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On July 13 2012 05:51 skeldark wrote: If you mean an Maximum MMR we are not sure if it exist. When it exists this would be terrible because it would destroy the skillfunction on the high end. We just hope blizzard is clever enough not to build one in or build it only in the match finding algorithm.
The designer in the UCI video clearly stated that a maximum MMR cap exists, and it appears to be an actual MMR cap, not just a tweak to match-finding. I'm guessing there must be a reason that they strictly capped the MMR.
What I've speculated in the past is that an MMR cap at the top is required to balance off the fact that there's now an MMR floor at 0, because there were bugs in early seasons relating to Bronze players winding up with negative MMRs and never being able to go positive again. Capping the MMR at both ends may be necessary to prevent a floor from causing constant MMR inflation. I don't know whether that's actually the case, though, it's just a guess.
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Hey skeldark just wanted to say thanks for all the work you've done and the info that you've provided. Great thread.
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On July 13 2012 06:28 Lysenko wrote:Show nested quote +On July 13 2012 05:51 skeldark wrote: If you mean an Maximum MMR we are not sure if it exist. When it exists this would be terrible because it would destroy the skillfunction on the high end. We just hope blizzard is clever enough not to build one in or build it only in the match finding algorithm. The designer in the UCI video clearly stated that a maximum MMR cap exists, and it appears to be an actual MMR cap, not just a tweak to match-finding. I'm guessing there must be a reason that they strictly capped the MMR. What I've speculated in the past is that an MMR cap at the top is required to balance off the fact that there's now an MMR floor at 0, because there were bugs in early seasons relating to Bronze players winding up with negative MMRs and never being able to go positive again. Capping the MMR at both ends may be necessary to prevent a floor from causing constant MMR inflation. I don't know whether that's actually the case, though, it's just a guess.
They fixed the 0 floor different with am very stupid patch. Your mmr can still go under 0 the only diffrence is , he dont show it to you. The problem is not only for tier 0 bronze, for all tiers under master! So noone have to feel bad because he see 0 points. The adjusted points dont follow the skill points anymore. This make also sure the f function always give you points. It was never a problem of the skill- system, its a problem of the system that hides the MMR . We have to throw half of our data away because of this and it delayed our work because no one know of this tiercap before and we calculated wrong results all the time.
The reason they would patch an high mmr cap is : Top level player dont find any opponent because next opponent online is out of range for the match finding system.
This however will screw the hole skillpoints at the top ! And the only reason someone would do such a patch is: -To lazy to write a patch for the match finding system -Not aware of how bad a cap would be for the system.
A clever solution would be: -change the match finding system that its more loose at the top or if you are lazy - program the cap only in the match finding system when you give him the skillpoints of the players but dont change the skill rating system at all
Because they only changed the frontend ( player points in bnet profile ) for the under 0 problem i think they are clever enough to dont cap in the backend for the high mmr problem
My theories is they caped in the beginning and when the realised their mistake they bring up the "loose match making " patch 1 month ago. But this patch was also needed because the drastic drop in sc2 players.
My data shows so far no clear cap at the top. But cant say for sure yet
On July 13 2012 06:48 geoIOPS wrote: Hey skeldark just wanted to say thanks for all the work you've done and the info that you've provided. Great thread. thank you.
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On July 13 2012 06:50 skeldark wrote: Your mmr can still go under 0 the only diffrence is , he dont show it to you. The problem is not only for tier 0 bronze, for all tiers under master! So noone have to feel bad because he see 0 points.
No, you don't understand. The 0 point I'm talking about was the 0 point for the underlying MMR value, not the displayed point value. This only affected low Bronze, and caused a bug where low Bronze players could not ever increase their MMR, because negative MMR values were misinterpreted as very large positive values when the system would update MMR scores after a game. This has been fixed by placing a hard floor at 0 MMR (which is not the same as 0 displayed points and does NOT affect anyone in any higher league.)
My data shows so far no clear cap at the top. But cant say for sure yet
Whatever your data says, the designer is on record stating that there is in fact an actual MMR cap. If you come to the conclusion that your data says otherwise, you're reading it wrongly.
Incidentally, the issues with GM league started when they instituted this cap, probably because the cap affected more than the top 200 players.
The reason that I speculate that inflation may be the reason for the MMR cap is that by placing a hard floor at 0, players who lose but do not go below that floor will nevertheless be adding more MMR points into the system every time they lose, which essentially causes upward pressure on all the other scores. Adding a complementary cap at the high end would cancel this out. This is true whether MMR is zero sum or whether there are other mechanisms in place to handle inflation.
