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Here are a few ways mmr inflation could hypothetically happen. First of all, Valve could probably tell us what's going on regarding mmr themselves and save us from having to read reddit posts by maths students. Dotabuff could probably tell us something useful too.
1) There is an mmr floor of zero. So while in the model, mmr gain/loss is zero-sum, in reality it may not be. The existence of loss-bots is documented, and these bots may occupy the floor, "creating" mmr.
2) New accounts could systematically be calibrated at above-average mmrs. Higher-skilled players could be more likely to make smurfs, or valve's calibration system could be over-estimating mmr, or other reasons. Regardless of reason, calibration at non-average mmr will change the average mmr.
3) Even if the average mmr is non-changing, observe that that highest mmrs are increasing. There may be the illusion of inflation at high mmrs. Imagine stretching a slinky. In fact, people may be talking about high-skill mmr inflation when they speak about inflation.
4) While ideally the total mmr pool (and mmr average) should not change, this is not the same thing as saying median mmr cannot change. Recall that {4,4,4,4} and {1,5,5,5} have the same average but a much different distribution. The distribution could skew non-normal for a multitude of reasons. So far there is no evidence of this happening, but there has been a lack of data.
My point is that there are a lot of assumptions in certain refutations that are not true by necessity.
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Northern Ireland22212 Posts
u get some mmr sinks as a result of abandons
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I think you are missing the most likely point:
The number of players increases, and every new player adds mmr points (his calibration mmr) to the overall pool. Independant of the fact that his calibration mmr may be too high or too low. Now of course it depends on the distribution, but lets have a look at the following (extremely exaggerated) example:
It starts with 2 player, A and B, calibrated at 1000 MMR. However, A is much better than B and eventually takes away all his MMR, and the MMR exchanges stabilize at A with 1500 MMR and B with 500 MMR. Now player C, who is exactly as good (or bad) as B, enters the game, with his MMR also starting at 1000.
If want to keep the ratio of A having 3 times as much MR as B (and therefore also C), this gives
A: 1800 MMR
B: 600 MMR
C: 600 MMR
If we want to keep the absolute difference of 1000 MMR points, we would obtain
A: ~1666 MMR
B: ~667 MMR
C: ~667 MMR
So the simple fact that C enters the game increases the MMR of both A and B.
(I havent checked yet, but it might be that in this example, and therefore maybe my theory, would fail if C would be calibrated at <500, MMR)
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Yes, but that is a case of the system "over-estimating mmr."
In your example, if C enters at his "true" mmr of 500 (the same as B), then there is no absolute movement and average mmr goes down. But if we "assume" a normal distribution of entering players, there is no net movement of average mmr in the long run.
You give a good illustration. You are right I had some wording problems.
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I don't think valve adds people at too high mmr. More like at a too low mmr since people that are at 7k now can't calibrate a new account at >5k. They are a very small part of the sample but generally speaking I've found that any smurf I make will climb in mmr when playing ranked. (Havn't made a new one in close to a year now though.)
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MMR slowly deflates relative to skill as the player pool gains experience. But since most calibrating players are relatively new, I would expect the average calibrated MMR to decrease over time.
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There's one point you didn't bring up, which is the difference in skill at high levels. There's no uniform measure of skill that applies very well across all ranges of MMR. The higher you go, the more intricate details of gameplay start to make a large impact in how a match plays out and the sheer amount of them makes it impossible for one person to control them all flawlessly. This leads to players specializing in certain aspects of the game, like tempo controlling, making space, farming and all others. Those who are better at more of those aspects will naturally win more games over time and we all know how much effort is required to master a lot of them. There's not really inflation, just a few very good players winning more games due to the small pool of players to pick out teams with low standard deviation of MMR from.
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i played dota since the beta and when they got calibrated at 3,9k. So i played around 3,8-4k mmr, which at that time was solid players. I ve improved a lot since then (I would say), but I am still around 4,2 - 4,3k so I didn't have a significant raise in mmr. So I would say from my perspective that the mmr didn't inflate too much. When I played a smurf it was also rated at 3,9 k I belive. That would speak against a signification deflation at the low end 4k bracket.
