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WhatisProtoss
Korea (South)2325 Posts
On November 04 2007 01:13 cmr.Pent wrote: Well, you are a fag! If s1 = s2 then 1/(1 + exp(s2 - s1)) = 1/(1 + exp(0)) = 1/(1 + 1) = 1/2 = 50% Okay. Then explain his first point. Why does he have the number of terran to be twice as much as zerg or protoss, then feign surprise when the number of terran is 50%, zerg, 25%, and protoss 25%?? Idiot. | ||
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Wonders
Australia753 Posts
On November 04 2007 01:18 WhatisProtoss wrote: Okay. Then explain his first point. Why does he have the number of terran to be twice as much as zerg or protoss, then feign surprise when the number of terran is 50%, zerg, 25%, and protoss 25%?? Idiot. He has terran twice as much as zerg and protoss based on the matchup percentages. He 'feigns surprise' (more like exclamation), presumably because he has successfully demonstrated how such a model of progaming might work, and how it agrees with the current figures. Learn some maths before you go calling the maths bullshit. | ||
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Cascade
Australia5405 Posts
Let us focus on the main model! The toy model is only an illustration. On November 04 2007 00:14 cmr.Pent wrote: What a great job! My respect Cascade! I agree that precise TLPD statistics would be of invaluable help in testing your model. What's more, I guess you could actually perform multivariate optimization to get those 4 parameters from empirical data. You could minimize say least square deviation between theoretical and TLPD percentages vectors. I'm sure Mathematica has some robust routines for that. By the way, are you familiar with this model: Lotka-Voterra equation? I guess I could yes. Seems like a lot of work though. Im still hoping that someone will be able to find statistics for this without having to add up loads of things in TLPD. I've not heard of that model under that name, but I've done similiar models in some math course long ago.  You also have similar things in chemistry with different molecules that brakes or accelaretes other processes iirc.On November 04 2007 01:05 MoNKeYSpanKeR wrote: Didn't read the entire thing, but i would imagine i could sum up what your going to say in about a paragraph. Z kncoks out all protoss out of leagues, which is the anti terran, and terran dominates Zerg, so without any Protoss to stand in a Terrans way he wins. And the fact that ZvP was considered the most imbalanced, meaning there would be so few protosses, and the few there were would get knocked out by a Z and then the Z inevitably falling to a Terran. Then we would have a lot of terrans who don't have protosses KOing them, and zergs getting beaten by terrans and then there being no protosses to balance the cycle due to it being more imbalanced then say ZvT. yes, that's a good summary.  What I continue to do then is: 1) Prove that it actually is so in my real modelas well. 2) Quantify if by making predictions of exactly what the race fractions will be. I'm not sure what you meant with the last paragraph. It will not loop around infinitely, but rather reach a stable state. Even if there are more terrans than toss, the zerg will still be ok since they really beat the crap out of the few P that are left, but only have a smaller disadvantage from the more numerous T. | ||
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MaTRiX[SiN]
Sweden1282 Posts
wouldnt this mean that even thougt your result is close to reality it still doesnt have to be correct? | ||
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niteReloaded
Croatia5281 Posts
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: 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? 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. | ||
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cmr.Pent
Russian Federation18 Posts
On November 04 2007 02:45 niteReloaded wrote: 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. Yes it is obvious when the op has explained it in detail. I don't think it was really obvious for everyone that Z>>P leads to Z's disadvantage. The most important thing though is that Cascade managed to describe the effect quantitatively. | ||
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Cascade
Australia5405 Posts
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. On November 04 2007 02:45 niteReloaded wrote: 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. 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. | ||
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ChessWhiz
United States260 Posts
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MaTRiX[SiN]
Sweden1282 Posts
On November 04 2007 04:57 Cascade wrote: 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. yes but I mean, with the imbalances you assumed you got race fractions that were close to reality, but since more than one imbalance could create that race fraction this doesnt really mean anything? we allready knew what the race fractions were, what's interesting is what the imbalances (if any) are... | ||
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Pinselstrich
43 Posts
This thread contains one or two nice ideas, but mathematical models for explenation of T dominance? Come ON, if you really knew enough about maths to formulate complex models on the basis a lots of variables, you simply would know that this hypothesis isn't viable at all. Even given that all the assumptions that are made prior to the equations were right (which I really doubt), there are lots of historical and random data that simply can't be managed in such a short abstract. And everyone who doesn't understand that is just a n00b at math... | ||
