Sc2 is imbalanced and the math to prove it

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03/12/2012 04:40 PMPosted by LGDmk
As a math major, I cringe every time you use the phrase "mathematical proof." This is not a proof. This is mathematical speculation.

Call it what you will, but if you really are a math major, you will know that there is a mathematical proof behind it. I have only covered the logic side of it in this thread (not everyone is a math major bud, so I have to appeal to them too), which is why you are calling it "speculation".

03/12/2012 04:42 PMPosted by xXDefianceXx
Let's play by your rules though. Let's say that all the races have 1000 people, all equal player bases, and zerg wins every match. Meaning they have 1000/1000 wins, while Terran and Protoss have some other win rate. You still say that all the races are balanced simple because they have 33% for all races. Which makes no sense. As that would obviously show that something is imbalanced about Zerg.

As I mentioned in the original article (if you would take the time to read it) because of Bnet's ranking system all winrates come out to 50/50. Its impossible for zerg to win every match, which is part of the core-logic of my article, which you have blatantly proved just now that you don't understand. If you would ask me some question to help clarify your understanding of it I would be happy to give you answers. But your constant trolling is beginning to annoy me ='(.
I think I get what your getting at, but I think in this case the definition of balance and "ease of use" is synonymous, although in certain circumstances they may be different. Its a classic straw man fallacy :)


Well, in that case, I agree with you.
Edit: I don't necessarily believe this is a problem, however.
Buddy, your logic is off. Your statistics are correct, but you forget that statistics alone can't give you the answer. My statistic professor repeats that just about every class.

Statistics may tell you that 90% of a certain league is zerg, but in what way does that mean zerg is overpowered? It may mean that players of that skill level prefer the zerg race. Starcraft 2 is a macro game, and zerg is the "macro" race.

And yes I read your whole post.

Also, you base your inference on a mathematical proof. Where is this proof? Anyone could cook up something based on a certain "formula" that may or may not exist. I'm not saying this proof doesn't exist, but you show no evidence of you using it.
Buddy, your logic is off. Your statistics are correct, but you forget that statistics alone can't give you the answer. My statistic professor repeats that just about every class.

Statistics may tell you that 90% of a certain league is zerg, but in what way does that mean zerg is overpowered? It may mean that players of that skill level prefer the zerg race. Starcraft 2 is a macro game, and zerg is the "macro" race.

And yes I read your whole post.

Also, you base your inference on a mathematical proof. Where is this proof? Anyone could cook up something based on a certain "formula" that may or may not exist. I'm not saying this proof doesn't exist, but you show no evidence of you using it.


Finally someone else who knows what their talking about, we can actually have a real discussion now!

Playing your ball: Statistics may tell you that 90% of a certain league is zerg, that says zerg is overpowered because of the nature of Battle.net's ranking system--that players who win more go to higher leagues, and people who lose more go to lower leagues. A race dominating a higher league is therefore overpowered, and a race dominating lower leagues is therefore underpowered.

Uh, no. There's nothing 'mathematical' about your argument, here. You've done nothing more than acquire statistics. You've applied no metrics to them, not margins of error, no nothing. You've appealed to an extreme version of the converse (i.e. "what if one race had 100% in a certain league?") justify an absolute proportionality between balance and league distribution, despite the fact that this is clearly not the case because leagues are a closed system and admit of no comparisons to other sets.


Like I said, I am appealing to those without a math major. Hopefully you're reasonable enough to see past this.


That aside, the entire post is moot in light of the fact that balancing can only really be done for the highest level, as anything else is seeking to remedy problems of player skill, not imbalance.

I would completely disagree in that imbalanced aspects of the game magnify problems of skill, and hence you must measure the balance across all levels of play, not just the highest levels.

03/12/2012 05:02 PMPosted by DAWings
Your other issue exists in the different skill levels required to learn a race.

Covered this already :), and the error you are mentioning is caused by the random bias.
Is this another Protoss OP thread?
03/12/2012 05:04 PMPosted by Protostitute
Is this another Protoss OP thread?



shhhhhh.
03/12/2012 05:04 PMPosted by Protostitute
Is this another Protoss OP thread?

lol, no. Its a general balance thread, if anything it attests to how balanced Protoss is :).
I admire your attempt to use facts to back up your claim. I don't mean that sarcastically, I also admire your concession that this is by no means definitive. Such thinking is far too rare on these forums.

However, this analysis will always be flawed because people can switch races at any level. You don't have to pick one race and stick with it, I saw someone else mentioned random and you said it didn't make much difference. The title suggests you lack the humility that your OP says you have. Also, I believe terran is generally underrepresented in higher leagues but overall close to average representation because most n00bs prefer terran, since they are the humans and they are the campaign race. This is admittedly a personal inference and nothing more.

Thank you for your attempt to use statistics to back up your claim but I suspect it was a thought you had before you saw these stats and went looking for them to prove it. I would probably do the same but once again, it's all just a hunch, nothing more.
Thanks for the good manner Derski =D.

03/12/2012 05:21 PMPosted by Derski
I suspect it was a thought you had before you saw these stats and went looking for them to prove it.


Quite to the contrary actually, I was expecting the stats to super-favor zerg and say that zerg is underpowered. But considering the graph and random bias zerg is far better off than I would have ever dreamed.

03/12/2012 05:21 PMPosted by Derski
However, this analysis will always be flawed because people can switch races at any level.


Yes, that is a flaw, but I would think it has minimal impact--it happens little enough, and so long as the overall race usage percentages stay close to 33.33%, I think it is negligible.
Don't you need to account for total population per race as well? If zerg has 25% fewer players compared to the other races (made up number), in a perfectly balanced scenario that will skew the numbers to make zerg look underpowered.