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People forget that grinding MMR takes time, because of all of the factors of variance involved. Even the best players dont get to 7 or 8k MMR overnight. I think a lot of what people are experiencing which they attribute to MMR inflation is simply the MMR of the player pool diffusing out.
Think of a drop of dye in a glass of water, like the dye initially everyone was at a much more similar MMR, and time has allowed the better players to disperse from the average, and also the worse players have dispersed as well. The end result is that the average skill level of games at your MMR will remain the same, but the range of skill levels within the same game will be much smaller.
So when your games may have looked like this:
+ Show Spoiler +Player 1- 4100 (3500 TSR)
Player 2- 4150 (5000 TSR)
Player 3- 4125 (4300 TSR)
Player 4- 4200 (4200 TSR)
Player 5- 4170 (4200 TSR)
Now your games look more like this:
+ Show Spoiler +
Player 3- 4350 (4300 TSR)
Player 4- 4200 (4200 TSR)
Player 5- 4200 (4200 TSR)
Player 6- 4225 (4300 TSR)
Player 7- 4250 (4275 TSR)
Player 1- 4100 (3500 TSR) is matched with lower players
Player 2- 4150 (5000 TSR) is matched with higher players
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If I get time after university I might make a simulation which should show what is most likely happening with MMR. I would have to make estimates for things like players who quit the game, rate of abandons per game, and number of games played per player but it should be interesting to see the results. My expectation is that near 0 MMR there will be a swell of players, with a cutoff at 0, and an otherwise skewed normal distribution curve. The curve as a whole should get bigger as number of players increases but the mean and so on should not change significantly.
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United States12244 Posts
On October 16 2015 11:11 Birdie wrote:
If I get time after university I might make a simulation which should show what is most likely happening with MMR. I would have to make estimates for things like players who quit the game, rate of abandons per game, and number of games played per player but it should be interesting to see the results. My expectation is that near 0 MMR there will be a swell of players, with a cutoff at 0, and an otherwise skewed normal distribution curve. The curve as a whole should get bigger as number of players increases but the mean and so on should not change significantly.
That's my expectation as well. Possibly with a little bump where the more competitive players divide from the less competitive.
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i mean there prolly isnt inflation who knows (what is even the definition of inflation?)
average mmr is prolly the same
but im sure if its a gaussian distribution what is happening is that
its going from leptokurtic to platykurtic or maybe im just talking out of my ass
also its definitely becoming more positively skewed
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On October 16 2015 11:11 Birdie wrote:
If I get time after university I might make a simulation which should show what is most likely happening with MMR. I would have to make estimates for things like players who quit the game, rate of abandons per game, and number of games played per player but it should be interesting to see the results. My expectation is that near 0 MMR there will be a swell of players, with a cutoff at 0, and an otherwise skewed normal distribution curve. The curve as a whole should get bigger as number of players increases but the mean and so on should not change significantly.
do u use R?
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On October 17 2015 23:36 ChunderBoy wrote:Show nested quote +On October 16 2015 11:11 Birdie wrote:
If I get time after university I might make a simulation which should show what is most likely happening with MMR. I would have to make estimates for things like players who quit the game, rate of abandons per game, and number of games played per player but it should be interesting to see the results. My expectation is that near 0 MMR there will be a swell of players, with a cutoff at 0, and an otherwise skewed normal distribution curve. The curve as a whole should get bigger as number of players increases but the mean and so on should not change significantly. do u use R?
I haven't used it yet but perhaps I'll learn it just for the simulation. I was planning on using C for the simulation and probably graph.js for the graphs or something similar.
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How many 7k MMR are there? 50?
I think they are a few handful of people that will win >50% of the game regardless of the situation. Imo, MMR inflation seems to be a myth.
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EPT
