Jump to content


How dispersion and aimtime actually work ( maths inside)

aimtime dispersion accuracy gun handling maths graphporn

  • Please log in to reply
50 replies to this topic

brumbarr #1 Posted 29 November 2017 - 09:35 PM

    Lieutenant General

  • Player
  • 38626 battles
  • 6,326
  • Member since:
    07-30-2012

*
POPULAR

After a thread on the forums about  aimtime and how it works. I decided I wanted to figure it out exactly. All we know for now is that aim time is the time it take to reduce the aimcircle to 40% its size, dispersion is something that  say show much the circle gets bigger and accuracy is the size of the aimingcircle when fully aimed. However, we do not know  the exact relations between these 2 and how exactly they  influence the size of the aiming circle at all times.

So thats what I set out to do, finding a mathmatical description of the size of the aimingcircle. The method is simple: measure the size of the aimingcircle for different tanks and speeds in a trainingroom.   Thanks for uglycousin for giving me a second person to set up the trainingroom.

To measure the size of the circle, first I  did the test driving in the room. Then I watched the replays and paused at certain moments. I then took a screenshot of  my whole screen, makign sure I was always in 8x zoom. Then I took those screenshots into paint and measured the circle diameter in pixels.

I will now describe the process and results of my investigation. But if you dont want to read that, scroll down tot he conclusion on the bottom.

Disclaimer: the following formulas are NOT what WG uses, I made a linear  model that describes the size of the aimingcircle as close as possible. 

 

Aiming circle bloom

I assumed there where 3 variables that had an influence on bloom: speed, dispersion and accuray. I tried to do test in which I held 2 variables constant to  see the influence of 1.

I started  with gathering data of 2 different dispersion numbers for which I picked 4 tanks with different accuracy and measured the size at each speedincrease of 10 untill 50 kph.

These are the raw results:

 

Spoiler

 

From that I made a graph of the dispersion in function of speed , and calculated the gradient  of the graph assuming linear increase.  Then obviously  the  aiming circle size = C*v+accuracy.

With V=speed and C being the gradient, which consist of unknown  factors. To check the linear approach was decent I plotted the model and experiment:

 

Spoiler

 

As you can see the linear approach to the speed factor isnt perfect but not massivly different, only in the middle it differs.  I am happy enough with this.

Now we need to determine what the C factor consist off. Since there are only 2 variables left, it has to consist dispersion or/and accuracy components.

 

As you can see in the data, with the same dispersion numbers, the aiming circle fort he same speed is bigger when the accuracy is bigger.  So there has to be an accuracy factor in C,  which is proportional to accuracy.   

Here you can see accuracy vs circle size:

 

Spoiler

 

As you can see, the increase isnt marginal. We can now rewrite our formula as:

Size=Acc(D*v+1)

With D an unknown factor containing dispersion in some form.  As we can see, size of aiming circle is directly proportional to accuracy. So an increase in accuracy of 25% will results in 25% better gun handling.  This is why the E50/E50M have such amazing gun handling , their dispersion isnt great , but good, but due to the very good accuracy their gun handling is much better than at first glance.  The WZ-132-1 has the exact same dispersion values, so you would think the gun handling would bet he same, but no, since it has 33% worse accuracy is will have 33% worse gun handling, which is massive! Thats more than a vstab! 

Next task is determining the factor D. The only  variable left is dispersion, so I tested different tanks with differnt dispersion at the same speed, their accuracy was different, but thats fine, sicne we can normalise for that.    These numbers showed that the factor D was proportional to the dispersion values, so D=c*dispersion, with c an unknow constant.

Now the formula looks like this:

S=Acc(c*d*v+1)

Determining c was done by plottign the experminetal result and  trying some numbers until the model best fits the experiment. I took c=0.68.

The influence of dispersion can be see in this graph:

 

Spoiler

 

Now we have a formula that gives a perfect description of aiming circle size in function of all variables.  Next up is determing a  the time it takes fort he circle to shrink, or the actuall aiming time for the tank.

Aiming time:

We know aiming time is the time it takes fort he circle to shrink by 60% its startign size.

So we can write:

S1=S2*(4/10)^(t/T) with T=aiming time, S1 size after time t, S2= starting size.

Solving this for t we get: t=T*(log(S1/S2)/log(4/10)).

We can now determine the time it take from any speed to reach any size we want.

To determe the time it takes to fully aim, jsut replace S1 by the accuracy of the gun. Note this time is independant of accuracy! ( which is logical, since it needs to go to  a smaller circle but also does it faster, these 2 cancel out)

Plotting this for 3 different tank in fucntion of time comming to a stop from a speed of 50 (40 for conway) we get:

 

Spoiler

 

Influence of equipment/skills etc.