Incidentally, the developers of this system are not lazy, and they do simulate extensively the effects of their changes before implementing them. However, they do have to balance a large number of competing design goals, which means any choice they make won't be perfect.
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US DATA ONLY
Terran Average MMR, STD 1559.214909, 546.131097
Protoss Average MMR, STD 1620.764863, 509.5809733
Zerg Average MMR, STD 1672.129547, 495.3121321
TWO SAMPLE T-TEST RESULTS
T-Stat, T vs Z T-Stat = -5.693 P = .0000001386
T-Stat, P vs Z T-Stat : -2.872 P = 0.00472
T-Stat, T vs P Tstat = -3.03 p = .00238
Histogram of T MMR for normality check:
![[image loading]](http://i.imgur.com/FNzvx.png)
Anderson-Darling Test for Normality (T only)
![[image loading]](http://i.imgur.com/7kVqA.png) With a p slightly greater than .05, we cannot reject normality of the data. However, the weakness of this statistic indicates that normality should be scrutinized in the interpretation.
Assumptions - MMR is an independent, fair indicator of skill. - MMR is approximately normal. - There is no sampling bias between races, however there is a sampling bias towards higher average skill. - Cause-effect cannot be established by this test.
With over 99% confidence, we can reject the null hypothesis that the averages are equal in all 3 matchups. This is not surprising given the quantity of data, in addition to a maximum 7% difference between T and Z in average MMR.
The data for T appears approximately normal, but the study does not conclusively show that MMR is normal.
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On July 13 2012 07:33 Lysenko wrote:Show nested quote +On July 13 2012 06:50 skeldark wrote: Your mmr can still go under 0 the only diffrence is , he dont show it to you. The problem is not only for tier 0 bronze, for all tiers under master! So noone have to feel bad because he see 0 points. No, you don't understand. The 0 point I'm talking about was the 0 point for the underlying MMR value, not the displayed point value. This only affected low Bronze, and caused a bug where low Bronze players could not ever increase their MMR, because negative MMR values were misinterpreted as very large positive values when the system would update MMR scores after a game. This has been fixed by placing a hard floor at 0 MMR (which is not the same as 0 displayed points and does NOT affect anyone in any higher league.) Whatever your data says, the designer is on record stating that there is in fact an actual MMR cap. If you come to the conclusion that your data says otherwise, you're reading it wrongly. Incidentally, the issues with GM league started when they instituted this cap, probably because the cap affected more than the top 200 players. The reason that I speculate that inflation may be the reason for the MMR cap is that by placing a hard floor at 0, players who lose but do not go below that floor will nevertheless be adding more MMR points into the system every time they lose, which essentially causes upward pressure on all the other scores. Adding a complementary cap at the high end would cancel this out. This is true whether MMR is zero sum or whether there are other mechanisms in place to handle inflation. Incidentally, the developers of this system are not lazy, and they do simulate extensively the effects of their changes before implementing them. However, they do have to balance a large number of competing design goals, which means any choice they make won't be perfect. I do understand very good and i know what im talking about.
The 0 line problem was not just a unsigned int problem. If this would be the case the fix would be 1 line of code.
About mmr cap that exist in all leagues: The problem is that the f function gives points depending on opponent adjusted points. If your mmr are down he gives a minimum point change. It always gives you points even if you don't deserve them. This way the system make sure you stay above 73 points all the time. If it does not do that, you would fall at 0 ( bad because people cry) and also he f function would give you so few points on a win that you loose them fast and stay at 0 ( people cry more) The mmr dont care for this because its above 0, but because blizzard subtracted the offset from it, Now the adjusted points follow the Dmmr. And this one can be very easy negative! The cap make sure the adjusted points can not follow the dmmr under 73. In bronze tier 0 there is nothing to subtract any-more but you still stay above 73
And this is not the only bug of the system. They have more and tried to fix them. On few they gave up because they realised that the fix would make other problems.
All this only to hide the mmr.
We can not confirm a 0 line or deny it because blizzard allows no one to go under 73 mark of his tier so 73 is the minimum mmr we can see in our data.
To the blizzard video. When we learned something than not to trust blizzard! In the beginning we calculated with numbers blizzard published at battlenet about the leagues. We take them as indicator until we realised they can not be true. Its just plain impossible. . If they are true you run into logic mistakes. We thought the mistake is on our site for very long time.
