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SC2 Ladder Analysis: Part 2 - Page 4

Forum Index > SC2 General
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Invictus
Profile Blog Joined September 2009
Singapore2697 Posts
August 08 2010 06:57 GMT
#61
Read half the post and im already amazed. This would definitely be helpful to new players in determining how they promote/demote from leagues
Lee Jaedong Fighting!
baeracaed
Profile Blog Joined June 2009
United States604 Posts
August 08 2010 06:57 GMT
#62
Very interesting, thanks for this.
(☞゚ヮ゚)☞ Cookies! ☜(゚ヮ゚☜)
paralleluniverse
Profile Joined July 2010
4065 Posts
August 08 2010 07:09 GMT
#63
On August 08 2010 15:32 brad drac wrote:
Show nested quote +
On August 08 2010 15:12 paralleluniverse wrote:
Being favored is almost certainly based on comparing your displayed rating to your opponents MMR.

Yes, this is meaningless and deceptive, and doesn't actually tell us who is really favored to win.

Yes, it *should* compare your MMR to your opponents MMR.

And no, there is no discontinuity in skill level, as you move up leagues. Matchmaking is great and is purely based on MMR, and is separate from the disastrous ranking system.

Do we have evidence for this? Isn't it possible that a player is displayed favoured if his MMR is greater than your own minus a factor based on sigma? Or something along those lines. I don't really see how you could directly compare displayed rating to MMR considering displayed ratings are division independent, not to mention league independent, while MMR is an absolute measure of a player's success in the system.

The evidence is that your opponent is always favored until you play lots of games, and from then on, teams are nearly always even.
MangoTango
Profile Blog Joined June 2010
United States3670 Posts
August 08 2010 07:37 GMT
#64
Woah, I'm going to have to read this all over again when I'm not drunk at 3:30am.
"One fish, two fish, red fish, BLUE TANK!" - Artosis
Nyovne
Profile Joined March 2006
Netherlands19135 Posts
August 08 2010 11:30 GMT
#65
Thanks for taking the time to put this together. Great read .
ModeratorFor remember, that in the end, some are born to live, others born to die. I belong to those last, born to burn, born to cry. For I shall remain alone... forsaken.
ZapRoffo
Profile Blog Joined April 2010
United States5544 Posts
Last Edited: 2010-08-08 12:09:22
August 08 2010 12:08 GMT
#66

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.


Yeah, well, you know, that's just like, your opinion man
Sanguinarius
Profile Joined January 2010
United States3427 Posts
August 08 2010 14:10 GMT
#67
Excellent read, thanks for taking the time to post that.
Your strength is just an accident arising from the weakness of others -Heart of Darkness
leonghk12
Profile Joined April 2010
13 Posts
August 08 2010 14:14 GMT
#68
english please...haha great post anyway.
Master of All Trades
brad drac
Profile Joined May 2010
Ireland202 Posts
Last Edited: 2010-08-08 14:33:52
August 08 2010 14:33 GMT
#69
On August 08 2010 15:47 Excalibur_Z wrote:
[snip]
For the record, though, displayed ratings are not division independent -- they're comparable across all divisions in a league because everyone in that league is playing against (mostly) the same player pool. I'm going to be careful about taking this too far because there's little evidence to support it, but it's an idea to throw out there that makes rating values translatable across leagues.

I hope you're right about this, but I'm less sure than I was previously. When I was promoted to diamond(a newly made division) the system said I had about 220 bonus pool, but that turned out to be just a glitch and when I logged in the next time all but a dozen or so were gone. If players put in a new division don't receive a bonus pool equivalent to players who've been in same league divisions for much longer, it'll mean players who were slower to rank up will have to have a proportionally better record to have similar ratings. Maybe previous bonus pool points are modified directly into the rating you receive initially on promotion, I have no means of figuring that out. Is that what you're proposing?

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.

I've actually found that once I hit ~300 diamond, my points gained and points received minus bonus pool balanced out very close to even. Below that level, I was getting much larger points boosts though. This has just been my experience so far, I haven't played too many matches at this level yet(diamond is hard).
Saying what we think gives us a wider conversational range than saying what we know.
SnakeChomp
Profile Joined May 2010
Canada125 Posts
August 08 2010 14:34 GMT
#70
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.


I think it is entirely reasonable to assume that your displayed rating value is allowed to swing upwards very quickly when you win in if the displayed value is much less than your actual MMR. This is how it works in WoW after all. The bonus pool is a relatively simple addition to this which just works like rest xp to help players who are not able to play as often keep up (in terms of ladder ranking) with those who can.