Now that we have every formula we need we can quantify the influence of equipment/skills/directives/modules. To do so simply multiply the variable that gets influenced by (1-0,01*improvement in %). Dispersion values only get influenced by vstabs and the smooth ride skill.Other equipment only influences the accuracy value.

Note that the same improvement to acc or dispersion results in a bigger improvement in size for what improves acc than what improves dispersion. Vstabs for example do not make the size of the circle shrink by 20%, they make the increase in size  less by 20%.

 

Lets take a look at a common dillema:vstabs vs gun laying drive, lets try this on 2 different tanks:

 

Spoiler

We can clearly see what the difference in vstab and gld is, vstab makes the circle smaller, so you start smaller but the decrease is still the same, gld starts at a bigger size but then starts to decrease faster, catching up tot the vstabs. In the BCs case, the time to fully aim is actually lower when equiping gld than when equiping vstabs.

Matmaticly, gld decrease the total time to aim by 10%,  whereas vstabs decrease the total time to aim by subtracting 20% *initial size. To know wether vstabs or gld is better depends on the tank and how much you want to aim, you can determine this by pluggin in the numbers and plotting it for each vehicle, sicne i twill be different for each.

As general rules however, these apply:

  • Bad dispersion + bad aimtime

Vstab better, unless you  fully aim from full speed.

  • Bad dispersion + good aimtime

Vstab better, unless at high speed when fully aiming.

  • Good dispersion + bad aimtime

Vstabs always superior

  • Good aimtime + good dispersion

Vstabs always superior

 

 

Conclusion and TLDR:

  • Accuracy has a massive  influence on aiming circle size on the move, they are proportional.
  • Aiming circle size is proportional to speed/dispersion.
  • To determine what gun has better actual gun handling: multply accuracy with dispersion, the lower the numbers the better the gun handling.
  • Size of aiming circle= Acc(0.68*d*v+1)
  • Time to fully aim = Aiming time*(-log(0.68*d*v+1)/log(4/10))
  • Vstabs is superior to gld in most situations.
  • Influencing accuracy gives a better boost than influencing dispersion values.

 

Whats next?

Next up I need to investigate how turning the turret and hull   effect dipsersion and work with the above formulas.

 I wil also try to combine this with  my previous thread where I determined shot distribution in the aiming circle, then I can plot change to hit a target vs time and determine the optimal time to shoot.

 

 

I hope you enjoyed the read and that i twill help you  determinign how a tank will perform. I hope that youtubers do become aware that accuracy has a massive influence over dispersion, as  currently reviews are misleading since they dont know what actually effects gun handling. Spread the word!



jack_timber #2 Posted 29 November 2017 - 09:50 PM

    Captain

  • Player
  • 33450 battles
  • 2,082
  • Member since:
    07-26-2014

A lot of work went into this, very informative:)

A question though...

Aim time is quoted at 3 seconds, just use this as an example. That is to reduce aim circle by 60%. If I wait for an additional 1 second does this make it more accurate?

 



brumbarr #3 Posted 29 November 2017 - 09:52 PM

    Lieutenant General

  • Player
  • 38626 battles
  • 6,326
  • Member since:
    07-30-2012

View Postjack_timber, on 29 November 2017 - 09:50 PM, said:

A lot of work went into this, very informative:)

A question though...

Aim time is quoted at 3 seconds, just use this as an example. That is to reduce aim circle by 60%. If I wait for an additional 1 second does this make it more accurate?

 

 

ofcourse, aiming circle decrease continuously, only stops when the accuray value is reached.

 

In this case it would decrease by another 27%. 

The decrease in size in 1s can be calculated as  1-(4/10)^(1/aim time)


Edited by brumbarr, 29 November 2017 - 09:58 PM.


Homer_J #4 Posted 29 November 2017 - 09:59 PM

    Field Marshal

  • Beta Tester
  • 28771 battles
  • 30,124
  • [WJDE] WJDE
  • Member since:
    09-03-2010

View Postjack_timber, on 29 November 2017 - 08:50 PM, said:

A lot of work went into this, very informative:)

A question though...

Aim time is quoted at 3 seconds, just use this as an example. That is to reduce aim circle by 60%. If I wait for an additional 1 second does this make it more accurate?

 

 

View Postbrumbarr, on 29 November 2017 - 08:52 PM, said:

 

ofcourse, aiming circle decrease continuously, only stops when the accuray value is reached.

Unless you mean waiting an extra 1 second after it stops which a lot of people suggest to allow for lag.



ExclamationMark #5 Posted 29 November 2017 - 10:11 PM

    Colonel

  • Player
  • 16775 battles
  • 3,727
  • Member since:
    04-12-2013

Great info, good work brumbarr.

