Conclusion:
The 3 races playrate per ladder in graph looks like a nervous system from shoulder to an arm. top kek
Zerg probably is played less because it is by far the most unorthodox infrastructure system which may scare new players.
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Tl;DR: batz still making stuff up to QQ about zerg, lifes not fair, terran imba, protoss imba, everyone but batz is stupid, etc.
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Definition of mean say you are wrong
(_Mean - Wikipedia).
Mean is the central value of discrete set of values. So you canât put mean at 8k because 8k is not central value.
WinrateOfPlayerA = 1 / (1 + 10 ^ ((RatingOfPlayerB - RatingOfPlayerA) / 400)
-700 - -800 give 100
So itâs 10^100/400
700 - 800 give -100
So itâs 10^-100/400
So we have (1/10)^100/400
Translation you are wrong
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For a fixed domain that is true, not for an infinite nor relative domain. Elo is ranked relative to the mean, so you can technically pick any mean you want and the system builds a pool of rankings around that number value. Itâs entirely arbitrary and has no real world meaning.
Nope. Elo maps a difference in ranking to a win-rate. It doesnât matter if the playerâs elo value is negative, positive, large or small - the win-rate is the same for a given difference in ranking. Your calculations are wrong because in one you calculate the win-rate for player A and in the other you calculate the reverse which is for player B.
Quite the contrary, Mr. Troll, the facts about the ladder in this thread are just that - facts. They are not made up, or are you accusing rankedftw of falsifying ladder data?
The point of this thread is to estimate what parameters can cause the SC2 ladder to produce these observed facts. The SC2 ladder is basically an algorithm, and weâre finding what variables solve for this solution. They are as real as of a solution to the SC2 ladder algorithm as 2 is to the equation 2*x=4.
Rejection of mathematics is not a valid argument.
I too could make a graph and create parameters to make it look however I wanted. I could then alter those parameters to look a different way if I so chose.
Absolutely brilliant!
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First, the goal isnât to make it look âhowever I wantâ. Itâs to match the SC2 ladder output. Second, I highly doubt you have the math / CS background required to do so. Itâs a very rare skill set. Third, there are a fixed number of potential outputs due to the constraints of the program, so it is, by definition, impossible to make it output anything you want - what you want must be within the constraints of what is a possible output of the program.
It appears your math/cs background wasnât sufficient to consider several problems with your assumptions. Here are a few:
1-assuming 0.1% of players quit every 10k games.
2-assuming 1% of the active player base switches races every 10k games
3-ignoring added players to the player base.
4-ignoring MMR decay for players that periodically play, but donât consistently do so.
All youâve done here is created an artificial scenario that mimicked SC2 ladder. You havenât demonstrated balance issues or anything else. There are 1,000 ways you could mathematically create a graph mimicking SC2 ladder.
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Itâs not an assumption. Itâs a testable hypothesis. If they are true then the conclusion will match the observations. Have you never heard of the scientific method?
Itâs called occamâs razor. You want the simplest solution that is capable of solving the problem. Zergâs high and low league representation can be explained using only a few parameters in a simple ladder simulation.
âWhatâs that, newton? You made some math about that thing called gravity. All youâve done is create an artificial scenario that mimics gravity! Itâs not real gravity!â
The point of math is to mimic real world behaviors kiddo. Thatâs literally what math is.
Itâs a testable hypothesis. If they are true then the conclusion will match the observations. Have you never heard of the scientific method?
The scientific method doesnât assume the hypothesis is true merely because the results match the hypothesis. It always considers other possibilities. And also considers possible errors in variables. Youâve assumed at least 5 variables here that might not be accurate.
Itâs called occamâs razor. You want the simplest solution that is capable of solving the problem.
You think this is the simplest solution? Wouldnât a far simpler solution be that players tend to not like playing zerg, therefore theyâre less represented? Why do you assume your hypothesis provides the simplest solution?
Newtons math didnât assume half a dozen variables to âproveâ gravity. He found and proved the variables in order to prove gravity. In your ridiculous example (comparing your math to Newton? Really?) you assume gravity to be whatever you need it to be to fit your hypothesis. Rather than experimenting to determine what gravity actually is.
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Yes that is what the testing is for. Hence the âtestableâ in âtestable hypothesisâ.
You mean like ghosts? I guess itâs possible gravity is due to ghosts! I guess itâs just a fluke that all of Newtons math was able to make so many accurate predictions!
That doesnât come even remotely close replicating the ladder results, sorry.
Youâre ignoring half of Occamâs razor. Itâs the simplest theory capable of explaining the observation.
Let me get this right, Newton showing that his variables are able to accurately mimic the behavior of gravity is âproofâ, but showing that these variables accurately mimic ladder behavior isnât? 
I see youâre not really interested in considering the potential flaws in your analysis. Sounds good. Bye.
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I welcome that with open arms. Thatâs not what you are doing, though. Youâre holding my analysis to a standard that is borderline math-denial. Thereâs plenty of things to criticize about it, but going full-gestapo and saying math is fake is pretty severe and invalid.
NoâŚIâm pointing out that your results matching reality doesnât mean that your results are the cause of reality.
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Thatâs a philosophical argument, sweetie, which means weâre back in the realm of math denial. All math merely mimics reality. If it mimics it well, itâs a statistical predictor. If it mimics it really well, itâs generally considered to be causal. With complex and volatile systems, like this, literally the best that is possible is a statistical predictor.
If being able to match your results to reality doesnât equate to proof, then youâve rejected math and science.
I assume you mean causal. Not casual. And noâŚmimicking something âreally wellâ doesnât mean the results are causal.
I can predict the weekly rate of drownings extremely well based on viewing the rate of ice cream purchases. Those rates mimic each other âextremely well.â I honestly canât believe I have to explain âcorrelation does not equal causationâ to someone claiming to have such superior math skills.
Your math mimicking reality does not prove your math is reality. Thereâs not another way to say that. It is one possibility. It is not proof.
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An honest person couldnât read my posts and come to that conclusion, which means youâre a troll. If that is wrong, then you have mistakenly come to a horribly wrong conclusion, and I encourage you to re-read my posts.
I highly doubt that but I get the idea you are trying to get across. The difference is in the volatility and unkowability of the domain of problems precludes assumption that a strong correlation equates to proof. The SC2 ladder is quite complex, but nowhere near the ârealâ world. Itâs actually very easy to define the mechanics of how it works.
Youâre claiming that because your mathematical equation âmimics reality really wellâ that is proof that it the cause of our reality.
In other words, because your math correlates strongly with reality, you believe it causes reality.
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No thatâs literally the opposite of what Iâve said.
âIf it mimics it really well, its generally considered to be causal.â
LikeâŚthat line is literally âif it correlates with reality well, its generally considered to be causal.â