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Lies, Damn Lies, and Statistics

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suckerfish
Profile Joined April 2010
United States31 Posts
Last Edited: 2010-08-16 21:47:25
August 16 2010 21:11 GMT
#1
At the risk of fanning the flames of an already controversial topic...

I've been playing around a little with Shadowed's new SC2 stats website. If you haven't already seen it, I highly suggest taking a looking at it: http://sc2ranks.com.

In particular, I've been studying the data on the stats tab of the website. It seems to me that over the course of millions of games, the win rate seems fairly well balanced across all three races. No matter whether you filter by region or by player division, the difference between the top-winning race and the bottom-winning race is always < 2%. (the only discrepancy I've been able to find to this is in the Latin America region, where the difference between high/low is < 3%)

I'm no statistician, but a win-rate difference of < 2% between the races sounds like a pretty damn well-balanced game. Then again, given that the sample size is millions of games, maybe 2% is statistically significant.

Now, one piece of information that's missing is the race matchup percentages. Overall, each race seems to be winning the same percentage of games, but there's no information currently on that website to determine if each race matchup shows the same percentage. Hypothetically speaking, it's possible that Zerg wins 100% of the time vs Protoss, and loses 100% of the time vs Terran, but the stats page will still show an overall win rate of 50% for Zerg, which would seem to indicate balance (which is obviously not the case in this example).

Anyway, I guess the point I'm trying to make is that, given the statistics from this website, it's hard for me to reconcile all these reports of race imbalance (even from well-respected players) when the numbers just don't seem to support this.

Am I missing something here? Are the numbers just misleading, and not telling the whole story?

EDIT: Okay, some people have provided me with a good explanation of what I was missing. The long and the short of it is that win percentage isn't a measurement of race balancing or skill level, it's a measurement of how well Blizzard's matchmaking works. Thank you to those who provided a very reasonable answer to my very serious question.

Incidentally, there are stats that support the claims of race imbalance at high-level play: http://www.sc2ranks.com/stats/race/all/1. Note that very highly ranked Terran players are squeezing out both Zerg and Protoss players. If the races were balanced correctly, one would expect to see roughly 30% for each race at every ranking score -- but that's not the case at very high levels.
Kelberot
Profile Joined July 2010
Brazil364 Posts
August 16 2010 21:12 GMT
#2
Am I missing something here? Are the numbers just misleading, and not telling the whole story?

Isn't it obvious?

or do you really believe there's a zerg conspiracy of miserable pro gamers trying to make easy money?
iEchoic
Profile Blog Joined May 2010
United States1776 Posts
August 16 2010 21:14 GMT
#3
The numbers don't indicate any imbalances, and everyone who is impartial will recognize that, people still try to twist it. That's not to say the game is perfectly balanced, but numbers don't support a Z imbalance.

People will say that it's the same because the system tries to keep you at the same win%, but if that were the case with Zerg, there would be less representation in the diamond league than other leagues due to matchmaker pairing up with lower-skilled opponents. This isn't the case.
vileEchoic -- clanvile.com
suckerfish
Profile Joined April 2010
United States31 Posts
August 16 2010 21:14 GMT
#4
Actually, no it's not obvious to me. How is it that, across millions of games, the difference between top and bottom race is < 2%, regardless of region or division?

No, I don't think there's a Zerg conspiracy, but how do you explain the numbers?
Nokarot
Profile Blog Joined April 2010
United States1410 Posts
Last Edited: 2010-08-16 21:24:20
August 16 2010 21:15 GMT
#5
Any chance you can filter that by diamond-league only and run the numbers again? Never used the site so I have no idea.

And yes, I've heard the age old argument that, one, stats don't matter, and two, that diamond-league-play can't be the only factor in selling a game to millions of people to have fun with. I'm just curious is all.

Edit: I'm really bad at math-- I dropped out of high school and I'm an art major, damn it! Can someone explain to me how every race can have a ~55% win ratio? Maybe I'm missing something, but if you average the winning ratio of ALL players in the world and its above 50 (which would be one winner and one loser for each match) then you're missing the statistics for games somehow?

I'm filtering by "all players in north america". If the average win:loss ratio is 55:100, that means that 5% is fucked up somewhere. If 5% is fucked up, I have trouble believing the other 95% is completely accurate :X Unless, of course, my math-badness is not understanding something very basic.