Block Quote

 So an increase in accuracy of 25% will results in 25% better gun handling.  This is why the E50/E50M have such amazing gun handling

 

So that explains why the E50 actually has superior gun handling to the M46. The dispersion values are worse, but the far better accuracy in fact makes the E50 superior in that regard.



brumbarr #6 Posted 29 November 2017 - 10:14 PM

    Lieutenant General

  • Player
  • 38626 battles
  • 6,326
  • Member since:
    07-30-2012

View PostHomer_J, on 29 November 2017 - 09:59 PM, said:

 

Unless you mean waiting an extra 1 second after it stops which a lot of people suggest to allow for lag.

 

ah, idk about that. Hard to account for lag,  but even if that was the case, dont bother, fully aiming is almost never worth it unless you have no risk of getting shot at and the target wont move out of sight and you wont sacrfice any dpm to do so.

Homer_J #7 Posted 29 November 2017 - 10:21 PM

    Field Marshal

  • Beta Tester
  • 28771 battles
  • 30,124
  • [WJDE] WJDE
  • Member since:
    09-03-2010
Anyway, great work.  I wonder if the guys at tanks.gg could incorporate it to give effective dispersion figures the way they do with the equally misleading hull traverse figures.

brumbarr #8 Posted 29 November 2017 - 10:22 PM

    Lieutenant General

  • Player
  • 38626 battles
  • 6,326
  • Member since:
    07-30-2012

View PostExclamationMark, on 29 November 2017 - 10:11 PM, said:

Great info, good work brumbarr.

 

So that explains why the E50 actually has superior gun handling to the M46. The dispersion values are worse, but the far better accuracy in fact makes the E50 superior in that regard.

 

yup.

Dava_117 #9 Posted 29 November 2017 - 10:26 PM

    Lieutenant Сolonel

  • Player
  • 19508 battles
  • 3,327
  • [T-D-U] T-D-U
  • Member since:
    12-17-2014
Nice job! Nice to see some scientific method on the forum! Thank you brumbarr (and also to uglycousin for the crucial help)!

brumbarr #10 Posted 29 November 2017 - 10:30 PM

    Lieutenant General

  • Player
  • 38626 battles
  • 6,326
  • Member since:
    07-30-2012

View PostHomer_J, on 29 November 2017 - 10:21 PM, said:

Anyway, great work.  I wonder if the guys at tanks.gg could incorporate it to give effective dispersion figures the way they do with the equally misleading hull traverse figures.

 

That would be a great idea, not sure what kind of number you could put there then, I would prob put  dispersion*acc, but that number doesnt look very nice, maybe multiply by 10 ?

Dr_Oolen #11 Posted 29 November 2017 - 10:53 PM

    Lieutenant

  • Player
  • 21833 battles
  • 1,608
  • [IDEAL] IDEAL
  • Member since:
    03-13-2012

Not to put down your work. But anyone who ever put 2 minutes into thinking about dispersions/accuracies/aimtimes knew this several years ago.

 

And actual numbers were already calculated and are for example in tank inspector (the maximum disersions on hull movement/traverse/turret traverse).


Edited by Dr_Oolen, 29 November 2017 - 10:58 PM.


brumbarr #12 Posted 29 November 2017 - 10:59 PM

    Lieutenant General

  • Player
  • 38626 battles
  • 6,326
  • Member since:
    07-30-2012

View PostDr_Oolen, on 29 November 2017 - 10:53 PM, said:

Not to put down your work. But anyone who ever put 2 minutes into thinking about dispersions/accuracies/aimtimes knew this several years ago.

 

And actual numbers were already calculated and are for example in tank inspector (the maximum disersions on hull movement/traverse/turret traverse).

 

I doubt they knew the exact formula, or that accuracy has influence on gun handling. It wasnt common knowledge anyway.

I had fun doing this regardless :P



Homer_J #13 Posted 29 November 2017 - 11:10 PM

    Field Marshal

  • Beta Tester
  • 28771 battles
  • 30,124
  • [WJDE] WJDE
  • Member since:
    09-03-2010

View PostDr_Oolen, on 29 November 2017 - 09:53 PM, said:

Not to put down your work. But anyone who ever put 2 minutes into thinking about dispersions/accuracies/aimtimes knew this several years ago.

 

Knew? No.

 

I knew dispersions worked by multiplying the base accuracy, yes.  But not by how much a 0.11 dispersion made a .29 accuracy circle bigger.

 

Never used tank inspector, I need something online because I can't install stuff at work.



_Anarchistic_ #14 Posted 29 November 2017 - 11:37 PM

    Second Lieutenant

  • Player
  • 39048 battles
  • 1,081
  • Member since:
    01-07-2015

wow, some effort , thank you

 

if I may, your comment on e50 accuracy vs 132-1, does that mean there is an argument for BIA+Vents instead of  Vstabs? (and then food if you can afford the credits)

 

after all, BIA and Vents (+food)  also help aim time so does the aimtime plus accuracy outweigh the soft stas boost of vstabs?