So in the above example, instead of the player with a higher MMR gaining rating due to the addition of diamond's MMR threshold and displayed rating (which is a highly arbitrary algorithm and doesn't make much sense given that displayed ratings cannot be compared between two players), it is instead simply: if you win you will gain rating based off the difference between the two players MMR additionally modified by the difference of your displayed rating and your MMR. If displayed rating is < MMR, the rating gain will be higher than if they were equal or if displayed > MMR (which only occurs due to the bonus pool).

Such a system implies though that display ratings will quickly converge towards your MMR and then slowly exceed your MMR due to the bonus pool. I don't think enough players have a display rating high enough to test this though, would need to be 2000+ up in diamond. Once players are there we can observe their point gain/loss compared to earlier games to determine if the displayed rating gain slows once it reaches MMR.
barrykp
Profile Joined August 2010
Ireland174 Posts
August 08 2010 14:47 GMT
#71
Ok, how does all of this tie into displayed rating and the whole “favored” deal? If you remember back to WoW, ratings changed based on a direct comparison of your displayed rating to the other team’s MMR. So if your current rating was 500 and you were playing people with MMRs of 2000, your rating would jump significantly after every win because of the wide disparity. Now, we’ve identified that on the loading screen quite often players are seeing the other person as favored and the opponent (who is nominally “favored”) also sees his opponent as favored! How can this be? The theory put forth here is the system is again comparing your displayed rating to your opponent’s hidden MMR.

The reason for this is so that the system brings you toward your MMR more quickly. kzn explains:

On August 08 2010 14:30 kzn wrote:
Show nested quote +
How it works was like this: Say you've got a MMR of 2500, and you start a new team. It starts at 0 rating, but the matchmaking system will match you with other players of MMR 2500. If you lose a game, your team rating would not change at all. If you won, it would increase by 47 (a hard cap that was in place at least when I played). This was not explained as arising due to an interaction between the team rating and the opponent's MMR, however - it was explained as the system trying to get your team's rating as close as possible to your team's MMR rapidly.

I think you have misunderstood Kzn's clarification. I think he is suggesting that the system compares your displayed rating to your current MMR and not your opponents (not that this makes much of a difference mathematically since, in theory, your MMR and your opponent's should be very similar). Having a large difference between your displayed rating and your MMR will result in the system skewing rating changes to favour reducing that difference. Eventually your displayed rating becomes very close, or the same as, your MMR. At least that's how I think it works in wow.
Lecture me some more on how to play please; I need help.
ZapRoffo
Profile Blog Joined April 2010
United States5544 Posts
August 08 2010 15:16 GMT
#72
On August 08 2010 23:34 SnakeChomp 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.


I think it is entirely reasonable to assume that your displayed rating value is allowed to swing upwards very quickly when you win in if the displayed value is much less than your actual MMR. This is how it works in WoW after all. The bonus pool is a relatively simple addition to this which just works like rest xp to help players who are not able to play as often keep up (in terms of ladder ranking) with those who can.

So in the above example, instead of the player with a higher MMR gaining rating due to the addition of diamond's MMR threshold and displayed rating (which is a highly arbitrary algorithm and doesn't make much sense given that displayed ratings cannot be compared between two players), it is instead simply: if you win you will gain rating based off the difference between the two players MMR additionally modified by the difference of your displayed rating and your MMR. If displayed rating is < MMR, the rating gain will be higher than if they were equal or if displayed > MMR (which only occurs due to the bonus pool).

Such a system implies though that display ratings will quickly converge towards your MMR and then slowly exceed your MMR due to the bonus pool. I don't think enough players have a display rating high enough to test this though, would need to be 2000+ up in diamond. Once players are there we can observe their point gain/loss compared to earlier games to determine if the displayed rating gain slows once it reaches MMR.


Like I've said a bunch of other places, the bonus pool will not continually inflate ratings, since if you exceed your MMR your ratings increase will eventually (quickly if you play frequently) be offset by winning fewer points than you would if your rating were not above your MMR.
Yeah, well, you know, that's just like, your opinion man
drunkensolo
Profile Joined March 2010
Germany56 Posts
August 08 2010 16:15 GMT
#73
very interesting, thx for your mathematical kinda inside look^^
Caponed
Profile Joined July 2010
United States46 Posts
August 08 2010 17:10 GMT
#74
I think a better system than "Blizzard checks MMR after every 30 games" would be "You get promoted when your sigma is below a certain threshold." This would improve the game's certainty factor, and, though it would take longer to get you where you need to be, would probably put you in exactly the right spot. Maybe even set certain sigma thresholds along the way, i.e. the system checks your MMR at sigma 100, 75, 50, 25 and adjusts your positioning accordingly.