Also, obligatory "stats don't mean a whole lot in regards to balance" comment goes here.
beep beep boop
eNtitY~
Profile Joined January 2007
United States1293 Posts
Last Edited: 2010-08-16 21:16:35
August 16 2010 21:15 GMT
#6
That's not a good basis for this kind of argument.
http://www.starcraftdream.com
suckerfish
Profile Joined April 2010
United States31 Posts
August 16 2010 21:16 GMT
#7
On August 17 2010 06:15 Nokarot wrote:
Any chance you can filter that by diamond-league only and run the numbers again? Never used the site so I have no idea.


Here: http://sc2ranks.com/stats/region/diamond/1/all

You can also limit it to the Top 100 players world wide too: http://sc2ranks.com/stats/region/diamond/1/100
HubertFelix
Profile Joined April 2010
France631 Posts
August 16 2010 21:17 GMT
#8
Don't you understand that the AMM works like that? The average player's ratio is 1win/1lose.
SlowBlink
Profile Joined August 2010
United States102 Posts
August 16 2010 21:17 GMT
#9
In other news, matchmaking works on battlenet 2.0. At least they got something right.
catamorphist
Profile Joined May 2010
United States297 Posts
Last Edited: 2010-08-16 21:20:48
August 16 2010 21:17 GMT
#10
On August 17 2010 06:12 Kelberot wrote:
Show nested quote +
Am I missing something here? Are the numbers just misleading, and not telling the whole story?

Isn't it obvious?

or do you really believe there's a zerg conspiracy of miserable pro gamers trying to make easy money?


What? I mean, seriously, what? What does this post mean?

I think that most people are in agreement that Zerg is OK at mid-diamond and below levels, and claim that there's only an imbalance in pro play. Specifically, the most common complaint seems to be that Terran especially have too many viable strategies against Zerg, and it's hard to reliably scout and defend against all of them, and that's a problem that only shows up at a very high level of play; the level at which you start saying "My opponent can be doing X, Y, or Z, so here's my plan to distinguish between X, Y, and Z and appropriately handle each possibility." At lower levels, just plain execution and mechanics is much more important.

Also, I'm not convinced that the racial statistics found like this are meaningful; if all the Zerg players had poor results, and Terran and Protoss had some good players, some with poor results, then the Zerg players would tend to match up with other Zerg players & with the worse Terran and Protoss players to maintain a reasonable win/loss ratio, right?
http://us.battle.net/sc2/en/profile/281144/1/catamorphist/
MangoTango
Profile Blog Joined June 2010
United States3670 Posts
August 16 2010 21:19 GMT
#11
2% is going to be statistically significant at n~10m, but as any student of statistics knows, the t-test doesn't say how much the populations are different, just that they are. The differences are minute ate best.

Then again, this doesn't preclude a T>Z>P>T rock-paper-scissors dynamic, which many people believe is the case.
"One fish, two fish, red fish, BLUE TANK!" - Artosis
Sadistx
Profile Blog Joined February 2009
Zimbabwe5568 Posts
August 16 2010 21:20 GMT
#12
It's been mentioned several times already that the ladder is designed to have ~50% win rate among all players. However those stats are meaningless since balance can only be aptly judged at the very top.
suckerfish
Profile Joined April 2010
United States31 Posts
August 16 2010 21:21 GMT
#13
On August 17 2010 06:17 catamorphist wrote:
I think that most people are in agreement that Zerg is OK at mid-diamond and below levels, and claim that there's only an imbalance in pro play.


But the stats don't even support this claim. If you look at the Top 100 players in each region, the difference is still < 2% for each race: http://sc2ranks.com/stats/region/diamond/1/100
rextyrann
Profile Joined July 2009
Germany41 Posts
August 16 2010 21:23 GMT
#14
another one going on about the winratios without regarding the mm...

again.

you could just read a bit in the forum and save yourself the work of making a new thread. close plz...
Attris
Profile Joined September 2009
United States175 Posts
August 16 2010 21:23 GMT
#15
No really, everyone needs to keep making more of these posts. I just really don't see enough of them.
Are you serious? |sRs| www.srejects.com
tacrats
Profile Joined July 2010
476 Posts
Last Edited: 2010-08-16 21:23:52
August 16 2010 21:23 GMT
#16
That information is useless and yes you are missing quite a bit.

