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HonestTea
5007 Posts
The Korean SC community has been experimenting with mathematical models for years already.
Mathematical models are not meant to tell us whether Bisu will beat Savior. They do not predict single game results, or even champions. (Well, except for Etter's math).
Mathematical models are useful for judging the overall big picture, for treating each player and each result as a piece of data. We can find some interesting correlations and maybe reach some conclusions. As long as everybody understands that the models are not to be the end all, they will open a new area of discussion. In particular, they help us understand macro trends.
Cascade's OP has already led to good discussion.
What I'm trying to say is this:
1) Cascade, thanks for an awesome post.
2) WhatIsProtoss, why do you feel entitled to post your bullshit?
BECAUSE IT'S NOT YOU WHO TOOK THE TIME TO ACTUALLY COME UP WITH THIS SHIT
if you're going to be a critic, at least be a good one.
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Haha, still up. xD
Well, that's what I meant with "at the end of the day." Of course you do some calculating in between, but basically you say "skill + race" modified by your opponents "skill + race" = your winning probability? My problem with this is, as I said, not the definition by itself (that is one of the ideas I actually like) but the definition of the parameters and especially their loading, which could easily end up beeing arbitrary.
I'm trying to point out the difficulty of getting viable readings as long as you don't mass lots and lots of data, which you can't, because there have been many changes regarding maps, gameplay and game structure (-> patches), that cannot be accounted for in a model. Not mentioning that this doesn't have to be the end of it at all, Starcraft still seems to be evolving. And evolution -as we all know- is a random process. (Hehe, now I'm being rethorical)
Next problem, "when comparing with actual statistics (if we can find some eventually...)": from which years do we take them. Does it make sense to take anything before that last patch, is old school SC comparable to today's SC and so on. I don't want to be pessimistic again, but it could end up in not having enough material, because one has to rule out different things for various reasons.
Haha, till now I posted on far to many forums, just ask my ex-girlfriends ( xD ), but I really don't care who thinks what of me, as long as the person I'm writing to understands. 
Cheers.
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HonestTea
5007 Posts
No harm done by you, Pinselstrich. Your contributions were good discussion.
Good night.
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You have bad hand writing... ... ... =D
jk, nice write up! 
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MaTRiX[SiN]
Sweden1282 Posts
thougt some more about this, if the race distributions was decided by imbalance wouldnt the terran numbers continue to grow as we go further into tournaments?
in this thread: http://www.teamliquid.net/forum/viewmessage.php?currentpage=1&topic_id=52660
you can see how the race fractions are roughly the same at all stages off progaming, which would imply that there being more terrans than protosses and zergs has to do with something else.
edit: didnt remember the thread as well as I thougt :p the race distributions seems to change at the offline qualifier stage but not after that...
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Have to say, good work Cascade. I used to think like some of the poster that modeling and economics in general were pretty much fluff compared to like biology or other hard sciences, but I've really come to appreciate how much of it influences our policymaking and government.
To those of you who claim that quanitfying the imbalance has no significance, you should keep in mind that a lot of our lives is significantly shaped by people who made models of how we would act. For example, amount of money you're being charged for your credit card bill (i.e. monthly minimum percentage) is highly tied to mathematical models of how much and how quickly you'll return it.
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On November 04 2007 12:23 Pinselstrich wrote:Haha, still up. xD Well, that's what I meant with "at the end of the day." Of course you do some calculating in between, but basically you say "skill + race" modified by your opponents "skill + race" = your winning probability? My problem with this is, as I said, not the definition by itself (that is one of the ideas I actually like) but the definition of the parameters and especially their loading, which could easily end up beeing arbitrary. I'm trying to point out the difficulty of getting viable readings as long as you don't mass lots and lots of data, which you can't, because there have been many changes regarding maps, gameplay and game structure (-> patches), that cannot be accounted for in a model. Not mentioning that this doesn't have to be the end of it at all, Starcraft still seems to be evolving. And evolution -as we all know- is a random process. (Hehe, now I'm being rethorical) Next problem, "when comparing with actual statistics (if we can find some eventually...)": from which years do we take them. Does it make sense to take anything before that last patch, is old school SC comparable to today's SC and so on. I don't want to be pessimistic again, but it could end up in not having enough material, because one has to rule out different things for various reasons. Haha, till now I posted on far to many forums, just ask my ex-girlfriends ( xD ), but I really don't care who thinks what of me, as long as the person I'm writing to understands. Cheers.
Ok, so we seem to be down to basically one issue: how the f do we choose the imbalances??
You are making two points and I agree on both of them.
1) Making up percentages from what we personally believe are the correct imbalances is not very scientific. This would be remedied if it would be possible to find statistics of games on all maps for, say, the last 6 months, and statistics on the number of active progamers of each race. I've been asking for these number during 3 pages now, but they refuse to appear. Is the best foreign page on progaming really not capable of delivering such basic statistics? 
2) even if we get statistics, how long back should we go? This is probably my major concern with the application of the model. While not an issue with the model itself, it still makes the application a lot more complicated.
a) If we go to far back in time, imbalances will no longer be the same, due to strategical evolution and maps (and patches).
b) If we do not go far back enough, we will get few games and low (=bad) statistics.
i've been suggesting 6 months as compromise between these two issues, but I'm not sure.
We should play some games sometime. 
