Hello everyone,

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!

-SS

Author: Edrard (RU server)

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.

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:

- for the bad up to above average: 3.4 percent

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

- for the good players: 6.05е-15 percent

- for unicums: 6.52е-32 percent

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

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

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:

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

For good players, it is

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

For really bad players, it is

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%

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 :)

Mathematically expected team for an above average player:

1.4014014 bad + 11.2112112 bad up to above average + 2.247247246 good + 0.14014014 unicum

Mathematically expected team for a bad player:

2.387387386 bad + 11.2112112 bad up to above average + 1.26126 good + 0.14014014 unicum

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.