If anyone thinks that the information on sc2ranks in its current state can provide insight to imbalance is dense.

This has been discussed countless times i suggest you read some other threads before posting another one of the exact same thing.
DTown
Profile Blog Joined April 2010
United States428 Posts
Last Edited: 2010-08-16 21:29:09
August 16 2010 21:24 GMT
#17
On August 17 2010 06:14 iEchoic wrote:
The numbers don't indicate any imbalances, and everyone who is impartial will recognize that, people still try to twist it. That's not to say the game is perfectly balanced, but numbers don't support a Z imbalance.

People will say that it's the same because the system tries to keep you at the same win%, but if that were the case with Zerg, there would be less representation in the diamond league than other leagues due to matchmaker pairing up with lower-skilled opponents. This isn't the case.


This is exactly what is happening. The diamond league is huge, and there is much variation of player skill within the diamond league. Plenty of zerg's can get into diamond league, because doing so is not particularly difficult. It could still be--and I firmly believe is--the case that the close win-rate percentages are strictly proof that Blizzard's AMM system is working as intended. Zerg players' win-rates are similar to those of other races because on the margin, zerg players in each division are being matched up with "less skilled" terrans, for example. All of this can happen within each division without statistically skewing the race representation stats too far one way or the other, and this would certainly enable (by a large margin) enough margin of error to cast a high degree of suspicion on the validity of conclusions drawn from win-rate percentage comparisons.

tl;dr Seriously, please stop trying to use this data as statistical evidence in support of either argument (Terran OP/Terran not OP), it is just plain not a valid source of data.

edit: typo
StaR_Robo
Profile Joined May 2010
Australia229 Posts
Last Edited: 2010-08-16 21:27:27
August 16 2010 21:24 GMT
#18
[image loading]

That is the win ratio summary for diamond league. I have the analysis cut by a slightly different level of detail on Sanctuary Stats. Actually shows a higher average ratio and probably not much more variance.

Don't forget that the only race info we have is favourite race so the matching of that to games played by actual race is not exact. If you play 99 games as zerg and 100 as protoss you will be shown as protoss for your favourite race
Working to spread StarCraft II through http://rts-sanctuary.com - replays, stats, streams and more ...
Chriamon
Profile Joined April 2010
United States886 Posts
Last Edited: 2010-08-16 21:27:02
August 16 2010 21:25 GMT
#19
On August 17 2010 06:14 iEchoic wrote:
[...] if that were the case with Zerg, there would be less representation in the diamond league than other leagues due to matchmaker pairing up with lower-skilled opponents. This isn't the case.

That doesn't really make sense to me. How can you just outright say, 'this is what we would see' when there are so many variables. Lets say it were the case, you can clearly see that there are a lot less Zs overall, perhaps the only ones who stick with Z are just much better at it. Or perhaps there would be more representation in the other leagues than diamond, its just that the majority of that 'representation' has now switched to a different race. Basically, the idea that win rates are relatively even because of the matchmaking system, I would say is true. This supports niether imbalance nor balance, it simply supports the fact that the matchmaking system works. If Z were imbalanced, there are other stats to look at, win rate wouldn't be the best thing to look at.

Simply look at the win rate of random. Ooooh look at that! Its the same as the other 3 races! The Random players must be just as good as players of the other 3 races!
http://us.battle.net/sc2/en/profile/274906/1/Blaze/
SlowBlink
Profile Joined August 2010
United States102 Posts
August 16 2010 21:26 GMT
#20
On August 17 2010 06:21 suckerfish wrote:
Show nested quote +
On August 17 2010 06:17 catamorphist wrote:
I think that most people are in agreement that Zerg is OK at mid-diamond and below levels, and claim that there's only an imbalance in pro play.


But the stats don't even support this claim. If you look at the Top 100 players in each region, the difference is still < 2% for each race: http://sc2ranks.com/stats/region/diamond/1/100


This whole premise is flawed. What you're trying to say is that since zerg players win 50% of the time, there is no imbalance for zerg. What you don't take into account is the fact that Blizzard's matchmaking system is specifically designed so that you come out with a 50% win/loss record. Battle net will match you up against a player of equal skill so to speak, and reevaluate your skill based on whether you win or lose. With this mechanic you can have pro level zergs getting matched with plat/gold level terrans, simply because the zerg player is losing more to higher level terrans. Then when they beat the lower level players, it balances out their win/loss to 50%.

tl;dr- all this proves is that battlenet matchmaking actually works.
Lunares
Profile Joined May 2010
United States909 Posts
August 16 2010 21:26 GMT
#21
On August 17 2010 06:20 Sadistx wrote:
It's been mentioned several times already that the ladder is designed to have ~50% win rate among all players. However those stats are meaningless since balance can only be aptly judged at the very top.


