WG would you be so kind to answer a simple question: Is winrate among the player populace normal distributed or not

[Pappus]

You have all the data so it would be great to know. Maybe just plot a little chart for us so we can look at the shape.

 

I am assuming it is, but it isn't necessarily so

[DFens_666]

http://maplesyrup.sweet.coocan.jp/wows/ranking/tableofaccounts.html

 

edit:

nvm just scroll down

[principat121]

1 hour ago, Pappus said:

You have all the data so it would be great to know. Maybe just plot a little chart for us so we can look at the shape.

 

I am assuming it is, but it isn't necessarily so

The more tricky question is this: Would you believe Wargaming if they state that the distribution is normal, or would you not? 

[Leo_Apollo11]

Hi all,

 

1 hour ago, DFens_666 said:

http://maplesyrup.sweet.coocan.jp/wows/ranking/tableofaccounts.html

 

Scary stuff... isn't it...

 

 

Leo "Apollo11"

[eliastion]

9 minutes ago, Leo_Apollo11 said:

Hi all,

 

 

Scary stuff... isn't it...

 

 

Leo "Apollo11"

I wonder now, what is scary there?

[floribe2000]

This is the WR distribution of all players with more than 250 random battles and public stats (ignore the red bars, the blue ones are the important ones and the red ones are also not 100% correct, there was a calculation error)

 

[Leo_Apollo11]

Hi all,

 

33 minutes ago, eliastion said:

I wonder now, what is scary there?

 

That 98+% of players you encounter are worse than you...

 

 

Leo "Apollo11"

 

[Bear__Necessities]

2 hours ago, DFens_666 said:

http://maplesyrup.sweet.coocan.jp/wows/ranking/tableofaccounts.html

 

edit:

nvm just scroll down

I forgot how depressing it is looking at those numbers.....

[waxx25]

Pretty much what i expected. Honestly didnt realise I was so far on the right side of that bell curve.....although my stats will be private until I hit rank 1. Got to rank 2** and havent mentally prepared myself for the las 3* lol.

[Pappus]

48 minutes ago, floribe2000 said:

This is the WR distribution of all players with more than 250 random battles and public stats (ignore the red bars, the blue ones are the important ones and the red ones are also not 100% correct, there was a calculation error)

 

Will this hold if you remove the filters like GK & tier 10? Cause that is a normal distribution and it also doesnt settle around 50%, but slightly lower which is what I assumed

[lossi_2018]

Can someone explain for us plebs what it is we are looking here? It reminds something I've seen on a trip I think

[TeaAndTorps]

3 hours ago, DFens_666 said:

http://maplesyrup.sweet.coocan.jp/wows/ranking/tableofaccounts.html

 

edit:

nvm just scroll down

I'm don't know loads about statistics. People who do, is it surprising that the top of that curve is at about 48%? Intuitively it feels as though it should be closer to 50%, but I suspect there's some kind of explanation that's reasonably obvious to people who have studied any maths past the age of 16.

 

Also, I feel terrified to discover I'm... not that bad in the universal scheme of things? 

[floribe2000]

Vor 1 Stunde, Pappus sagte:

Will this hold if you remove the filters like GK & tier 10? Cause that is a normal distribution and it also doesnt settle around 50%, but slightly lower which is what I assumed

The overall stats are overall stats, as indicated by the name. It doesn't matter what tier you chose to compare against them. And as I said, the Kurfürst bars are wrong, the title is also misleading, there are no overall T10 stats in that image. Sorry for the confusion, something like that happens during datamining :D

Keep in mind, it's nothing official

[SV_Kompresor]

21 minutes ago, lossi_2018 said:

Can someone explain for us plebs what it is we are looking here? It reminds something I've seen on a trip I think

Which part?

[ColonelPete]

16 minutes ago, TeaAndTorps said:

I'm don't know loads about statistics. People who do, is it surprising that the top of that curve is at about 48%? Intuitively it feels as though it should be closer to 50%, but I suspect there's some kind of explanation that's reasonably obvious to people who have studied any maths past the age of 16.

 

Also, I feel terrified to discover I'm... not that bad in the universal scheme of things? 

• Division players reach higher winrating and non-division player reach lower WR than expected
• skill improves with number players (on average), which means that the few experienced players get better results than the mass of less experienced players

[Thorsvald]

In math (statistics) a Normal like distribution of probability is a function that depicts the probability of a random value to be in a certain range and is symmetrical with data centered beside the mean.

 

For example: You  are about to kidnap take 50 random people of your country and to write his shoe size in a chart with the amount of human beings that have each of the expected  shoe size.

If you calc the mean you will realize that most people is around it. For example if the mean is an EU 42, most people will be at 43,44, 40,41 and will decrees as you ae nearer to the limits.

If you put that data on a graph with the value that you are measuring in the horizontal axis an the number of people in each value on vertical axis you will get something like this:

 

Because of his shape resembling a bell it's called Gauss bell.

