lucio do.
I’m getting pretty good at zen. Averaging about 30% accuracy usually, i judge that to be slighlty below average. I hope thats a decent start, but for the life of me its like its easier to lose Sr than it is to gain it. just today i spent all day climbing just 60 sr. It’s an endless loop, regardless of the support played. I’ve already tried playing utility supports, health pouring supports. The only thing that seems to make a slight difference is boosting the luck shots of dps…or “popping off” with 3+ kills in a row.
Not sure there’s ever enough time spent improving…its an ongoing exercise…I watch a lot of ml7 unranked to gm or flats or emongg…mainly for positioning. I comm enemies often ( wish they’d put a ping system in the game because I’m direction challenged with call-outs 
)
i have friends that play every season…although I’ve noticed some arn’t playing as much anymore.
Here are 4 games: 2 on a win streak, 2 on a loosing streak.
wins: 58D983, 996NP8
losses: N88EDW, 1AAHG3
perhaps I’m seeing things through rose tinted glasses.
As a heads up, I’m not flaming or mocking you, I’m inquiring because I do actually care about people enjoying the game.
Apologies, currently reading a technical document so I cannot look at this time. I’ll respond in a couple hours.
no worries, thank you 
Is this a discussion about climbing or a discussion about having 11 different accounts and having hard games no matter where they are on the ladder. Because of mmr rigging, any sudden climb will face vs. smurfs faster than you rank up (sr). It’s so noticeable but maybe you need to have many accounts boosting and climbing to really notice it.
It’s a conversation between Dove and I which doesn’t involve you. But since you asked.
If your MMR doesn’t belong in the rank your account is in, the games are harder because:
A. You’re being outclassed by your teammates and enemies and you aren’t being helpful toward your team.
TLDR: you’re not good enough to be there
B. The system is trying to push you down the ladder where you belong.
k so tldr it’s rigged
I’m hardstuck diamond, and yet my silver account fights a lot of smurfs - people on my main diamond friends list. It finds the other smurfs via mmr and matches you with/against them. As soon as I notice someone too good for the rank I add, pm, and find out they’re in a discord I’m already part of.
There is zero rank integrity. Rigging tries to compensate for smurfing and lack of resets. Stop defending it you’re just making yourself look like a boosted.
Fake is not synonymous with redundant.
50-50 isn’t biased, is it? Not every coin is properly balanced and can be biased. However, you can attempt to use unbiased coins and you can limit the amount of tolerable bias. “Forcing” out bias isn’t “rigged,” it’s fair by definition.
Yes, it is a game of skill and climbing the ladder demonstrates that skill. Is a Diamond player more skillful than a Gold player? Yes or no?
No, it literally is not. If we followed your logic, “forcing” a high school soccer player to play games in a high school league is “rigged.”
Making you play against people of your own skill level and matching solo players to teams for even matches is not rigged. And it doesn’t matter how much the hard-stuck complainers want to post about it.
No, it isn’t. Random can put a Bronze player in GM or Diamond player in Silver. Nothing about that is logical or fair. Random makes SR a completely meaningless ranking system.
Yep and all the hard stuck kids will come crying back to the forum about how “unfair” and “rigged” the system is because the other team gets 6 2700 Plat players while your team gets 5 1800 Silver players. Talk about “handicapping.”
Do you want your games to be unfair? I don’t want to waste 10 minutes of my life kicking the hell out of Silver players for next to no SR. If that’s your circus, go play a different game.
I know that. You are matched on the basis of MMR. Solo players are distributed to make the teams as fair as possible. MMR = SR unless your account is fresh or your SR is high enough to decay.
No, you just don’t understand what entropy means, how to measure it, nor apply the concepts. I gave you a list for why it doesn’t hurt the ladder. Feel free to substantively respond.
Manual data mining plucked out 122,414 accounts with a mean SR of 2266. How many alts at 3000 SR do you think there needs to be to shift the mean player performance up to 2500?
Please explain why the distribution is still normal every time we look at it–whether that data comes from manually mining or from Blizzard. Why aren’t all these alts skewing the distribution?
Well, what is the statistical effect then? How much do you think you’re being held back?
Walk the talk, fam. I love data.
Great. Let’s see the trajectory data. Pretty wild that GM players can go from unranked to GM in one sitting, right?
Open elo systems have a linear trajectory. SBMM systems have a near sigmodial trajectory.
No, my first season I placed ~2600 and moved up from there.
That’s because the player base is dwindling and generally veteran players are the ones sticking around. More experienced players tend be better at the game. That causes the average performance of players on the ladder to increase. Meaning if you didn’t improve, you dropped in rank because you are always measured against other players.