Edited by _Anarchistic_, 29 November 2017 - 11:39 PM.


brumbarr #15 Posted 30 November 2017 - 12:31 AM

    Lieutenant General

  • Player
  • 38626 battles
  • 6,326
  • Member since:
    07-30-2012

View Post_Anarchistic_, on 29 November 2017 - 11:37 PM, said:

wow, some effort , thank you

 

if I may, your comment on e50 accuracy vs 132-1, does that mean there is an argument for BIA+Vents instead of  Vstabs? (and then food if you can afford the credits)

 

after all, BIA and Vents (+food)  also help aim time so does the aimtime plus accuracy outweigh the soft stas boost of vstabs?

 

hmm, I think that depend entirely on the  tank, what the aimtime, speed and dispersion values are. 

I could work out what the bonus is for a specific vehicle, but not in general as its different for each tank.

 

Either way, the choice isnt realyl vstabs or vents + bia+ food. You can have the last 2 with the vstabs aswell, so than the vstabs combination will always give the better bonus than the vents combined with the rest.



Pvt_Duffer #16 Posted 30 November 2017 - 12:45 AM

    Lieutenant Сolonel

  • Player
  • 16658 battles
  • 3,145
  • [WJDE] WJDE
  • Member since:
    05-11-2011

I am too much tomato to worry about vstab over vents or similar, my own failings are bigger than small % advantage conferred by either,

I also likely have more vents laying about than vstabs (and a lot more tanks that don't take vstabs!?),

 

Food for thought though.

 

Thankyou.

 

o7



_Anarchistic_ #17 Posted 30 November 2017 - 02:30 AM

    Second Lieutenant

  • Player
  • 39048 battles
  • 1,081
  • Member since:
    01-07-2015

View Postbrumbarr, on 30 November 2017 - 12:31 AM, said:

 

hmm, I think that depend entirely on the  tank, what the aimtime, speed and dispersion values are. 

I could work out what the bonus is for a specific vehicle, but not in general as its different for each tank.

 

Either way, the choice isnt realyl vstabs or vents + bia+ food. You can have the last 2 with the vstabs aswell, so than the vstabs combination will always give the better bonus than the vents combined with the rest.

 

most time people argue over vents vs optics, I like optics hence why I asked and on some tanks, eg t00lt vstabs useless anyway

brumbarr #18 Posted 30 November 2017 - 08:10 AM

    Lieutenant General

  • Player
  • 38626 battles
  • 6,326
  • Member since:
    07-30-2012

View Post_Anarchistic_, on 30 November 2017 - 02:30 AM, said:

 

most time people argue over vents vs optics, I like optics hence why I asked and on some tanks, eg t00lt vstabs useless anyway

 

actuallt,  the T100 gun handling really isnt that good, since it has very bad accuracy it has the same gun handling as an obj140, which most people use vstabs for.

Dr_Oolen #19 Posted 30 November 2017 - 08:41 AM

    Lieutenant

  • Player
  • 21833 battles
  • 1,608
  • [IDEAL] IDEAL
  • Member since:
    03-13-2012

View PostHomer_J, on 29 November 2017 - 11:10 PM, said:

Knew? No.

 

I knew dispersions worked by multiplying the base accuracy, yes.  But not by how much a 0.11 dispersion made a .29 accuracy circle bigger.

 

Never used tank inspector, I need something online because I can't install stuff at work.

 

Well, "everyone" knew dispersions multiply the base accuracy proportionaly to whatever the dispersions are applied on (hull traverse/movement/turret traverse). Personally the only think i didnt "know" and am interested in is whether there is some maximum limit and how the 3 different dispersions are added - whether there are some diminishing returns or not.

 

Basically, lets say your max dispersion on hull movement is 8, on traverse 5, on turret traverse 5. If you move at max speed all those things, what happens? Does your actual accuracy really get all the way up to 8+5+5 or does it not? Thats basically what for me is the only thing left to know about how all this stuff works. And perheaps one might want to ask whether there are some delays/intervals/smoothing functions or whether its literally always calculated only as function of current speeds/traverses with aimtime being the only mechanism that lowers the size of aiming circle.

 

EDIT: what i mean by there beind delays or not is the fact that when playing tonks with good turret dispersions the aiming circle barely increases in size, which made/makes me believe that aiming time, so to say, is "working" 24/7 and on these tonks it happens to be good enough to basically cancel out most of the expected turret dispersion. Its also where the "c=0.68" could have come from for the most part.


Edited by Dr_Oolen, 30 November 2017 - 09:25 AM.


Thejagdpanther #20 Posted 30 November 2017 - 08:53 AM

    Brigadier

  • Player
  • 34566 battles
  • 4,424
  • [TKBS] TKBS
  • Member since:
    07-16-2012
No sigma?





Also tagged with aimtime, dispersion, accuracy, gun handling, maths, graphporn

1 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users