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Find out your winning chances in ladder matches - Page 3

Forum Index > SC2 General
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JackDragon
Profile Joined February 2011
525 Posts
August 18 2011 16:31 GMT
#41
On August 19 2011 00:51 IronDoc wrote:
Show nested quote +
On August 19 2011 00:44 JackDragon wrote:
On August 18 2011 23:44 BlasiuS wrote:
On August 18 2011 23:38 JackDragon wrote:
On August 18 2011 23:10 Not_That wrote:
On August 18 2011 22:57 JackDragon wrote:
On August 18 2011 22:07 Not_That wrote:
On August 18 2011 22:02 JackDragon wrote:
Is this official or were did you get the numbers from? I was certain that time of the match also affected points but whatever. I do think that there is a relation betwen skill gap and points but...
I'm not sure you are correct


It's not official, it's something I thought of and I explain how I came to the numbers I did in the OP.

Match duration definitely does not affect points. You can read about it in the ladder sticky.

I can't find were it says that the points aren't reflecting game length, or that it only reflects mmr gap.
I mean even so it is a bit to simplified to actually work. Saying that the skill is constant and that it only works when you have reached your true mmr makes it not very usefull.

What I mean is this:
"The important thing to remember is that "favored" does not always mean "better" unless both players' points have approximately reached their MMRs. Until that time, the "favored" indicator only serves to determine how many points a match is worth, and is not an indicator of skill."

which mens that both have to fit their mmr for your formula to even be true.


It states specifically that points won/lost are only based off of who won in another thread by excalibur_z. In the sticky it can be seen from the part discussing the favoured system. If you won more points for longer games, score, or anything else it would be entirely abusable.

It's not true that both players' points have to fit their MMR for my formula to be true. It is sufficient that your points match your MMR for you to be able to calculate what was your chance to win. It would only be required for your opponent's MMR to match his points for the formula to be also applicable to your opponent.
The part you quote is referring to the 'favored' / 'slightly favored' / 'even' caption at the beginning of matches, and how both sides can see each other as 'favored', etc.


Small note although I hate to make this any more complicated than it already is, but I can not resist:
If for some reason you are confident that your opponent's current points better reflect his MMR than your current points reflect your MMR, then it is entirely possible to calculate your winning chances based off of his points won / lost - simply calculate HIS winning chances, and yours are equal to 100 minus his chances. Just be sure you aren't counting his bonus pool points.

I found the thread and post else I wouldn't be able to qoute from it right? I just can't find within that post were it says that it is pure mmr. I am dyslectic so it is possible that I missed it but please show me.


yes you missed it, it's right here:

On February 22 2011 15:13 Excalibur_Z wrote:
Promotion
By outperforming the rest of your league, it is possible to get promoted into a higher league. If you are in Bronze but playing against Gold players, you would expect to be promoted to Gold, but that doesn't always happen immediately.

This is because the system requires a certain degree of confidence before players can be moved to a new league, otherwise they would bounce around from league to league too frequently for leagues to be meaningful. That confidence is measured in two ways:

First, the player must prove that he is capable of maintaining a certain level of skill. This is done by measuring the moving average of a player's MMR. The below image should help demonstrate. When this moving average stabilizes within the confines of a league, a player can be promoted into that league.

[image loading]

The second factor is a "confidence buffer" that exists between leagues. That is, if a Bronze player is only slightly better than the lowest-rated Silver players according to his moving average, that is not reason alone to promote him, even though he has crossed into the Silver MMR region. If that player slumped, he would fall right back into Bronze within a couple of games, only to return to Silver a couple of games later, making his promotion far less meaningful. Leagues are sticky, therefore the moving average must cross beyond the destination league's confidence buffer, cementing that player's position within the higher league. In the picture above, the confidence buffer is represented by the yellow glow region.

Note that these are the only two factors required for promotion. Any in-game behaviors or statistics beyond winning, losing, and the opponent's MMR are not relevant to the system.



