分到坑队友的概率 Wargaming数据向解析天梯分房

　　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!

　　今天咱还是来谈谈天梯分房一事，不过这次的主讲是Edward，是首个效率评级的创始人，所以他很了解这玩意。SS问了下他对此事的观点，下面就是他所说的。

　　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.

　　我的观点是，按水平分房是完全没必要的。重要的一点就是高玩的数量相比起坑货而言不知道少到哪里去了(比例基本上是1：10)，而对于那些顶尖高玩，这一比值更是变为1：100.从坑到一般水平的范围，玩家的分布是线性的，因此每当你进入战斗的时候，根据概率论，己方队伍的水平和对方的应是差不多的。当然，队友全是2B而对手全是NB的情况也是可能发生的，但如果你把战斗场次这一样本数量拓展到无穷大，出现上述情况的概率就和队友全NB而对手全2B的情况一样大。总体上说，分布总是相同的，鉴于好玩家的数量还是可观的，在己方队伍里出现一两个高玩的可能性还是蛮大的。不过咱还是来看个例子：

　　et’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:

　　比方说我们有1000名玩家，在他们中有100名确实很坑，800名低于平均水平，90名玩的不错，10名是大神。让我们看看在整个团队中只由一组构成的概率。

　　- for the bad up to above average: 3.4 percent

　　由低于平均水平的玩家组成：3.4%

　　- for the really bad players: 3.68e-14 percent

　　由神坑组成的概率：3.6*10^-14%

　　- for the good players: 6.05е-15 percent

　　由玩得不错的玩家组成的概率：6.05*10^-15%

　　- for unicums: 6.52е-32 percent

　　由大神组成的概率：6.52*10^-32%

　　Based on mathematical expectation, the most probable group you will get is:

　　基于数学期望最有可能的构成是：

　　1,5 very bad + 12 bad up to above average + 1.35 above average + 0.15 unicum

　　1.5个神坑+12个低于平均水平+1.35个高于平均水平+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:

　　事实证明大神们一般会在1~7场战斗后退出游戏。因此在绝大多数时间里你会被分到一个绝对标准的团队里。不过他们可以通过由三个高于平均水平的玩家组队来打破。(也有可能是三个大神)这就是WG不允许三人以上组队的原因。让我们看一看三个大神被随机分到一组的概率：

　　c(10,3)/c(1000,3) = 0.000072216505082237 %

　　For good players, it is

　　三个玩得不错的玩家概率为

　　c(90,3)/c(1000,3) = 0.07069995847551 %

　　For really bad players, it is

　　三个神坑的概率为

　　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%

　　但是并不是所有三人组队的都是大神，事实证明如果你进行无穷大场游戏，那么你遇到好分房和坏分房的概率是一样的。因此得到的一个很重要的结论是：如果你不停的和一个非常不错的玩家组队这种事情发生的概率是正常情况下的 0.097311740598314%

　　Mathematically expected team for an above average player:

　　团队中有一名高于平均水平玩家的数学期望：

　　1.4014014 神坑+ 11.2112112 低于平均水平玩家+ 2.247247246 不错的玩家 + 0.14014014 大神

　　Mathematically expected team for a bad player:

　　团队中有一名神坑的数学期望：

　　2.387387386 神坑 + 11.2112112 低于平均水平玩家+ 1.26126 不错的玩家+ 0.14014014 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.

　　不幸的是，Edrard对于提交的问题没有时间解释或回答。但我认为其中隐含的信息是明确的。