Now after we have the real offsets we can tell the published numbers are total wrong. I dont know if they wanted to fool us or if they did an mistake ( they publish them every season tho) or if someone posted them who did not know what he was talking about. B
And would you say in an interview:
"We invented this very complex system so we can hide the real skill form the user but this system had a lot of bugs so we had to cap in this system, so people dont drop even if their skill-value drop!" Or would you say: " We make a cap for mmr at 0" And thats not even wrong. They made a cap but for dmmr. But this guy will for sure not talk about dmmr and how they hide information from the user.
I can say for sure if there is an mmr cap at the top, no player i track reached it yet! Pro players have still different values on the ladder. ( and i have most of them in my db) look at the datafile even in this small one i use here you can see it.
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I know you dont trust my statistic skills. But if we talk about the ladder system i study it for month and i know a lot about it. All arguments you bring up i discussed with others already for very long time.
You however saw the video we found long time ago. One of our many sources for mmr and by far not the best one.
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On July 13 2012 06:10 lolcanoe wrote:Show nested quote +On July 13 2012 05:53 VediVeci wrote: Im all for the rigorous application of statistics, but I think you may be a bit too high up in your ivory tower here. This is clearly not publishable work, on that everyone seems to agree. It is however, clever manipulation of the data which returned some interesting results. There comes a point where you need to accept this for what it is because you aren't getting anywhere with what you're doing. If by clever manipulation you mean random incoherent manipulation than fine. But there is no ivory tower here - all these basic tests are taught in every college-level stats course. The t-test, SD, and mean, and normality caveats aren't complex entities that require much explanation. As far running the test, I've only been avoiding it because the data itself has gone through so many changes and critiques over the past days. No point in running the test on data that is still being accumulated or filtered. Skeledark, assure me that the datafile in the OP is up to date with the most recent corrections and I'll do the test as soon as I get back from work.
Requiring someone to have a college education is a bit of an ivory tower buddy. And his manipulations were clever, even if they were wrong.
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On July 13 2012 08:13 VediVeci wrote: Requiring someone to have a college education is a bit of an ivory tower buddy. I'm not requiring anyone to have anything. My criticisms are objectively based on the analysis and not the source.
There is no ivory tower here. I've proven that my methods can be applied in a statistically coherent and easily understandable way, so your accusations that my suggestions are impractical (or "ivory tower") are pretty moot.
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On July 13 2012 08:13 VediVeci wrote:Show nested quote +On July 13 2012 06:10 lolcanoe wrote:On July 13 2012 05:53 VediVeci wrote: Im all for the rigorous application of statistics, but I think you may be a bit too high up in your ivory tower here. This is clearly not publishable work, on that everyone seems to agree. It is however, clever manipulation of the data which returned some interesting results. There comes a point where you need to accept this for what it is because you aren't getting anywhere with what you're doing. If by clever manipulation you mean random incoherent manipulation than fine. But there is no ivory tower here - all these basic tests are taught in every college-level stats course. The t-test, SD, and mean, and normality caveats aren't complex entities that require much explanation. As far running the test, I've only been avoiding it because the data itself has gone through so many changes and critiques over the past days. No point in running the test on data that is still being accumulated or filtered. Skeledark, assure me that the datafile in the OP is up to date with the most recent corrections and I'll do the test as soon as I get back from work. Requiring someone to have a college education is a bit of an ivory tower buddy. And his manipulations were clever, even if they were wrong. dont worry im very confident im better educated than him. and i did not manipulate any data also you can argue you want more but not that it is wrong. It did not follow the standard way and many people did not understood what i did but not understanding is not a valid prove for wrong.
With over 99% confidence, we can reject the null hypothesis that the averages are equal in all 3 matchups. This is not surprising given the quantity of data, in addition to a maximum 7% difference between T and Z in average MMR.
time for an excuse isnt it?
On July 13 2012 08:21 lolcanoe wrote:Show nested quote +On July 13 2012 08:13 VediVeci wrote: Requiring someone to have a college education is a bit of an ivory tower buddy. I'm not requiring anyone to have anything. My criticisms are objectively based on the analysis and not the source. There is no ivory tower here. I've proven that my methods can be applied in a statistically coherent and easily understandable way, so your accusations that my suggestions are impractical (or "ivory tower") are pretty moot.