But thats talking about promotions, not points. You could also see that as number of points don't matter when it comes to promotions. Which is true, points don't matter. So they don't actually say that time have nothing to do with points gained.

Also IronDoc, what I mean is doesn't his argument base on that likelihood in winning does sum to zero? I would argue that for the formula to be correct our likelihood of winning needs to sum to zero or it won't add up.

Example from my last game: I won 13 points he lost 12 points (before bonus pool) and so I had 45.83% chance to win right? And he would have 50% chance of winning. And this would mean that there is 4.17% chance for it to be tie or what? well I guess that could be but...

Point being. If the persons likelihood of winning don't add up you can not say that your formula appropriately reflects the truth.

But if his points reflected his mmr and yours did, then the points would zero sum too. You can only look at the points (and infer a likelihood of winning) on the side of a player whose mmr and point value are close enough to be assumed identical. Essentially, the thing is that if the points won/lost don't zero sum, at least one players' points are not reflective of mmr.

Indeed that makes sense.

Not_That. I don't really know much about how mmr works to know if the numbers fitt so I don't know if how to compare mmr. But If i undestand it right IronDoc summed it up nicly.

I guess the thing missing then would be to know how close you are to your mmr and how close your opponent are to his. Before then I don't think we can comfirm or deny this theory.
aksfjh
Profile Joined November 2010
United States4853 Posts
August 18 2011 16:37 GMT
#42
Well, as long as your points are close to your MMR, it should be roughly accurate. The only thing to consider is that, if your MMR grows or shrinks too fast, these points might not correctly reflect your MMR and chance of winning.
JackDragon
Profile Joined February 2011
525 Posts
August 18 2011 17:15 GMT
#43
So there is a way to find out your mmr?
Excalibur_Z
Profile Joined October 2002
United States12235 Posts
August 18 2011 17:22 GMT
#44
On August 19 2011 00:44 JackDragon wrote:
Show nested quote +
On August 18 2011 23:44 BlasiuS wrote:
On August 18 2011 23:38 JackDragon wrote:
On August 18 2011 23:10 Not_That wrote:
On August 18 2011 22:57 JackDragon wrote:
On August 18 2011 22:07 Not_That wrote:
On August 18 2011 22:02 JackDragon wrote:
Is this official or were did you get the numbers from? I was certain that time of the match also affected points but whatever. I do think that there is a relation betwen skill gap and points but...
I'm not sure you are correct


It's not official, it's something I thought of and I explain how I came to the numbers I did in the OP.

Match duration definitely does not affect points. You can read about it in the ladder sticky.

I can't find were it says that the points aren't reflecting game length, or that it only reflects mmr gap.
I mean even so it is a bit to simplified to actually work. Saying that the skill is constant and that it only works when you have reached your true mmr makes it not very usefull.

What I mean is this:
"The important thing to remember is that "favored" does not always mean "better" unless both players' points have approximately reached their MMRs. Until that time, the "favored" indicator only serves to determine how many points a match is worth, and is not an indicator of skill."

which mens that both have to fit their mmr for your formula to even be true.


It states specifically that points won/lost are only based off of who won in another thread by excalibur_z. In the sticky it can be seen from the part discussing the favoured system. If you won more points for longer games, score, or anything else it would be entirely abusable.

It's not true that both players' points have to fit their MMR for my formula to be true. It is sufficient that your points match your MMR for you to be able to calculate what was your chance to win. It would only be required for your opponent's MMR to match his points for the formula to be also applicable to your opponent.
The part you quote is referring to the 'favored' / 'slightly favored' / 'even' caption at the beginning of matches, and how both sides can see each other as 'favored', etc.


Small note although I hate to make this any more complicated than it already is, but I can not resist:
If for some reason you are confident that your opponent's current points better reflect his MMR than your current points reflect your MMR, then it is entirely possible to calculate your winning chances based off of his points won / lost - simply calculate HIS winning chances, and yours are equal to 100 minus his chances. Just be sure you aren't counting his bonus pool points.