The part about the matchmaking is true. The system is designed to give 50% win/loss rate to everyone it can.

However i wouldn't say its true that balance can only be aptly judged at the very top. Balance in the silver/gold leagues is a very important thing to blizzard as well because they don't want to have a game where it's unbalanced for 99% of players. However it is also true that generally if you can balance for the top of the league it should be mostly balanced for the rest of the league.

A real problem right now is determining if the whole TvZ situation is a result of true race imbalance or if it's mostly map imbalance due to too many chokepoints on maps. Its probably a combination of both.
andrewlt
Profile Joined August 2009
United States7702 Posts
August 16 2010 21:28 GMT
#22
You already hit upon the reason. Somebody did a study on BW proleagues in Korea and the win rates of T over Z, Z over P and P over T is around 52-54%. The overall win% for each race would be 50%, even though none of the matchups are.
dcberkeley
Profile Joined July 2009
Canada844 Posts
August 16 2010 21:28 GMT
#23
Another casualty of being mislead by statistics.

It's one thing to have numbers but another thing entirely to interpret the numbers correctly.
Moktira is da bomb
Zato-1
Profile Blog Joined March 2009
Chile4253 Posts
Last Edited: 2010-08-16 21:39:08
August 16 2010 21:28 GMT
#24
OP: Do a small thought experiment with me, will you?

Imagine that you know 3 players among the vast numbers of players on Battle.net. Skill-wise, two of them (who play Terran and Zerg) belong in mid Platinum. Another one (Protoss), skill-wise, belongs in mid Gold.

However, in this hypothetical example, Zerg is so massively underpowered compared to the other two races, that other T and P players who belong in mid platinum will generally crush Zerg players of the same skill level.

So, our Zerg player, who skill-wise belongs in mid platinum, gets bumped down to Gold. There, he's facing other somewhat-skilled Zergs and less-skilled Protoss and Terran players. There, he can compensate for his weaker race with his greater skill. And he will achieve the same winrate as the less-skilled Protoss in Gold, and the equally-skilled Terran in Platinum; roughly 50%.

Battle.net matchmaking is DESIGNED to make everyone have roughly the same winrate over a large number of games (unless they're at the very top or at the very bottom), ergo the winrate and rating of the pack of players at the middle means squat. The only things it could reveal would be matchup-specific imbalances; for instance, if you had T>Z, Z>P, and P>T, then players would tend to lose versus the race they're weak against and win versus the race they're strong against.

If you want to know whether imbalances exist, go look at the very top; if one race is hugely over-represented, it's a fair assumption that some of the players there might not belong at the very top, skill-wise, while others of the under-represented races who don't quite make it rank-wise, do belong there, skill-wise. Or, ask the progamers; if they, who know and understand the game best of all, generally agree on an imbalance, then that's also telling.
Go here http://vina.biobiochile.cl/ and input the Konami Code (up up down down left right left right B A)
alexanderzero
Profile Joined June 2008
United States659 Posts
August 16 2010 21:30 GMT
#25
The game could appear completely balanced at most levels of play, but where it really matters is at the top between pro-gamers. A significant imbalance may only become apparent when the players have a certain amount of skill. That is why I don't consider these kinds of numbers to be necessarily revealing.
I am a tournament organizazer.
Random()
Profile Blog Joined August 2004
Kyrgyz Republic1462 Posts
August 16 2010 21:30 GMT
#26
You need tournament statistics for this to make sense, ladder is useless.
ModernAgeShaman
Profile Joined January 2008
Norway484 Posts
August 16 2010 21:30 GMT
#27
saying that because each race wins 50% of their games does not mean things are balanced, people just love to believe that in my opinion. hypothetically, if protoss had some sort of uber strat that was unstoppable once executed versus a terran but due to poor play and mistakes made by the protoss, the terran was able to win 50% of the time. but the other 50% of the time, the protoss did everything right, and no matter what the terran did or how he prepared, it resulted in a loss. is this balanced just because there's a 50% win rate? i surely don't think so
QuakerOats
Profile Joined April 2009
United States1024 Posts
August 16 2010 21:32 GMT
#28
Statistics are meaningless when it comes to balance and I don't understand why everyone keeps trying to bring them up. Skill is always the number one factor when it comes to winning. And so you will never see 70% TvZ winrate because the system will just pair Terrans up with better Zergs until they start losing.

