Source:http://ftr.wot-news.com/2014/10/02/edrard-why-is-skill-mm-a-bad-idea/
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Hello everyone,
大家嚎， 

today, we’re going to talk about skill MM. Again. I must admit, this topic is not exactly a favourite of mine. But I know someone, who knows a lot about statistics. That’s right, Edrard, the creator of the first efficiency rating – so he really understands this stuff. I asked him on his opinion and here’s what he had to say on the matter (translated from Russian of course). Enjoy!
今天我们要再来讨论一下水平分房了。我必须要承认，我个人并不喜欢这个话题。但是我知道有个知道很多数据的人。没错，就是第一版eff效率值的制作者，Edrard.所以他对这个真的很了解。我问了他的看法，以下是他对此问题的会有（从毛文翻译过来的）。以上。

-SS

Author: Edrard (RU server)
原作者：Edrard（毛服的） 

My personal opinion is, that the skill MM is definitely not needed. For one: there are far fewer good players than bad players, in a ratio of somewhere around 1 to 10 and really good players roughly 1 to 100. When it comes to the range from bad up to above average players, the distribution of such players is linear, therefore every time you enter a battle, according to the probability theory, you’ll have basically roughly the same teams. Of course, there is a chance that you will have a team full of bad players and the opponent will have a team full of above average players, but if you take an infinite number of battles, then the amount of such battles will be equal to the kind where you have the above average team and the opponent has noobs. In general, the distribution is always the same. Since the amount of good players is still large enough, the probability of having at least one on your team to be quite high, but let’s have a look at an example.
我个人的观点是，水平分房这东西根本没有必要。首先：高手的数量要比菜鸟的数量少太多了，比例大概是1:10的样子。而真大神的比例大概在1:100。而从菜鸟到一般人的玩家数量分布上是呈一个线性分布的，所以你每次进入战斗的时候，根据概率学理论，你每次遇到的队伍都是差不多的。当然了，同样你还有可能会遇到自己队全都是菜鸟，而对面队伍全都是高手玩家的情况。但是如果用无限量的场次来考虑的话，这种战斗的数量就和你们队全是高玩，而对面队伍全是菜鸟的战斗数量差不多。总的来说，分布都是一样的。鉴于高手的玩家数量还是够大， 让你的队伍中存在一名高手的几率还是蛮大的，但是先来看个栗子。

Let’s say we have 1000 players. Of them, 100 are really bad, 800 are bad up to above average, 90 are good and 10 are unicums. Let’s have a look at the probability of having the entire team consisting of only one of those groups:
比如说，我们有1000人。其中100人是烂到不行的那种，800人处于菜鸟~一般人的区间内，90个高玩，10个真大神。我们来看一下整个队伍中只包含一种玩家的情况的几率： 

– for the bad up to above average: 3.4 percent
全都是菜鸟~一般人: 3.4%

– for the really bad players: 3.68e-14 percent
全都是烂到不行的玩家：3.68e -14 % 

– for the good players: 6.05е-15 percent
全都是高玩：6.50 e-15 %

– for unicums: 6.52е-32 percent
全都是大神：6.52e-32% 

Based on mathematical expectation, the most probable group you will get is:
从数学方面的考虑来看，你最有可能遇到的队伍是这样的： 

1,5 very bad + 12 bad up to above average + 1.35 above average + 0.15 unicum
1.5个菜逼，12个菜鸟~一般人+1.35个高玩+0.15个大神

It turns out that the unicum ends up in something like 1 of 7 battles and so, most of the time, you will play in an absolutely standard team. This is where the platoons come in – they can break the pattern by bringing 3 players of above average skill (or, heaven forbid, unicums) into the battle – that’s why Wargaming decided not to implement any platoons of more than 3 players. Let’s see what is the chance of 3 unicums ending up in one battle randomly:
这样看的话，每7场就能够碰上一个大神的样子，除此之外的时间你都会在一个绝对标准的队伍中进行游戏。这就是为什么出现了组队—可以打破这个规律，把3个超过一般人的玩家（或者天理不容的三大神）带入一场战斗—这就是为什么WG决定不要实装超过3人玩家组队的机制。我们来看看如果三个大神在随机战斗中能碰到一起的概率是多少：

c(10,3)/c(1000,3) = 0.000072216505082237 %
对于高玩来说，概率是
c(90,3)/c(1000,3) = 0.07069995847551 %
对于菜逼来说，概率是
c(100,3)/c(1000,3) = 0.097311740598314%

But since the platoons don’t always have to consist of 3 unicums, it turns out that if you consider an infinite number of games, you will meet the same amount of good platoons and bad platoons. The most important conclusion however is that when you are platooning with very good players, you constantly, in 100 percent of cases, drop into battles the probability of which to happen is under normal circumstances 0.097311740598314%
但是鉴于组队的玩家并不总是三个大神，所以从无限的游戏局数上来考虑的话，你碰到高玩组队和菜逼组队的数量是一样的。但是最重要的结论是，当你和大神组队在一起的时候，你会一直，100%的几率进入到在常规情况下只有0.097311740598314%几率才会出现的战斗中。

Also, if you yourself are a good player, you are knowingly putting yourself in a better position, as your team will always have at least one good player. The same thing goes for bad players. And since some players have higher winrate than others – it’s all on them 🙂
还有，如果你自己就是高玩的话，你其实就是故意把自己放在了一个有利的位置，因为你们队伍中肯定会有一名高玩保底。菜逼也是同样。鉴于部分玩家比其他人的胜率要高—全靠他们了:) 

Mathematically expected team for an above average player:
对于一名高玩的队伍构成的数学期望值：

1.4014014 bad + 11.2112112 bad up to above average + 2.247247246 good + 0.14014014 unicum
1.4014014个菜逼+11.2112112个菜鸟~一般人+2.247247246个高玩+0.14014014个大神

Mathematically expected team for a bad player:
对于一名菜逼的队伍构成的数学期望值： 

2.387387386 bad + 11.2112112 bad up to above average + 1.26126 good + 0.14014014 unicum
2.387387386个菜逼+11.2112112个菜鸟~一般人+1.26126个高玩+0.14014014个大神 

Edrard submitted this with a note that unfortunately, he doesn’t have time to explain or answer any questions, but I think the underlying message is clear.
Edrard回复的时候特意说明由于各种原因，他没办法解释/回答任何问题，但是我觉得他要表达的意思已经很明显了。