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Statistical analysis: Expected number of win/loss streaks

Statistics Analysis Streaks Simulation

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Jukkis74 #21 Posted 15 January 2019 - 04:11 PM

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There are natural (i.e. ’non-rigging’;) reasons why autocorrelation (win-streaks, loss-streaks) can be expected to happen a bit more than in pure random distribution. In my guess, most important ones might be ’flow’ and ’tilt’, both about players performance level at the moment. Flow is increased performance after wins, tilt is decreased performance after losses.

 

I have not tried jylpah’s code, but adding flow/tilt mechanism to simulated results could be quite straightforward. For example, if players winrate is 55%, adjust likelihood of win to 58% after win, and to 52% after loss. This +-3% is pure guess, but calculating simulated streak lengths allows us to better understand how much an effect we are likely to see from totally expected autocorrelation reasons.

 

Another claim is that WG will rig the games for good players (so that they will have more challenge) or for bad players (so that they can feel good about the game). Simulating these aspects, and then comparing to real distributions, is one additional way of proceeding.



jylpah #22 Posted 15 January 2019 - 09:34 PM

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View Postgallabru, on 15 January 2019 - 01:03 PM, said:

I will try to paste the graph (only 50 games) later

 

Here is the Matlab code (comments are not necessarily my view). I used the Matlab generator instead of a Box-Muller transform. I assumed Matlab was doing better.



For 100000 battles, numerically you get 3% of unfair games (my definition was that the difference in averages WR of teams is larger than the distribution of WR across all players), 0.4% of noob teams (best WR below 48%). These were calculated as unfair_game/sample and noob_team/sample.

 

Obviously and funnily, the number of noob team increases rapidly with the WR of the player if he forgets to take his contribution to the team's statistics.

 

3% of 'unfair games'... say a typical clan has 40 members, 5 games a day... everyday, you get 6 rants in your chat about unfair games.

 

edit : sorry, if I paste the code, the signs are considered as emoticones. If you tell me how to avoid that...

re-edit : oops, a typo. Obviously in the comments, I always consider the best player of 'my' team

 

Interesting experiment!

 

Few data points from BlitzStars data (90k players)

  • Average Draw rate: 0.01023728
  • mean(WR): 0.5332775
  • mean(battle-count-weighted WR) : 0.5443612 !!!
  • variance(WR): 0.003586886

 

Naturally the (battle-count-weighted) mean WR over all the players cannot be higher than 50% and the average _battle-weighted_ WR has to be 50% - Draw rate / 2 = ~ 49.5%

 

PS. https://pastebin.com/


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jylpah #23 Posted 16 January 2019 - 06:54 AM

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View Postllo1, on 15 January 2019 - 01:08 AM, said:

Nice one...but did you take into account the number of players in a game, their wr, their Afk rate and their influence on the outcome of the battle.....all of which might in my opinion, increase the frequency and length of the win/loss streaks!

 

No, this was simple modeling based on average WR. In modelling it is always a question of simplifying and unless the exact workings of further details are known, the added details might not improve the model at all, but vice versa. The simplicity of this modeling does not make it bad, but in this rather powerful. Had I added all kind of team simulations you mentioned, no one - including myself - would have known are the results caused by some some weird modeling choice/error or by the mechanics of the underlying problem. This simulation is super simple. It is basically about a simulated (weighted) coin-thrown and observing the results.

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gallabru #24 Posted 16 January 2019 - 07:55 AM

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An easy approach to what Mighty_Wombat suggests would be to do the same simulation for an expected WR of + or -3% from your actual one. This would give boundaries for the streaks you could expect due to increased/decreased performance. 

?


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gallabru #25 Posted 16 January 2019 - 10:26 AM

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Jukkis74 #26 Posted 16 January 2019 - 04:32 PM

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View Postgallabru, on 16 January 2019 - 09:55 AM, said:

An easy approach to what Mighty_Wombat suggests would be to do the same simulation for an expected WR of + or -3% from your actual one. This would give boundaries for the streaks you could expect due to increased/decreased performance. 

?

 

Yes, when looking at win-streaks from +3 variant and loss-streaks from the -3 variant. And in similar way of thinking if/when observed (real) streaks are longer than full random with no autocorrelation would provide, it is possible to just try these +- variants to find out rough approximation of the autocorrelation-like effect that is happening in real world.

 

After the magnitude is established, it is possible to discuss in more rational way if that is likely to because of expected normal reasons for autocorrelation, or if we need ’rigging’ to explain the difference.



I_Fought_the_Law #27 Posted 17 January 2019 - 01:06 PM

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Am I getting this right, your trying to simulate the effects of rigging by other causes to disprove rigging?

gallabru #28 Posted 17 January 2019 - 04:19 PM

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First, we are trying to evaluate what are the distribution of losing/winning streaks using purely random numbers. Then, when you will provide significant distributions of 'experimental' losing and winning streaks, we will be able to make comparisons and see if there are deviations from statistical distributions. Basically, we are trying to go beyond 'Cum hoc ergo propter hoc'.