You did not only attack the analyse. You attacked every word i wrote and that in a very bm way from the beginning. You came in this thread and nostop rant what you dont like and what you want me to do and act like i have to do stuff that you want to have.
After said all this:
Thank you very much for your analyse. I will link it in the op!
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On July 13 2012 08:14 monkybone wrote:Show nested quote +On July 13 2012 07:41 lolcanoe wrote:US DATA ONLYTerran Average MMR, STD 1559.214909, 546.131097 Protoss Average MMR, STD 1620.764863, 509.5809733 Zerg Average MMR, STD 1672.129547, 495.3121321 TWO SAMPLE T-TEST RESULTST-Stat, T vs Z T-Stat = -5.693 P = .0000001386 T-Stat, P vs Z T-Stat : -2.872 P = 0.00472 T-Stat, T vs PTstat = -3.03 p = .00238 Histogram of T MMR for normality check: ![[image loading]](http://i.imgur.com/FNzvx.png) Anderson-Darling Test for Normality (T only) ![[image loading]](http://i.imgur.com/7kVqA.png) With a p slightly greater than .05, we cannot reject normality of the data. However, the weakness of this statistic indicates that normality should be scrutinized in the interpretation. Assumptions- MMR is an independent, fair indicator of skill. - MMR is approximately normal. - There is no sampling bias between races, however there is a sampling bias towards higher average skill. - Cause-effect cannot be established by this test. With over 99% confidence, we can reject the null hypothesis that the averages are equal in all 3 matchups. This is not surprising given the quantity of data, in addition to a maximum 7% difference between T and Z in average MMR. The data for T appears approximately normal, but the study does not conclusively show that MMR is normal. Very nice. But why does it gives so different results? As far as I can see there is over a 100 MMR difference between Z and T here. Us only
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On July 13 2012 02:09 monkybone wrote:Show nested quote +On July 12 2012 20:26 lazyitachi wrote:Can't believe this thread is still going on. + Show Spoiler +Problem statement: OP wants to measure e-peen size and compare between different races.
Data gathering: OP constructs a e-peen measuring tool that user directly inserts on a voluntary basis. User base are high hormone individuals who are very interested to know how big their e-peen is. Therefore, these individuals are most likely already at a higher percentile of e-peen length compared to the general population.
Measurement: Users measure e-peen whenever they are playing by themselves. This play will be contested with another user. The winner will have longer e-peen and vice versa thus the true size of e-peen is estimated based on such repetition. Some e-peen have been observed to fluctuate in size up to 1000 inches in a few days. How can it be? Can the true size of e-peen be so volatile? Should it not be stable? Seems like some measurement are taken while in the state of flaccidity.
If indeed the measurement needs multiple observation to settle on a true e-peen then does that mean any single observations is then unreliable and not credible? But we like e-peen so the more is better. Let's not care about that.
Methodology: The statistics earlier is based on the average over a long period of time before the individual has truly established his true e-peen thus if there are any upwards biased (likely because they are all looking to gain the next level of e-peen recognition), the value will be severely underestimated. Not to mention those single observations from more outdated time. Later it is changed to be the latest e-peen measures. Pssh.. we should ignore testing anyway let alone use the correct test tool.
Summary: Human have the shortest e-peens. Humanoid aliens bits and bug tentacles have imbalanced in size.
Wow, what an ignorant post...
Please tell me what is ignorant about it. It quite accurately describe what he did and wants to prove.. "Ladder Balance" His MMR reliability is not validated anyway. Just his own conjecture at this point. Its not like he is measuring and comparing against any actual number and neither can he proof one observation can yield the correct number. If it can then there is no way someone's "MMR" can change by significant degree which means his method is flawed or he did not account properly for unusable data. Given so much of the data is single obs, quite frankly his whole calculation is unreliable anyway.
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On July 13 2012 08:24 skeldark wrote: dont worry im very confident im better educated than him. and i did not manipulate any data also you can argue you want more but not that it is wrong. It did not follow the standard way and many people did not understood what i did but not understanding is not a valid prove for wrong.
The standard "way" is standard for a reason - you set baseline standards for comparisons so that you can make meaningful conclusions. Conclusions that both the community and fellow statisticians can agree with. If you want to move away from a standard you better have a spectacular reason to do so, and I just haven't seen strong evidence that conventional methods are going to work here.
