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Juggernaut41

How Math Can Help You Not Rage Quit (as much)

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I played my alt account a bit over the last few days and managed to post a blistering 35% WR despite a 1700 wn8 over 36 games. Of course I could have played better, but there was maybe 1 or 2 of the losses where better decision-making on my part could clearly have allowed us to win the game. Perhaps it was a higher number than that, but I didn't see it (even in retrospect). Super frustrating.

So for giggles, I decided to do the actual math of what the probability of that was. Too complicated, so I went with a very simple model of a coin toss... a 50% chance of a win/loss (ignoring ties and that I don't have a 50% WR) and calculated how many times it should be expected to have 10 losses in a row over 30,000 games. The short answer is the expectation is that it should happen 14.7 times over 30,000 games. So, if you play 15 games a day, you should expect to lose 10 in a row every 136.4 days. So... the next time you want to bust out that tinfoil hat*... come on back to the numbers 😉 

For the curious, the math is E(k) = 1/(p^1) + 1/(p^2)....+ 1/(p^k), where k = the number of throws (games) and p = the probability of a win (in this case 0.5). Here is the output table: 

image.png.baa91746b435272ebfc082de15cdfa38.png

 

To me this flips the anecdotal experience... as in... I experience far less bad runs than the probabilities indicate. I have definitely lost 10 in a row... but nowhere freaking close to 15 times**.  This would imply that rather than the conspiracy theories of the MM algo somehow penalizing you in certain situations that the reverse is true. That the algo is tuned to *lower* the statistical probability of bad runs. My bet? it isn't tuned one way or the other... as that level of tuning would imply an extremely complex optimization problem. I wont make a long post longer, but you can find server-wide WR stats by tank... and there is a pretty decent range around 50%... 

I knew DHOers were dying for a math post. You're welcome. 

* This post dedicated to @bergsteiger😉

** I re-ran this for a 52.25% WR... and that decreases the # of occurrences from 14.7 to 9.7... I can remember maybe 3 or 4... but that doesnt include some late late nights ... so maybe 😉 

*** I also ran it for a 48% WR (there are tanks in the game that have server-wide WRs around there) that increases number of occurrences from 14.7 to 20.8... or every three months if playing 15X per day... a 41% WR gets you a 10 in a row loss streak once per month. 

 

 

 

 

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after I lose 7 in a row...

I stop playing tanks.

yes, I'm a quitter

but then again

I don't put my fist through my monitor,

pound my keyboard into tiny pieces 

or throw my mouse across the room.

 

how often will I see 7 losses in a row?

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26 minutes ago, The_Dad said:

after I lose 7 in a row...

I stop playing tanks.

yes, I'm a quitter

but then again

I don't put my fist through my monitor,

pound my keyboard into tiny pieces 

or throw my mouse across the room.

 

how often will I see 7 losses in a row?

Roughly every 254 games assuming 50% WR. 

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9 hours ago, gpc_4 said:

I’m going to need a second opinion about all of this. 

Here is an intuitive way to think about it...  which includes some assumptions/definitions/qualifications I left out for the sake of brevity...

Clearly you have a 50% chance of a heads assuming a fair coin. If you conduct a high number of two flip trials, you will get heads half the time. So the “expected” result of a two flip trial is one head and one tail.

Each flip is independent of the previous flip (sorry folks, betting on red on a roulette wheel because red numbers have been running is nonsensical). So the first flip has a 50% chance, and to get the expected number of trials you divide 1 by .5 to get 2.

In order to get two in a row, the probability is 1 divided by (.5*.5). Because each flip is independent (the probability of the heads on the next flips has nothing to do with what happened on the previous flips), you have to add each probability of number of occurrences together. That’s where folks get tripped up intuitively. If you don’t believe me, I’m sure there is something on the inter webs to validate the maths. 

Edit: last one. What is the probability that you will get a heads on the next flip after 5 consecutive flips have been heads? 50%. What’s the probability that you will get 6 heads in a row? .097%. It matters both how you define the parameters and whether you are looking at the whole theoretical population or one sample (trial). As you approach infinite trials, your experienced reality will equal the probability. However, literally any combination is possible for one (low number of flips) trial. Ok, I’m done. 

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