Example: Let's say the #1 Zerg is equal in "skill" to the #1 Terran, #2 Zerg = #2 Terran, and so on. If there's an imbalance, the system will eventually work itself out so the #5 Terran is playing the #5 Zerg (who he can beat because of the imbalance) and the #4 Zerg (who he can't beat, because he is less skilled). 50% win rate. And so every single Terran would have a 50% winrate because there is always a better Zerg player, even with the imbalance. The problem only arises at the very top: the #1 Terran cannot lose. But for EVERY OTHER TERRAN there will be a 50% winrate.
suckerfish
Profile Joined April 2010
United States31 Posts
August 16 2010 21:35 GMT
#29
On August 17 2010 06:28 Zato-1 wrote:
OP: Do a small thought experiment with me, will you?


Ah, okay. Thank you for your explanation. You're the first person in this thread to actually answer my serious question in a reasonable manner, instead of simply saying, "You're an idiot, the answer is obvious". Thank you.

I think I've found some stats to back up your claims. Here's a breakdown of race rankings at each level of play: http://www.sc2ranks.com/stats/race/all/1

What's interesting to note is that the races seem to be reasonably balanced at the lower divisions, but at the top, Terran squeezes out both Protoss and Zerg.

Another thing that's kind of weird is there seems to be a lot of high-ranked Zerg in the lower four divisions, and practically no equally ranked Terran or Protoss. This seems really strange; I'm not sure what the explanation is for this.
kGold
Profile Joined July 2010
Canada66 Posts
August 16 2010 21:37 GMT
#30
On August 17 2010 06:26 SlowBlink wrote:

This whole premise is flawed. What you're trying to say is that since zerg players win 50% of the time, there is no imbalance for zerg. What you don't take into account is the fact that Blizzard's matchmaking system is specifically designed so that you come out with a 50% win/loss record. Battle net will match you up against a player of equal skill so to speak, and reevaluate your skill based on whether you win or lose. With this mechanic you can have pro level zergs getting matched with plat/gold level terrans, simply because the zerg player is losing more to higher level terrans. Then when they beat the lower level players, it balances out their win/loss to 50%.

tl;dr- all this proves is that battlenet matchmaking actually works.


This. Although it seems to be designed to give most people a 55-60% W:L ratio.

It takes an understanding of how the matchmaking works to realize that you can't say the game is balanced based on these stats.
If I lose to a noob, then what am I?
guitarizt
Profile Blog Joined March 2009
United States1492 Posts
August 16 2010 21:38 GMT
#31
I know blizzard likes stats and I know the stats show that terran seems to win a bit more than their fair share of games if you actually spend some time to interpret the numbers, but you don't have to be a statistician to realize that you don't have to be nearly as good of a player to win with t or p than as z. I'm random but I played zerg for about 80% of the beta and the only games I win anymore are games where I have to be significantly better than my opponent. Also zerg is boring as f to play and I've always hated the roach since phase 1 beta. I think it's going to be stuck like this for a while since it doesn't look like blizzard cares and even if they did the only way they'll fix things is by changing the values of stuff around. Maybe they'll make decrease ultralisk build time which might be balanced and even out the stats but it wouldn't make the game any better.
“There is nothing noble in being superior to your fellow man; true nobility is being superior to your former self.” - Hemingway
silencesc
Profile Joined July 2010
United States464 Posts
August 16 2010 21:44 GMT
#32
The matchmaking system makes people have about 50% W/L ratio, so 50% overall for all matchups makes sense. The real problems come on the pro level, where the W/L rates are way off of 50%, sure that's only .1% of the population, but it's the more high profile part. If pro's vs. pro's all say that TvZ is imbalanced, I would tend to agree.

