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On August 08 2010 21:08 ZapRoffo wrote:Show nested quote +
Therefore, a corollary here is that when determining rating increase, the hidden threshold value for your league is added to your displayed rating, then compared to your opponent’s MMR, for purposes of computing the gain/loss to your displayed rating.
Example: ExcaliburZ and I play a game. His MMR: 2600, sigma: 100, displayed rating: 300. My MMR: 2500, sigma: 50, rating: 150. Diamond’s MMR threshold: 2300. Excal wins because he rules. What happens?
- His MMR will increase
- My MMR will decrease
- Both of our sigmas will decrease
- His rating will increase. How? By comparing my MMR (2500) against his rating + diamond’s MMR threshold: 300 + 2300 = 2600, his gain is thus off 2600 vs my MMR of 2500
- My rating will decrease. In the same way: his MMR: 2600. My rating + threshold: 150 + 2300. Thus I lose points proportionally
This is not really consistent with we generally observe, which is at a rating of diamond 300 and being well above the skill that gives a likelihood of being demoted, people are gaining many more points than they are losing at equal matches. The fact that you gain more points at a low number of games indicate that the point gain formula either depends on sigma, or is still using a version of comparing displayed to opponents MMR.
This is the danger of using arbitrary values for illustration purposes. We do not know the actual threshold for any of the leagues. The numbers included in that quote are simply to make an example of what I was describing. The threshold values could be (and likely are) higher.
Also, MMR changes do take into account the sigma of both players. I do not know whether or not the change to displayed rating does, but it would not surprise me if it did.
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I feel like i just took statistics again XD but very interesting read like both parts
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On August 08 2010 10:59 s.a.y wrote:
Are you a rocket scientist?
Even better than that!
At least now we have a reasonable explanation for the matchmaking system / stuck-in-Plat glitch.
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Why do you assume Blizzard is using the normal distribution? I thought most rating systems use the logistic distribution nowadays.
From ChessBase.com,
"The final change made by the USCF – also made possible by the increased accessibility of computers – is the transition from a normal distribution to a logistic distribution. By observing a large number of results, the USCF determined that a logistic distribution most accurately extrapolated outcomes."
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Not much to say just wanted to let you know I enjoyed/appreciated the writeup Excal. 
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So I didn't want to start another thread, but I get the gist here that "displayed rating" (points) doesn't really matter? I was looking at a friend who is in Bronze league and has more points than I do, in Diamond. I was just wondering how all of this meshes together.
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United States12244 Posts
On August 09 2010 06:31 VorcePA wrote:
So I didn't want to start another thread, but I get the gist here that "displayed rating" (points) doesn't really matter? I was looking at a friend who is in Bronze league and has more points than I do, in Diamond. I was just wondering how all of this meshes together.
Displayed rating matters for ranking players in the same league. It's not immediately obvious how rating translates across leagues but one theory we have is that you can add whatever the breakpoint is for your league in order to get your "global rating" (and I realize the danger of using this term). In the completely baseless hypothetical example I gave before, if it were something like 0 Bronze, 1000 Silver, 1500 Gold, 2000 Platinum, 2500 Diamond, then if you had 300 Diamond and your friend had 600 Bronze you would be the equivalent of 1800 points over him (bonus points would be excluded because they're the same for all players).
Again I'll state here that we absolutely do not know what the breakpoints are or even what the overall scale is. This was just our attempt to explain the seemingly arbitrary rating that you start with after a promotion or demotion. There's clearly some kind of rating translation, we just don't know what it is.
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On August 09 2010 02:46 vanick wrote:Show nested quote +On August 08 2010 21:08 ZapRoffo wrote:
Therefore, a corollary here is that when determining rating increase, the hidden threshold value for your league is added to your displayed rating, then compared to your opponent’s MMR, for purposes of computing the gain/loss to your displayed rating.
Example: ExcaliburZ and I play a game. His MMR: 2600, sigma: 100, displayed rating: 300. My MMR: 2500, sigma: 50, rating: 150. Diamond’s MMR threshold: 2300. Excal wins because he rules. What happens?
- His MMR will increase
- My MMR will decrease
- Both of our sigmas will decrease
- His rating will increase. How? By comparing my MMR (2500) against his rating + diamond’s MMR threshold: 300 + 2300 = 2600, his gain is thus off 2600 vs my MMR of 2500
- My rating will decrease. In the same way: his MMR: 2600. My rating + threshold: 150 + 2300. Thus I lose points proportionally
This is not really consistent with we generally observe, which is at a rating of diamond 300 and being well above the skill that gives a likelihood of being demoted, people are gaining many more points than they are losing at equal matches. The fact that you gain more points at a low number of games indicate that the point gain formula either depends on sigma, or is still using a version of comparing displayed to opponents MMR. This is the danger of using arbitrary values for illustration purposes. We do not know the actual threshold for any of the leagues. The numbers included in that quote are simply to make an example of what I was describing. The threshold values could be (and likely are) higher. Also, MMR changes do take into account the sigma of both players. I do not know whether or not the change to displayed rating does, but it would not surprise me if it did.