So if there's 100 total players of each race, but only 75 zerg players and they're all evenly distributed between my reduced set of leagues:

Bronze: T: 33 (36%), P: 33 (36%), Z: 25 (28%)
Silver: *same*
Gold: *same*


Assuming the same number of players play each race... (also forgetting random)

Ruin: I have already covered both these claims in multiple responses and in the original article. Please read it carefully rather than skimming through it, as I am not going to explain it again.


Where did you cover this? Because I've read the OP a couple of times now and I don't see where you address it. It saves everybody time if you quote the relevant section when making a reply like that.
I have concluded that this is a troll thread.

He cites math and that this is a proof, yet no math or proofs are given. It is a clever idea, but not one that is true.
03/12/2012 05:40 PMPosted by Philodox
Don't you need to account for total population per race as well? If zerg has 25% fewer players compared to the other races (made up number), in a perfectly balanced scenario that will skew the numbers to make zerg look underpowered.

Exactly. Note this statement from the third paragraph: "This is based off of the mathematical proof that race distribution across leagues directly corresponds to balance in the special case of equally used races."

I italicized the part relevant to your question. Its a special-case of balance measurement if the races are equally used. Considering that each races' average usage is pretty darn close to 33.33% its safe to say the existing state of Sc2 falls into this special case.

03/12/2012 05:40 PMPosted by Philodox
Where did you cover this? Because I've read the OP a couple of times now and I don't see where you address it. It saves everybody time if you quote the relevant section when making a reply like that.

1st paragraph of the Analysis section: "Do note that these charts are slightly biased because they don't account for Random players. Not a biggie though."

03/12/2012 05:51 PMPosted by oSaVicious
He cites math and that this is a proof, yet no math or proofs are given. It is a clever idea, but not one that is true.

The logic is given, which is something that those w/o math backgrounds can understand and that those with math backgrounds are smart enough to figure out on their own without diluting the thread. If you have problems with the fact that I am not going to hand-spell everything out for you, you don't have to read.
Buddy, your logic is off. Your statistics are correct, but you forget that statistics alone can't give you the answer. My statistic professor repeats that just about every class.

Statistics may tell you that 90% of a certain league is zerg, but in what way does that mean zerg is overpowered? It may mean that players of that skill level prefer the zerg race. Starcraft 2 is a macro game, and zerg is the "macro" race.

And yes I read your whole post.

Also, you base your inference on a mathematical proof. Where is this proof? Anyone could cook up something based on a certain "formula" that may or may not exist. I'm not saying this proof doesn't exist, but you show no evidence of you using it.




Finally someone else who knows what their talking about, we can actually have a real discussion now!

Playing your ball: Statistics may tell you that 90% of a certain league is zerg, that says zerg is overpowered because of the nature of Battle.net's ranking system--that players who win more go to higher leagues, and people who lose more go to lower leagues. A race dominating a higher league is therefore overpowered, and a race dominating lower leagues is therefore underpowered.


I don't think there is any race that is "dominating" any leagues on the ladder. Plus this could just mean Battle.net's ranking system is broke, because you seem to be leaving out the possibility that those Zerg, Terran, and Protoss players are just outplaying their opponents. It's quite possible that there can be 8 zerg in a top masters league, doesn't mean its automatically a op race. A different league can have 8 top terran in a masters league. You're ruling out the players skill....
please don't tell me the American education system is this bad... or tell me you're European or something. This post has me depressed about the future of my country.


Not to validate any of the discussion or lack thereof as to what balance actually is, but the American education system IS that bad, and there are several European education systems that are far superior.
The logic is given, which is something that those w/o math backgrounds can understand and that those with math backgrounds are smart enough to figure out on their own without diluting the thread. If you have problems with that you are not forced to read.

You cant figure out a proof very easily without any math or any of the steps taken to reach a conclusion. We have a premise and a conclusion based upon that premise. Nothing more. Further, this is still a statistical look at balance, winrate and tournament winrate are still very vital pieces of information to determine balance.

Blizzard tries to balance towards 50%, but they cant. Why cant they? Because there are all kinds of factors. I suck at ZvT but rock at ZvP, so if I face more protoss than terrans then I will win more. Other zergs might prefer ZvT over ZvP.

Generic league level is a better indication of SKILL rather than BALANCE.





Finally someone else who knows what their talking about, we can actually have a real discussion now!

Playing your ball: Statistics may tell you that 90% of a certain league is zerg, that says zerg is overpowered because of the nature of Battle.net's ranking system--that players who win more go to higher leagues, and people who lose more go to lower leagues. A race dominating a higher league is therefore overpowered, and a race dominating lower leagues is therefore underpowered.


I don't think there is any race that is "dominating" any leagues on the ladder.


Never once did anyone say that one race is "dominating" any leagues on the ladder, it was merely a point to illustrate that if a race does dominate a league on the ladder it can correspond to the balance of the game. And hence, by measuring differences in RPL's you can measure the balance of the game.

03/12/2012 06:00 PMPosted by oSaVicious
Further, this is still a statistical look at balance, winrate and tournament winrate are still very vital pieces of information to determine balance.

Sigh, I quote myself: "This is just one way of looking at the balance of Sc2, and is in no way conclusive. The only way we can achieve a truly accurate analysis is to compare & contrast several different analyses from multiple sources, each taking a slightly different view that focuses on other ways of measuring balance."

This is solid proof that you have not read and do not understand my article, and as such any comments you have made are bogus. Please read the entire article and make sure you understand it before posing.

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