However, for the regular player, like the one's on TL, it probably isn't as imbalanced as we think at our level, (I'm talking mid plat to mid diamond) so the huge imbalance threads are probably unnecessary. For instance, I'm mid platinum, and I think EMP is imbalanced because I see pro's use it to great effect and rape protoss armies twice their food size, but in my games, I've only been EMP'd once. Therefore, I think all the zerg tears come from people like IdrA and DIMAGA saying that the MU is imbalanced, and that they're going to move to terran, and not from personal experience.
Real Men Proxy Gate | TEAM LIQUID HWITINGGGG!! PROUD MEMBER OF UC DAVIS CSL TEAM | "If you don't give a shit about what gum you eat, buy Stride" - Liquid`Tyler on SotG 4/19/2011
TLOBrian
Profile Blog Joined March 2010
United States453 Posts
August 16 2010 21:45 GMT
#33
Could someone please lock this please? The discussion has been pummeled into the ground OVER and OVER and OVER. We know the TvZ matchup is broken, and we know that the stats won't show either side of the arguement.

The point is, there is no reason for this thread to be here. Since everyone has talked about this so damn much, blizzard is sure to do the correct thing for the TvZ matchup, and if not, people will still complain and it will be changed again. You guys have to have a little faith in blizzard. (I am being kind of hypocritical here...I don't really like blizzards balance changes.) They listen to the community. Resolved.

Mods please lock this and throw away the key.
Steven Bonnell II is the friggin man.
iEchoic
Profile Blog Joined May 2010
United States1776 Posts
August 16 2010 21:48 GMT
#34
On August 17 2010 06:28 Zato-1 wrote:
So, our Zerg player, who skill-wise belongs in mid platinum, gets bumped down to Gold. There, he's facing other somewhat-skilled Zergs and less-skilled Protoss and Terran players. There, he can compensate for his weaker race with his greater skill. And he will achieve the same winrate as the less-skilled Protoss in Gold, and the equally-skilled Terran in Platinum; roughly 50%.


And as I said, in your example, there would be a lower representation of zergs in diamond leagues compared to other leagues. This isn't the case - actually a higher % of zergs are in diamond than other leagues compared to the other two races. So this cannot be it.
vileEchoic -- clanvile.com
andeh
Profile Blog Joined August 2009
United States904 Posts
August 16 2010 21:48 GMT
#35
It looks balanced because all of the T players arent good enough/don't understand how to fully use their advantage with the race

If you looked at the games of the top 200 of each region I guarantee it'll be vastly different than grand totals.

once the strategies start becoming passed down to gold level we'll see a large tilt in the scale
suckerfish
Profile Joined April 2010
United States31 Posts
August 16 2010 21:50 GMT
#36
On August 17 2010 06:45 TLOBrian wrote:
Could someone please lock this please? The discussion has been pummeled into the ground OVER and OVER and OVER. We know the TvZ matchup is broken, and we know that the stats won't show either side of the arguement.

The point is, there is no reason for this thread to be here. Since everyone has talked about this so damn much, blizzard is sure to do the correct thing for the TvZ matchup, and if not, people will still complain and it will be changed again. You guys have to have a little faith in blizzard. (I am being kind of hypocritical here...I don't really like blizzards balance changes.) They listen to the community. Resolved.

Mods please lock this and throw away the key.


I'm sorry for flogging a dead horse, and I'm sorry I don't read every single message that gets posted on these forums. The question I was asking was in all earnestness: I very much did not know why the statistics did not jibe with anecdotal reports.

I was not trying to accuse anyone of being daft or biased. I simply wanted to find an answer to my honest question.
Sanguinarius
Profile Joined January 2010
United States3427 Posts
August 16 2010 21:53 GMT
#37
Yeah its the AMM that gives a close rating - which does work well. However, that doesnt mean the matchups are balanced.
Your strength is just an accident arising from the weakness of others -Heart of Darkness
Pyre
Profile Joined July 2010
United States1940 Posts
August 16 2010 21:55 GMT
#38
Someone should compare the Win/Loss of +50 Diamonds vs other +50 Diamonds only. This should give more of a realistic statistic.This could obviously bad changed to +25 diamond etc.
Liquid`Nazgul
Profile Blog Joined September 2002
22427 Posts
August 16 2010 21:55 GMT
#39
this is too misleading cause of AMM
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