Likewise, my education is really not too important - but since you brought it up, I work at one of US's top credit rating firms, have a finance/math background, and performed excellently in statistics coursework. Inconsistently presented statistics would ultimately have large implications to anyone in my career field (The SEC would probably come after us). For investment banks small miscalculations in risk statistics, like the under-estimate of tail risk in the housing crisis, could result in billions of losses. So unless you have a PHD in math or specializing in stats throughout college, I doubt you'll have a better grasp of the concepts here. Well actually, I doubt it simply because of the way you attempted the analyses.
On July 13 2012 08:24 skeldark wrote: time for an excuse isnt it?
Sorry? I'm not sure I understand you, which appears to a recurring theme here. Are you making fun of the fact that I qualified my conclusions with significant data or are you congratulating yourself for guessing correctly the first time around?
On July 13 2012 08:24 skeldark wrote: You did not only attack the analyse. You attacked every word i wrote and that in a very bm way from the beginning. You came in this thread and nostop rant what you dont like and what you want me to do and act like i have to do stuff that you want to have.
Misuse of statistics is a huge problem and creates unnecessary skepticism to legitimate conclusions. Just look around at how many people in this thread immediately turned their heads and said "it's just stats, i'd rather make arbitrary judgments on how pros are doing". You have to draw the right conclusions from right data. My "attacks" were pretty concise, my concerns were legitimate and fixable, and I put my mouth where the money was by proving it. Now you can say what you wanted to say with a much higher degree of precision and certainty.
As far as the tone of my remarks? I share the blame for letting things get personal. But as friendly advice I've learned (the hard way) in my workplace, there as an inverse correlation between the receptiveness of the presenter and the harshness of the critiques received.
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On July 13 2012 05:51 skeldark wrote:Show nested quote +On July 13 2012 05:47 hunts wrote:On July 13 2012 05:03 skeldark wrote:On July 13 2012 05:00 hunts wrote: Sorry if you answered this before somewhere, but do you have a rough estimate of the MMR ranges of each league? I'd really like to see that as it would be very interesting. depends on the server us / eu #START PROMOTE_OFFSETS bronce - master 0,754,1050,1280,1536,1993, On July 13 2012 05:00 BBS wrote: I failed to read about how you canceld out effects like disconnects or other cases in which the game is not representative :o I dont think that disconnects are race depending. Why should one race have more disconnects than another? TY, is there any information on how high masters MMR goes or about where GM starts? Or is that not available due to the nature of GM. I believe there's still a cap on masters MMR though, wonder if that number is available somewhere. ^^ i edited it out of the copy paste. Because this value change all the time and is not very accurate. +800 on master is a good hand rule for gm But gm is... fucked up. Its not top 200 at all. Its just a bad system. there is no cap for master mmr only lower leagues have a cap that they can not fall under 0 of their tier. If you mean an Maximum MMR we are not sure if it exist. When it exists this would be terrible because it would destroy the skillfunction on the high end. We just hope blizzard is clever enough not to build one in or build it only in the match finding algorithm.
If I'm not mistaken there is an upper MMR cap though. They introduced one after the incident with huk playing on TLOs account because it took him too long to find games with his MMR, but I'm not sure if they ever took it out.
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On July 13 2012 10:03 lolcanoe wrote: Misuse of statistics is a huge problem and creates unnecessary skepticism to legitimate conclusions. Just look around at how many people in this thread immediately turned their heads and said "it's just stats, i'd rather make arbitrary judgments on how pros are doing". You have to draw the right conclusions from right data. My "attacks" were pretty concise, my concerns were legitimate and fixable, and I put my mouth where the money was by proving it. Now you can say what you wanted to say with a much higher degree of precision and certainty.
This deserves to be repeated.
I'm a little taken aback at the OP accusing the statistician at Blizzard who developed the bulk of the system they use now of actively misrepresenting how their system works. If secrecy about their methods were so important to them, he simply wouldn't be out in public talking about their system.
I'm not saying that there's no value in what these guys have done, but the fact that there's a multilayer system of MMR -> MMR-derived adjusted point equivalent value -> adjusted points -> displayed points offers a lot of opportunity for mistaken interpretations about the deeper levels to creep in when analyzing what one can see on the surface.
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On July 13 2012 10:11 hunts wrote: If I'm not mistaken there is an upper MMR cap though. They introduced one after the incident with huk playing on TLOs account because it took him too long to find games with his MMR, but I'm not sure if they ever took it out.