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Jyvblamo
Canada13788 Posts
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Cascade
Australia5405 Posts
On November 04 2007 05:12 MaTRiX[SiN] wrote: yes but I mean, with the imbalances you assumed you got race fractions that were close to reality, but since more than one imbalance could create that race fraction this doesnt really mean anything? we allready knew what the race fractions were, what's interesting is what the imbalances (if any) are... We can see both the imbalances and race fractions easily from just looking at the statistics on all the maps, and by simply counting numer of players of each race. What this model does it that it explains how they fit togheter, and explains how they affect each other. It does not generate any previously unknown statistics about present och past progaming. A possible use is the one I adressed in the op: If there, for example, are too many terran for the organisers likeng. Too many mirrors maybe makes the view rates drop. they cannot directly change the race ratios with less that forbidding terran players to play, which probably would not help their ratings. They could however change the balance of the maps to indeirect effect the ratios of the races. my model helps them to understand how changes in map balance effects the race ratios. Did that answer your consern? On November 04 2007 05:26 Pinselstrich wrote: I agree with WhatisProtoss. This thread contains one or two nice ideas, but mathematical models for explenation of T dominance? Come ON, if you really knew enough about maths to formulate complex models on the basis a lots of variables, you simply would know that this hypothesis isn't viable at all. Even given that all the assumptions that are made prior to the equations were right (which I really doubt), there are lots of historical and random data that simply can't be managed in such a short abstract. And everyone who doesn't understand that is just a n00b at math... Welcome to Teamliquid. You need to be a bit careful with attacking people like that. I know my maths. And if I were not capable of "formulating complex models on the basis of a lot of variables", then they would have kicked me from my position as PhD in theoretical physics. That said: if you have opinions on my asumptions I invite you to express them and we can discuss them. As you can read in the op I am not myself convinced by all assumptions, so I'd be happy if yuo have some ideas of what should be changed. but please dont just tell me that I am wrong without specifying better than that. :/ | ||
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Pinselstrich
43 Posts
First, if you want to be anything but unscientific, state a clear hypothesis, all variables involved (including those possibly involved and the odds that they are/are not). Basically failing in that regard is what allready screws your whole model. You sure u got that PhD?... At university they would kick me out for such sloppy work. Your point 2: Winning probability as a function of skill difference? You can't be serious and if you are you don't know very much about e-sports or sports in general obviously. Especially if you consider that most progaming leagues are played in tournaments which of course screws any distribution, because maybe better players got kicked out earlier in the tournament. (fe Stork and Hwasin this MSL) btw in inferential statistics the expected frequencies can easily differ from observed fre's. That's what we have our lovely tests of significance for. the worst progamer of each race must have the same winning probability averaged over all other progamers. As you say yourself, this is very intuitive. I don't believe that players are kicked out simply based on their winning %, because in Korea SC is big business, it's about marketability, sometimes second chances, sometimes not, personality, teamplay and so on. Lots and lots of undefined factors. Also I believe that it is easier to kick terrans out, because they are easier to play and therefor there is a much larger pool of good T's that can take your place than with Z or P. But that's just my opinion... problem is, you have to proove the opposite or modify your hypothesis before you can go on, not just ignore it. Also, you have to realize that the less Protoss or Zerg players there are the more the Terran players will only train for TvT. Which reduces their skills level considering TvP and TvZ. At the end, I'd like to point out that through the history of SC there were different patches that very much influenced the statistical percentages of wins between the races. I can't understand how someone that calls himself serious mathematician can overlook this and the impossibility to find the REAL percentages of the imba's, because of this, especially if you look upon this matter historically. ... That's it for now, because as I scroll further through your abstract I realize that I'd loose very much time in specifying everything I don't like. And asking myself where'd you get that PhD from of course. xD | ||
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teamsolid
Canada3668 Posts