Either way, interesting read.
Empyrean
Profile Blog Joined September 2004
16992 Posts
August 08 2010 17:15 GMT
#75
Random question: did you use R to generate those graphs? Because they look suspiciously similar to R's basic graphics package ;D
Moderator
Excalibur_Z
Profile Joined October 2002
United States12235 Posts
August 08 2010 17:25 GMT
#76
On August 09 2010 02:10 Caponed wrote:
I think a better system than "Blizzard checks MMR after every 30 games" would be "You get promoted when your sigma is below a certain threshold." This would improve the game's certainty factor, and, though it would take longer to get you where you need to be, would probably put you in exactly the right spot. Maybe even set certain sigma thresholds along the way, i.e. the system checks your MMR at sigma 100, 75, 50, 25 and adjusts your positioning accordingly.

Either way, interesting read.


Well, we don't know specifically how many games it takes before you reach a review checkpoint, other than Browder's admission in the Best Buy livechat that the initial one occurs at about 30 games. That may not necessarily be true anymore (it was just a couple of weeks before release) because right now we're seeing people get promoted after 50, 40, 20, even 15 or so games (my 3v3 team was promoted after only 15 games, in fact). It's also possible that review checkpoints have been abolished entirely and that promotion depends entirely upon sigma and the league threshold, or that both factors are considered. There's really no way for us to know, but I agree that arbitrary checkpoint periods -- especially since the periods are not consistent or trackable -- don't make as much sense.
Moderator
AyJay
Profile Joined April 2010
1515 Posts
August 08 2010 17:26 GMT
#77
All this theory crafting makes my retarded head hurt
Excalibur_Z
Profile Joined October 2002
United States12235 Posts
August 08 2010 17:28 GMT
#78
On August 09 2010 02:15 Empyrean wrote:
Random question: did you use R to generate those graphs? Because they look suspiciously similar to R's basic graphics package ;D


We didn't make them. The top-down one is from a public .ppt from MS research Cambridge and the 3D one is from Google image search. :V
Moderator
Excalibur_Z
Profile Joined October 2002
United States12235 Posts
August 08 2010 17:35 GMT
#79
On August 08 2010 23:47 barrykp wrote:
Show nested quote +
Ok, how does all of this tie into displayed rating and the whole “favored” deal? If you remember back to WoW, ratings changed based on a direct comparison of your displayed rating to the other team’s MMR. So if your current rating was 500 and you were playing people with MMRs of 2000, your rating would jump significantly after every win because of the wide disparity. Now, we’ve identified that on the loading screen quite often players are seeing the other person as favored and the opponent (who is nominally “favored”) also sees his opponent as favored! How can this be? The theory put forth here is the system is again comparing your displayed rating to your opponent’s hidden MMR.

The reason for this is so that the system brings you toward your MMR more quickly. kzn explains:

On August 08 2010 14:30 kzn wrote:
How it works was like this: Say you've got a MMR of 2500, and you start a new team. It starts at 0 rating, but the matchmaking system will match you with other players of MMR 2500. If you lose a game, your team rating would not change at all. If you won, it would increase by 47 (a hard cap that was in place at least when I played). This was not explained as arising due to an interaction between the team rating and the opponent's MMR, however - it was explained as the system trying to get your team's rating as close as possible to your team's MMR rapidly.

I think you have misunderstood Kzn's clarification. I think he is suggesting that the system compares your displayed rating to your current MMR and not your opponents (not that this makes much of a difference mathematically since, in theory, your MMR and your opponent's should be very similar). Having a large difference between your displayed rating and your MMR will result in the system skewing rating changes to favour reducing that difference. Eventually your displayed rating becomes very close, or the same as, your MMR. At least that's how I think it works in wow.


Your rating is supposed to rapidly approach your MMR, that's true, but it doesn't make sense for your point gains to depend on your own MMR. There needs to be an external comparison which is why it has to compare against your opponent's MMR.
Moderator
Empyrean
Profile Blog Joined September 2004
16992 Posts
August 08 2010 17:39 GMT
#80
On August 09 2010 02:28 Excalibur_Z wrote:
Show nested quote +
On August 09 2010 02:15 Empyrean wrote:
Random question: did you use R to generate those graphs? Because they look suspiciously similar to R's basic graphics package ;D


We didn't make them. The top-down one is from a public .ppt from MS research Cambridge and the 3D one is from Google image search. :V


Ok. The contour map one definitely looks like it was generated in R :D

Just curious haha
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