 

Second, to me, but English is not my mother tongue and I may be wrong in my translation, 'bias' and 'rigging' covert the same semantic field but have different meaning.


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gallabru #29 Posted 17 January 2019 - 04:31 PM

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I have plotted, always generating random teams, for 200 battles, the cases where the best player of green team has 2%better WR than the best player of red team (+1) or vice-versa (-1). The value 0 would mean 'balanced'.

We can see a long 'generally unbalanced' MM series of 19 battles around battle 40 or 'un-balanced compensation' near battle 115 (10 battles).

 


Edited by gallabru, 17 January 2019 - 04:37 PM.

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jylpah #30 Posted 17 January 2019 - 10:20 PM

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gallabru, very nice to see there is one more stats-geek on the forums! I recommend to take a read to the paper I linked in the end of the first post. I haven't read (or understood) it fully yet, it is describing similar "streak" problem. I am thinking if I can find an analytical form for the expected mean value and variance of streaks in series assuming independent random events. Then it would be possible to run hypothesis testing with real data.

 

I have also worked on the python scripts to analyze replays (i.e. extract data form WoTinspector.com). My idea was to develop the script bit further to extract battle data and then run tests about whether MM or RNG are statistically worse or better after certain number of losses / wins. Once could do t-test for MM after a win vs. MM after a loss to see are those significantly different. Or MM when the streak turns.


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Mjr_Eazy #31 Posted 17 January 2019 - 11:22 PM

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There's a good explanation (or at least I think it is :)) here...

https://latin.stackexchange.com/a/2883

I hadn't heard your cum hoc ergo propter hoc, but had heard post hoc ergo propter hoc

 


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gallabru #32 Posted 18 January 2019 - 10:07 AM

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@Jylpah : Hey, I am not a stats-geek ! I am.. erm... well, anyway. ;)

Yes I think collecting data is a first good step. I should have a look at your Python code to see how I can use it.

@Mjr_easy : both work, you are right. 


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jylpah #33 Posted 18 January 2019 - 06:53 PM

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View PostMjr_Eazy, on 18 January 2019 - 01:22 AM, said:

There's a good explanation (or at least I think it is :)) here...

https://latin.stackexchange.com/a/2883

I hadn't heard your cum hoc ergo propter hoc, but had heard post hoc ergo propter hoc

 

 

Now you lost me :amazed:

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sixty_three #34 Posted 21 January 2019 - 06:36 AM

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Going off on a bit of a tangent, when I played Blitz, I quite often wondered why some posters here kept arguing that their latest losing streak *proved* the MM (at least prior to v5.3) wasn’t random.

 

And then yesterday I read this article and it prompted me to think about these people again. They could be less irrational than you might think:

 

https://theconversation.com/rationality-research-shows-were-not-as-stupid-as-we-have-been-led-to-believe-108218

 

In summary, it doesn’t prove there’s anything wrong with the statistical analysis being discussed in this thread.  But it perhaps does give a psychological insight into why some people think it’s all rigged.

 

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Strummer54 #35 Posted 21 January 2019 - 06:59 AM

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Theordore Riech, Froids no. 1 student wrote a book called Listening with the Third Ear, which,summarised,  placed a lot of value on intuition, our “gut” instinct then went on to elucidate with examples on how effective it is.

 

 


Tijgerhaai_XIV #36 Posted 21 January 2019 - 07:09 AM

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Which is why brain surgeons don't study hard because what use is book smarts. And Freud, last I checked, was pretty much wrong about everything.

 


Strummer54 #37 Posted 21 January 2019 - 07:28 AM

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View PostTijgerhaai_XIV, on 21 January 2019 - 07:09 AM, said:

Which is why brain surgeons don't study hard because what use is book smarts. And Freud, last I checked, was pretty much wrong about everything.

 

just jump in with both feet dude and criticise something you clearly aren’t familiar with.

 

 


Tijgerhaai_XIV #38 Posted 21 January 2019 - 07:55 AM

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One book from the extremely early days of psychology does not invalidate decades of research into the scientific method or centuries of it's practice.

The majority of claims about rigging are entirely empirically provable. And none ever have been. To appeal to gut instinct is nothing more than an appeal to authority and as such is a logical fallacy.

This does not make it wrong, but it has no place in a serious discussion.

 


Mjr_Eazy #39 Posted 21 January 2019 - 07:56 AM

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Thanks sixty_three, it is a very interesting article and the research paper is too...

It does offer an interesting explanation of why people expect certain sequences and why randomness is so hard for people to get to grips with...

Research paper is available in pdf for free below, as link in the article is behind a paywall...

https://pdfs.semanticscholar.org/c08a/b58e5cdeaa040ac209ac6d66cd802d9c7492.pdf

 


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Pururut #40 Posted 21 January 2019 - 10:24 AM

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I think I dont understand. Is the data from analyzing matchmaker which is random by its very nature reliable? Even if it is there are so many non-mathematical factors involved ranging from the stacking moral gain/loss, players willingness to take the game seriously, communicate and play as a team, etc. I appreciate the work but dont know whether if it is suited to analyzing the matter involved.

Edited by Pururut, 21 January 2019 - 10:24 AM.






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