On November 04 2007 05:26 Pinselstrich wrote: I agree with WhatisProtoss. This thread contains one or two nice ideas, but mathematical models for explenation of T dominance? Come ON, if you really knew enough about maths to formulate complex models on the basis a lots of variables, you simply would know that this hypothesis isn't viable at all. Even given that all the assumptions that are made prior to the equations were right (which I really doubt), there are lots of historical and random data that simply can't be managed in such a short abstract. And everyone who doesn't understand that is just a n00b at math... Um... that's why they're called models. Is economics also useless, just because it uses models and assumptions to represent real-life situations even when there are 100s of variables out there that can turn things around and each individual corporation has its own determinants for success? Not at all, because when you look at things on a large scale (like he is) these trends can actually be studied and can be applicable. | ||
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Pinselstrich
43 Posts
On November 04 2007 07:09 teamsolid wrote:Um... that's why they're called models. Is economics also useless, just because it uses models and assumptions to represent real-life situations even when there are 100s of variables out there that can turn things around and each individual corporation has its own determinants for success? Not at all, because when you look at things on a large scale (like he is) these trends can actually be studied and can be applicable. Exactly my point. Not all parts of course, but very large parts of economics ARE useless. Talking about large scale, if you look at the assumptions of the economic and following neoliberal agenda, namely: "If we have flexibly prices, wages and rates of interest there will exist an equilibrium at the labor market and everyone will have work." The hell everyone will. Models encourage ppl to make absolutistic statements, but how can you make such a statement if your model is based on probabilistic maths and assumptions? | ||
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0z
Luxembourg877 Posts
On November 04 2007 05:26 Pinselstrich wrote: I agree with WhatisProtoss. This thread contains one or two nice ideas, but mathematical models for explenation of T dominance? Come ON, if you really knew enough about maths to formulate complex models on the basis a lots of variables, you simply would know that this hypothesis isn't viable at all. Even given that all the assumptions that are made prior to the equations were right (which I really doubt), there are lots of historical and random data that simply can't be managed in such a short abstract. And everyone who doesn't understand that is just a n00b at math... WhatisProtoss is an ass, who doesn't deserve to be spoken to directly. Who knows what and to what extent is entirely his own business and vastly off-topic. In response to your contribution (and others'), this is how you do mathematical models of things. If you do a model of an ecosystem there are a lot of things you don't consider at first - disease, change of climate effects, etc. and still your model roughly works (gives you the general idea). If you want to be more precise you take more and more things into consideration and the model gets more and more accurate. To people who say the conclusion is obvious, sure it is, but if blizzard adds a fourth race, say wankers (W) and you have an imbalance which looks something like T : W 46% T : Z 56% T : P 41% P : Z 52% Z : W 53% P : W 44% and I ask you will there be more wankers than terrans in progaming after three months, it might just not come off the top of your head. | ||
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Night[Mare
Mexico4793 Posts
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Cascade
Australia5405 Posts
Pinselstrich: OK, I'll have a go as well then. if you get bored you don't need to reply, i wont hold it against you. it IS hard to discuss mattes like this on by just writing.May I ask which univerity you are at, and what you are studying? 1) Ok, first the op is not a paper sent for publication, nor an assignment at uni, but an opening post on a forum. It shouldn't be as formal, or noone would read it. Being scientific is not my first priority. Nevertheless I have in the beggining a paragraph on it's own saying "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." i can't see how that is not scientific enough for this forum. 2) you are listing a lot of things left out of the model altogether. This is interesting, and also important for the model. I have given each progamer only the property "skill" (apart from race), and measured their success only in winning ratio. You do not like that I set up a formula to calculate winning probability as a function of skill, but do not say why I shouldn't. First I do not have any more information about the players. In one specific match it will of course depend on a lot of other things like style, preparations, current confidence etc. I average over all those other effect. Point is that those effect will, in the long run, effect each race equally much, so they will not change the average outcome. And even if for example zergs (by some reason) tends to be extra nervous and play worse in ZvP, that will then be included in the imbalance. Same goes for bad luck in tournaments, being kicked out/allowed to stay due to behaviour, marketing etc. All these are factors that, as far as I know, effect all races equally, so they can also be ignored. T being replaced by other T easier than a zerg gets replaced by another zerg doesnt matter at all since I am looking only at race distribution. For all I care, they can change every terran on their team three times a day. And I cannot, need not prove it. These are assumptions that I make in my model. If i could prove it, they would not be assumptions. I've tried to argue why it is reasonable to assume them, i cannot do more. the point with terran training more for TvT is a very good one. Same thing as lefthanded tennis/badbinton/etc players are favoured. That actually would dampen the race ratios towards 33.3%. The imbalances I speak of are not the ones yuo call "real imbalances", but the actual statistics you would get if you take the 100 best players from each race and let them play each other (infinitely) many times on the current seasons maps. They cannot of course be found to arbitrary precison, but are still defenitely measurable. And you are so rude for insulting me about being bad at my job! FYI I was picked from quite many applicants. Ok, peace out. gl with your studies.  | ||