I found the thread and post else I wouldn't be able to qoute from it right? I just can't find within that post were it says that it is pure mmr. I am dyslectic so it is possible that I missed it but please show me.


yes you missed it, it's right here:

On February 22 2011 15:13 Excalibur_Z wrote:
Promotion
By outperforming the rest of your league, it is possible to get promoted into a higher league. If you are in Bronze but playing against Gold players, you would expect to be promoted to Gold, but that doesn't always happen immediately.

This is because the system requires a certain degree of confidence before players can be moved to a new league, otherwise they would bounce around from league to league too frequently for leagues to be meaningful. That confidence is measured in two ways:

First, the player must prove that he is capable of maintaining a certain level of skill. This is done by measuring the moving average of a player's MMR. The below image should help demonstrate. When this moving average stabilizes within the confines of a league, a player can be promoted into that league.

[image loading]

The second factor is a "confidence buffer" that exists between leagues. That is, if a Bronze player is only slightly better than the lowest-rated Silver players according to his moving average, that is not reason alone to promote him, even though he has crossed into the Silver MMR region. If that player slumped, he would fall right back into Bronze within a couple of games, only to return to Silver a couple of games later, making his promotion far less meaningful. Leagues are sticky, therefore the moving average must cross beyond the destination league's confidence buffer, cementing that player's position within the higher league. In the picture above, the confidence buffer is represented by the yellow glow region.

Note that these are the only two factors required for promotion. Any in-game behaviors or statistics beyond winning, losing, and the opponent's MMR are not relevant to the system.



But thats talking about promotions, not points. You could also see that as number of points don't matter when it comes to promotions. Which is true, points don't matter. So they don't actually say that time have nothing to do with points gained.

Also IronDoc, what I mean is doesn't his argument base on that likelihood in winning does sum to zero? I would argue that for the formula to be correct our likelihood of winning needs to sum to zero or it won't add up.

Example from my last game: I won 13 points he lost 12 points (before bonus pool) and so I had 45.83% chance to win right? And he would have 50% chance of winning. And this would mean that there is 4.17% chance for it to be tie or what? well I guess that could be but...

Point being. If the persons likelihood of winning don't add up you can not say that your formula appropriately reflects the truth.


Points earned also have nothing to do with how the game is played or how long the game is or any other in-game factor. There, I just said it =)
Moderator
Excalibur_Z
Profile Joined October 2002
United States12235 Posts
Last Edited: 2011-08-18 18:21:57
August 18 2011 17:50 GMT
#45
So this is an interesting topic because we've felt for a long time that MMR is zero-sum between any two players. The amount of MMR earned is directly related to your chances of winning a game, and in that regard it's no different from an Elo system. For example, in chess, a 1650-rated player would win over a 1550 player 64% of the time, and the amount of rating that either player stands to gain or lose will reflect that probability. And, quite obviously, points drift toward MMR. It then follows that if your points and your opponent's points each match their respective MMRs, their points earned and lost will be zero-sum. This is all assuming sigmas are equal though which they're not always and Vanick yelled at me about and sigma influences MMR change and Elo has no sigma something something.

What is interesting to consider is whether we can determine those winning percentages based only on the points earned and lost because those don't always match up with MMR. One measure I use is if the opponent lost 12 points or earned 12 points (excluding bonus pool) for a game, then it must mean that my MMR is roughly equal to his points barring any division offsets. For example, the other day Vanick and I played a 2v2, we're in Diamond and they're in Master league. They only had about 50 adjusted points while we had about 200, and they lost 12 points from our game while we won 12 points. This meant that our MMRs were close to each others' points, but also meant our points were of equal value. Given knowledge of division tier offsets, we could then determine that based on the 150-point difference, there was a very high probability that we were in the highest Diamond tier.

I'll definitely have to think about this more. Outcome probability is obvious when you're talking about MMR vs MMR, but things get cloudier when you're trying to go in reverse by analyzing point gains since those aren't always zero-sum. Good topic.

EDIT: Forgot about the impact of sigma ffffffffff.
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