OK I was misunderstanding anyway, I see what the example means now.
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As a low ranking platinum player, I lost to all of the diamond players I faced and lost to most of the platinum players too, but the system decided to promote me to diamond for some reason. Blizz seriously needs to iron out some of these bugs haha.
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Ty for informative post even if i brought back bad memories of Stats, Linear Algebra and Diff Eq.
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Does anyone have information about how often will ladder resets occur?
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On August 09 2010 07:20 Calidus wrote:
Ty for informative post even if i brought back bad memories of Stats, Linear Algebra and Diff Eq.
its not bad. statistics junkies like me will see that this is a fair system. didn't sirlin talk about this earlier?
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Its not really hard to make a fair system, though. The question is more how good is the system, to which the answer actually depends a lot on how the system is implemented.
TrueSkill has the dubious "feature" of being absolutely awful if the implementation is done badly and amazing if its done right. The SC2 implementation so far seems to be pretty average.
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On August 09 2010 06:19 carwashguy wrote:Why do you assume Blizzard is using the normal distribution? I thought most rating systems use the logistic distribution nowadays. From ChessBase.com, "The final change made by the USCF – also made possible by the increased accessibility of computers – is the transition from a normal distribution to a logistic distribution. By observing a large number of results, the USCF determined that a logistic distribution most accurately extrapolated outcomes."
From my understanding reading the TrueSkill whitepapers the chess ranking systems use a logistic distribution because it is better suited to chess. TrueSkill, and by extension all Xbox games that do matchmaking, uses a Gaussian distribution. I'm not a statistician so I can't argue the relative merits between the two. That is, my knowledge of statistics is pretty good, but the pros and cons of each distribution as applied to game ranking systems would be an interesting paper to read
I am presuming MS Research had a decent insight into the usefulness of a Gaussian distribution; ease of implementation/computation would not surprise me. I would be interested in the reasons for using a logistic distribution over a Gaussian one in videogames.
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A very informative post!
Question: I read in the section describing the graphs where probabilities for player 1 and 2 are shown.
"Also note that this does not need to be circular when looking at a top-down section. If players have different confidence values it will look like an ellipse."
The 3d curve that could be thought as "combination of two of the 2d" curves. Is it a combination of 2 different players curves which it seems reading the section I quoted.
Then it seems like the system has already found another player (aka system has already found a match) if it combines the two players curves into the 3d shape? *confused*
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On August 09 2010 17:17 papaz wrote:
A very informative post!
Question: I read in the section describing the graphs where probabilities for player 1 and 2 are shown.
"Also note that this does not need to be circular when looking at a top-down section. If players have different confidence values it will look like an ellipse."
The 3d curve that could be thought as "combination of two of the 2d" curves. Is it a combination of 2 different players curves which it seems reading the section I quoted.
Then it seems like the system has already found another player (aka system has already found a match) if it combines the two players curves into the 3d shape? *confused*
The way I understand it is the system would create these graphs with each player also searching for a game. I imagine the system chooses the closest to even graph if one within the sweet spot is not found after a certain amount of time.
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Assuming this is what blizz have, it's probably reasonable to assume people with win/loss ratio that differ significantly from 50% (lets assume 90%) will have a very high sigma, the system will keep matching these guys to players with much higher MMR, and they will keep beating them, causing further inflation in the sigma until they reach a point where their MMR peaks at the top of the pack. This could partially be a reason why people with these win records are stuck in a certain league.
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Makes sense to me, great post. Finally can understand this whole ladder thing lol
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On August 09 2010 10:34 Phanekim wrote:Show nested quote +On August 09 2010 07:20 Calidus wrote:
Ty for informative post even if i brought back bad memories of Stats, Linear Algebra and Diff Eq. its not bad. statistics junkies like me will see that this is a fair system. didn't sirlin talk about this earlier?
I remembered 1 things from my stats class last semester: Statistics are like bikinis. What they reveal is suggestive, but what they conceal is vital. ~Aaron Levenstein
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Not trying to downplay your work here, but I don't see any evidence anywhere that it actually works this way. I know you said it's just speculative, but your speculation should be based on some sort of evidence right? That led you to believe it works this way? Right now all I see is "I'm about to describe one of many possible ranking systems that SC2 may or may not use with equal probability".
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EPT