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Pinselstrich
43 Posts
@0z: LoL, ty, I'll keep that in mind. xD I know what you mean, but if you make such a model you have to explain every single thing you used in it and try to explain why you didn't account for others. As I am used to see most models inapplicable for reality because of their lack of explenation, I still have my doubts about this one. And I am just one person with a single brain, imagine about 30 guys like me bringing up new and new factors that should be considered. What I'm trying to say is that making a model alone and without qualified help is like Sisyphos-work. @Cascade: Of course you can, I do statistics and sociology specialising on economy in Vienna. Maybe that's the reason why I don't like models, most of which I've encountered were not applicable for RL situations. Math is only kind of my hobby, so don't expect too much. But from experience I know, it's one thing to analyse the past and present, but a completely different story to forsee the future with a model. 1) Yeah, you're right. But normally we take the 0-hypothesis and try to proove the opposite. If you can't you approove your alternative hypothesis (which would be what your topics about). But since you don't seem to like testing theories, instead calling it "model", I can overlook that. It is indeed a topic in an internet forum. 2) I noticed that, so the thing you name "skill" is each players winning ratio at the end of the day? You see, I don't think that every short run effect will affect each race equally in the long run. Since there obviously are differences in gameplay and difficulty of gameplay between the races (some maps tend to favor some races, Monty Hall for instance). So you'd have to connect the racial ratios with the maps on which the games are played, for the obvious imba's there are sometimes. So there are not only factor influencing the short run, but also the long run IMO. You're argumenting with something we call "central limit theorem" and you're right with it. I apologize, it really doesn't matter what race you are in that regard. Well, then argue. xD Yeah, and also that P's and Z's will train more PvT and ZvT if T dominates. And the fewer Ps and Zs there are, the more these few will be raping the T's and could end up dominating. IMO that's the reason why it's impossible to have one race dominating the others as long as the game itself is balances (what I believe that SC is, finally). That's the problem. In statistics we have things we call expected frequencies and observed frequencies. The EF are the thing you mean with letting the best players play infinitely, the OF are reality. And if you have both you can first use measures of compound to see if there's a relation between your expectation and reality. If you're lucky and there is you have to make some tests of significance to be sure that youre experiment isn't just a methodological artifact. As long as you don't do that, from statistical perspective your tables are obsolete and have no viability at all. About youre PhD I was just kidding, don't take anything personally when it's 2am + beer here. xD | ||
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Cascade
Australia5405 Posts
We seem to be ok on 1). regarding 2: Um, skill is not the same as winning probability. But the winning probability can be calculated if you know both players skill. That is explained in the op. This probability is however modified by which races are playing by giving the favoured race a boost in skill. Also explained in op.I think the issue here is this: I am averaging over everything. And yes, the imbalances ARE effected by which maps progamers a playing on. If they suddenly change to maps where Z>>T (I wish...) then I would have to use a new TvZ imbalance parameter in my model. And yes, since this model is based on averages and statistics, this will only be accurate if many games are played. So as you say, when comparing to actual statitics (if we can find some eventually...) we need to take errors into account (with the normal sqrt(n) and see how many sigmas of I am and yadayada). The values that pop out of my model doesn't have errors though, since I'm doing the calculation for infinitely many games. Yeah, I though you were fooling around on the PhD, but you never know on t3h Int4rW3b!! If you're not an experienced forum-poster, then take an advice and be careful: While that kind of fooling around is very funny and enjoyable IRL, the joke part does not always transfer very well into the written words, and you risk ending up in stupid arguments. remember to drink plenty of water befor you go to bed to avoid the hangover tomorrow. | ||
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