 

The curious fact about it is that is the distribution followed by natural events. If you see a Normal distribution that it's pretty far from the natural mean it's something wrong about it. Also if you look at the shape of the bell you can determine several things if for example it's shape is too flat or sharp (kurtosis).

 

In any case, WOWS WR following a normal dist. centered on 48% WR it's more than ok for me. Just as WOT this game is not an easy game to learn.

[DFens_666]

24 minutes ago, TeaAndTorps said:

I'm don't know loads about statistics. People who do, is it surprising that the top of that curve is at about 47%? Intuitively it feels as though it should be closer to 50%, but I suspect there's some kind of explanation that's reasonably obvious to people who have studied any maths past the age of 16.

 

The median is at 47~48%. Basicly the super high WR players force more players below 50%. The equivalent for 65% players would be 35% players - and those hardly exist. So there have to be more players between 40-49% to make up for that.

[rnat]

20 minutes ago, Thorsvald said:

a Normal like distribution of probability is a function that depicts the probability of a random value to be in a certain range and is almost symmetrical [...]

A Gaussian distribution is fully symmetric around the mean.

20 minutes ago, Thorsvald said:

The curious fact about it is that is the distribution followed by natural events. If you see a Normal distribution that it's pretty far from the natural mean it's something wrong about it. Also if you look at the shape of the bell you can determine several things if for example it's shape is too flat or sharp (kurtosis).

You can actually prove that for a number of numbers/events , each of which have distinct probability distribution the mean of those events approaches a Gaussian distribution (if it's variance converges sufficiently fast)

Also a normal distribution is what you'd expect for sufficiently large number of independent events UNLESS you have reason to expect a different distribution (Poisson ect. anyone ?)

[Thorsvald]

4 minutes ago, rnat said:

A Gaussian distribution is fully symmetric around the mean.

You can actually prove that for a number of numbers/events , each of which have distinct probability distribution the mean of those events approaches a gaussian distribution (if it's variance converges sufficiently fast)

Yes.

But although skewness on a G.D is 0 it depends on the size of data.

Sorry i was thinking on the example at same time i was thinking on defining it.

[eliastion]

29 minutes ago, TeaAndTorps said:

I'm don't know loads about statistics. People who do, is it surprising that the top of that curve is at about 48%? Intuitively it feels as though it should be closer to 50%, but I suspect there's some kind of explanation that's reasonably obvious to people who have studied any maths past the age of 16.

(...)

There is more than one factor that could explain that (or rather be part of the explanation). What comes to mind as, probably, the most important is: better players play more. Or players with more practice play better, the cause and effect direction isn't important in this case.

 

How it affects the average statistics can be explained on an artificial example: imagine 1v1 game with 10 players. The best player plays one match against each of the other players, results being:

Player #1: 9 matches, winrate 100%. Players #2-9: 1 match, 0% winrate.

The average winrate = 10%

 

Obviously, in WoWs it's much more nuanced, games aren't 1v1, there are a lot of bots (or players that play like bots) that spam battles and suck a lot - and we do have some re-rolls that get great WR despite having few matches. But overall, the correlation between number of battles and performance is positive and - in turn - contributes to below 50% average winrate.

 

There are also, of course, other factors - and many of them would actually drag the average up. But there's nothing too strange in them not evening out completely and the average ending up shifted away from 50% as a result.

 

[Saltface]

24 minutes ago, DFens_666 said:

65% players

Above 50% players also play more (more effect on WR because of #battles) and further compress downwards the WR

 

What is also funny is that a 50% WR player will be in the top 35% ranking and a 48% WR will be at the 50% rank.

Equally upwards at 52.5% WR you will be in the top 15% by Rank.

The slopes of the graph are very steep.

 

 

[Hanse77SWE]

First: What's this "Normal" you're talking about?

 

Second: My WR in randoms is 57.64% and the places me in the top 8% of the "known" playerbase. (Last time I checked.)

[Arrive_Alive]

10 minutes ago, Saltface said:

Above 50% players also play more (more effect on WR because of #battles) and further compress downwards the WR

 

I don't think so. Sure, if you're below 2.000 battles and it's your first account (and not resetted) you'll hardly have any good WR.

 

The people with 20k+ battles were more often red than purple in my MM-Monitor. Which is just sad.

[rnat]

30 minutes ago, Hanse77SWE said:

First: What's this "Normal" you're talking about?

Normal distribution is another wording for a Gaussian distribution. You can wiki it if you want.

 

48 minutes ago, Thorsvald said:

But although skewness on a G.D is 0 it depends on the size of data.

Size only matters here (beyond a certain point) if a Gaussian is a good approximation of the underlying distribution to begin with.

If you data shows significantly non-zero higher moments maybe look for a different model ?

[Hanse77SWE]

1 hour ago, rnat said:

Normal distribution is another wording for a Gaussian distribution. You can wiki it if you want.

If it's one thing I've learned in life is that "Normal" is the most abnormal thing there is.

 

"Lies, damned lies, statistics."