There is absolutely, positively a hard cap on Blizzard's matchmaking rating number. That's been stated explicitly by the developers. That doesn't mean there's necessarily a cap on the "MMR" value that the OP has derived from what's visible in the system, but he seems to not agree with the idea that those two numbers may not be equivalent.
As I indicated before, I'll have to wait until this weekend to put the time in to decide what I really think about this. Until then, though, I'll believe the developers over the OP on matters where they differ.
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First off I'd like to point out that the normality of the data doesn't really matter because of the Central Limit Theorem, so please stop discussing that like it matters.
Continuing with lolcanoe's analysis, I found the 99% confidence intervals for the difference in mean for each group.
Race Results + Show Spoiler +For US: ZvT (62.0, 164.6) PvT (8.9, 115.0) ZvP (3.3, 99.4)
For EU: ZvT (19.6, 108.6) PvT (18.3, 113.2) ZvP (-45.3, 42.0)
US and EU: ZvT (51.5, 118.8) PvT (28.9, 99.6) ZvP (-11.1, 53.2)
As for US vs EU, the 99% confidence interval for the mean difference in MMR is: (21.9, 77.1)
For each interval a positive difference indicates the mean of the first population is higher than the second, so for US vs EU it reads, 99% of such samplings will yield a result such that the mean MMR of the US player base is between 21.9 and 77.1 MMR higher than that of the EU player base.
The meaning of a 99% confidence interval for the mean is as follows: If we were to randomly pick samples of the same size* from each population and found the difference of the means between the groups, 99% of such samplings would result in a difference of means within the given interval.
*By same size I mean the same sizes as were sampled to construct the interval, so if the interval were constructed by sampling 10 Zergs and 15 Protosses, it would be random samples of 10 and 15, respectively.
I've provided the MATLAB code I used for the analysis if anyone can run it and wants to do analysis on future data:
Helper Function + Show Spoiler +function [lower,upper] = findInterval(pop1,pop2,confidence) mu1 = mean(pop1); mu2 = mean(pop2); s1 = std(pop1,1); s2 = std(pop2,1); n1 = length(pop1); n2 = length(pop2); diff = mu1-mu2; df = (s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1-1)+(s2^2/n2)^2/(n2-1)); tcrit = tinv(1-(1-confidence)/2,df); s = sqrt(s1^2/n1 + s2^2/n2); halfrange = tcrit*sqrt(s1^2/n1 + s2^2/n2); lower = diff-halfrange; upper = diff+halfrange; end
Main script + Show Spoiler +%script for calculating balance
%get data from file (would be ez if OP hadn't put quotes in the .csv, BAD!) fid = fopen('balance.csv'); str = char(fread(fid))'; fclose(fid);
omitFirstLine = '(?<=\n).*'; stripped = str( regexp(str,omitFirstLine):end ); %strip first line rawdata = textscan(stripped, '%s %s %d', 'delimiter',' \t\n,"',... 'MultipleDelimsAsOne', 1);
%define some constants (not saying protoss #1) protoss=1; zerg=2; terran=3; US = 1; EU = 2;
%combine into one big array col = length(rawdata{3}); data = zeros(col, 3); data(:,3) = rawdata{3}; for i=1:col if ( rawdata{1}{i}(1) == 'U') data(i,1) = US; else data(i,1) = EU; end if ( rawdata{2}{i} == 'z') data(i,2) = zerg; elseif ( rawdata{2}{i} == 'p') data(i,2) = protoss; else data(i,2) = terran; end end
%define filters tF = data(:,2) == terran; pF = data(:,2) == protoss; zF = data(:,2) == zerg; uF = data(:,1) == US; eF = data(:,1) == EU;
%construct the 99% confidence intervals based on a two-sided t-test %zerg vs protoss confidence = 0.99; place = eF | uF; %lets you quickly change if US,EU, or both (uF | eF) [zpLower,zpUpper] = findInterval( data(zF & place,3), data(pF & place,3),confidence); [ztLower,ztUpper] = findInterval( data(zF & place,3), data(tF & place,3),confidence ); [tpLower,tpUpper] = findInterval( data(tF & place,3), data(pF & place,3),confidence ); [UsEuLower,UsEuUpper] = findInterval( data(uF,3), data(eF,3), confidence);
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Skeldark, don't get down on those who are using weak and illogical arguments to disprove your work. Your work is top notch and objective and I don't see any flaws.
The nerfs have taken their toll on Terran, making Terran the weakest race and non-competitive. Terrans are struggling in all the top tournaments lately because they are not competitive anymore.
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