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On November 04 2007 19:55 MaTRiX[SiN] wrote:thougt some more about this, if the race distributions was decided by imbalance wouldnt the terran numbers continue to grow as we go further into tournaments? in this thread: http://www.teamliquid.net/forum/viewmessage.php?currentpage=1&topic_id=52660you can see how the race fractions are roughly the same at all stages off progaming, which would imply that there being more terrans than protosses and zergs has to do with something else. edit: didnt remember the thread as well as I thougt :p the race distributions seems to change at the offline qualifier stage but not after that...
I'm not 100% sure about this:
due to the exponential distribution in skill, the race disrtibution predicted in my model will be the same for any number of gamers.
I am though sure on this:
If you are looking at really low number, like 10 or less, stastical fluctuations will be to big, so you cannot really use an statistical aproach like mine. I Think top 30 kespa is about the smallest number of progamers you could look at with this method, and even that is really pushing it and will be subject to big errors.
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On November 04 2007 04:57 Cascade wrote:Show nested quote +On November 04 2007 02:07 MaTRiX[SiN] wrote:
"many different imbalances will correspond to the same race fractions, so it is impossible to go in the other direction."
wouldnt this mean that even thougt your result is close to reality it still doesnt have to be correct? The result is correct (if my model is correct at least). What it says it that IF the imbalances are X, THEN the race fractions will be Y. The fact that many different X will predict the same Y says that we CANNOT go the other way. That is, we cannot say "look, the race fractions are Y! That means that the imbalances must be X!". So the prediction goes in only one way. Show nested quote +On November 04 2007 02:45 niteReloaded wrote:On November 04 2007 00:56 WhatisProtoss wrote:Why is this a featured thread?? As long as a post contains pretty pictures and mentions Starcraft theories, is it put into Featured? Even if it's useless shit that nobody understands? I stopped reading as soon as I got to: I have now developed a mathematical model that explains how a Z>>P imbalance, together with smaller T>Z, P>T imbalances, causes a TERRAN dominance. This part makes sense. End of story. We don't need math to prove this. Math won't really prove it. We see that Z eliminates all the P, so terran can statistically beat the remaining Z without having to worry about playing against protoss. What's the point of all the weird math that makes no sense at all? 1) Progamers have different skill levels s. The number of progamers at a given skill s is proportional to
e^(-a s)
That is the the number of players falls of exponentially as skill increases. "a" is a parameter that decides how quickly the number of gamers fall. A large "a" means that the very best playes in the worlds is not THAT much better that the ones ranked around 100. A small "a" means that the top players completely own lower ranked players, even if they are not very mucher lower ranked.
This distribution can be discussed. Other ideas are welcome.
2) The probability of a player of skill s1 to beat a player of skill s2 is
1/( 1 + e^(s2-s1) ) e^(-a s) is not proportional to s (skill). It is not even exponentially proportional to s. Also, 1/( 1 + e^(s2-s1) ) = P(player of skill s1 to beat player of skill s2). Example 1: What if they have the same skill level? Probability = 1/1 = 100% Example 2: What if one has no skills at all? Probability = 1/(1+e^x) < 100% What the results SHOULD have been, if one person didn't have skills, the probability to win was 100%. And when the skill level was the same, the probability should be 50%. Why are people buying your bullshit mathematics? BECAUSE THEY DON'T READ IT. haha basically, my first reply sounded very much like this, but i thought i wouldnt put the guy down, he obviously put a lot of effort into it. But i agree tho, the idea is all thats worth mentioning here. Zerg overkills the terran killers which are then safe. Thats it. The rest of the post is messing around with made-up numbers put into basic equations. I guess people are surprised that math sometimes can actually be used for something, even if the whole story is obvious without it. Haha, that's sweet of you to not put me down at first! A habbit of a good poster. I see your point though. I think it is a matter of which level you want to do it at. I certainly agree that it is far from vital for the common teamliquidan to know exactly what race fractions comes out of a certain imbalance setting. But I'm working with research and have a habbit of doing this sort of things properly. Hopefully it was of interest for some. [#1]I do not think however, that this effect was common knowledge.) Maybe you didn't say that? I'm not sure exactly what you refer to with "the whole story", so just disregard if I've misinterpreted you. I also think that even though the exact percentages are not of great interest for most, it IS of interest that they CAN BE FOUND. This is my opinion as a physicist, and I completely understand if you do not agree on that point. Anyway, it would be kinda stupid to say that I COULD find exact values without explaining how I did it and presenting examples. EDIT: Just saw "made up numbers in basic equations". Hehe, ok, slightly unfair imo. The 4 numbers that needed to be "made up" I left for us all to find from statistics. And I don't know how to say this without sounding like a jerk so: I do no think very many on this board could have solved that model. I came of as an elitist now right? D'oh! again tnx for feedback.
#1. Ok maybe its not common knowledge, but to me, it seems very obvious that z>>p leads to T dominance. Almost as obvious to comment on it with a "duh".
as for the rest of the post, i still appreciate your work, i myself probly wouldnt know how to make it in mathematica and all that. My point was that usually, in projects like this, the advanced tools of math are used to make a discovery or tell us that something seemingly far fetched can actually work. In this case, you took an obvious(is it?) concept, put some numbers in equations and got some results. The solution didn astonish me personally, its on the same 'level' as the basic idea.
I hope i dont sound rude or anything, and im trying not to ^ ^. This is a good thing you did, certainly worth reading.
P.S. you dont sound like an elitist, you sound like an enthusiastic young man who's willing to use his probly newly-gained knowledge to try to explain some things not related to university. its a good thing.
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EPT
