39 replies to this topic

[MadestCat]

Damage distribution

A lot of people complain about "always doing minimum damage, all the time!". Parallel to that I felt, that the T34 does way too often 300 or 500 damage. Because of that I decided to take a closer look at the damage distribution.

What do we know or what do we think we know?
According to the WoT-Wiki the damage ist distrbuted according to the normal distribution. There are two values in this distribution worth looking at: µ and sigma. The expectation or mean value (µ) defines the center of the curve (highest value), the standard deviation (sigma) defines its width. Two examples:



What we see here:
- Minimum and maximum damage: Black dashed line
- Blue curve: Between minimum and maximum damage are 2 sigma (sigma = µ / 8). Therefor nearly 95,45% of all shots are between minimum and maximum damage.
- Red curve: Between minimum and maximum damage are 3 sigma (sigma = µ / 12). Therefor nearly 99,73% of all shots are between minimum and maximum damage.
Worth mentioning: I chose 2 und 3 sigma because these values are relevant at accuracy, too, according to the Wiki


Until now it was pure theory, now to the real thin with two question:
1. How is the damage really distributed?
2. What happens to the shots that fall theoretically below or above the minimum or maximum damage?

Question 1: How is the damage really distributed?
Because of the nice average of 400 (minimum 300, maximum 500) the T34 is a really nice test vehicle for this. Unfortunately the RoF is very low, so it takes a lot of time to get enough shots (and it's very expensive!). Therefor I took the QF 6 pdr, mounted on the M7/T21 which fires every 1.96 s. Thats fast enough to get enough shots to do a statistical analysis.

- Mean damage: 75
- Minimum damage: 56
- Maximum damage: 94


The diagramm now looks like this:




Still it's not clear, which diagramm is the correct one.
Therefor, here are the measured values (701 shots, blow ups and kills ignored):




Lets put both curves (2 sigma and 3 sigma) into this diagramm:

If one calculates the error between the measurement data and the two curves (3 Sigma: 0,44%, 2 Sigma: 0,16%, sum of errors^2), it's obvious, that the 2 sigma curve has a lower error and is most probably the correct aproximation.
One thing attracts our attention now:

Why are minimum and maximum damage so frequently, compared to other values?

With this in mind, lets come back to the second question:

2. What happens to the shots that fall theoretically below or above the minimum or maximum damage?
We now know, that the damage ist distributed by 2 sigma. This means that about 95.45% of all shots are between minimum and maximum damage. The rest of it, about 4.55%, has to be outside of minimum and maximum damage. Because of the symetryof the distribution, one half of the 4.55% shots, about 2.28%, has to be above maximum damage, the other half (also 2.28%) has to be be below the mimimum damage.


If you looks closely at the minimum damage, you can see that it should appear only in 0,55% of all shots. According to the measurements it happends a lot more frequently, about 2,5%. This is aproximately 2% higher than expected. Theses 2% are the 2.28% of all shots that do lower than mimimum damage. Apparently WoT is pushing all shots, which would do damage below mimimum, up to the mimimum damage. The same happpends with the maximum damage, all shots with above maximum damage are reduced to the maxmimum damage.


This portion is quite high and can not be ignored. Just to show you how frequent this ist: Maximum and minimum damage combined are more frequent than the medium damage. Usually feelings are not a good indicator for statistics, but this time the feelings were right, a lot of shots have minimum or maximum damage.

One question automatically comes to my mind:
What happends at the penetration calculation? Do we have the same phenomenon there? At least the distribution is similar ...

Solution:
All values below minimum or above maximum damage should be rejected and recalculated. Because of the calculation methode, one automatically gains two random numbers, so the number laying inside the boundaries should be chosen. If both values are invalid, a new damage value has to be calculated.


Link to the German thread: http://forum.worldof...chte-messwerte/

Edit: Syntax checked

[CptTriggerHappy]

You sir, have to much spare time.

[tobiash24]

well, i liked this. thanks.

[AngryBanana]

interesting stuff, I can already imagine this in silentstalkers Q&a translations

SerBtheTroll said:

-the higher than usual appearance of minimum and mazimum damage shots is not considered a problem

this actually partially makes the minimum damage conspiracy theorists right, because minimum damage will occur more often than expected by the distribution and also more often than max damage because more of the high damage shots are made 'invisible' by killshots

Edited by AngryBanana, 29 January 2013 - 01:01 AM.

[Gabblack]

That's awesome! I've always wondered about the frequently occured minimum damage on the top gun of the fredi and the E-75. Thanks for the answer! +1

[Kazadar]

Nice to see someone actually using math and logic instead of random whines with nothing to back it up.

[MadestCat]

Gabblack, on 29 January 2013 - 12:59 AM, said:

That's awesome! I've always wondered about the frequently occured minimum damage on the top gun of the fredi and the E-75. Thanks for the answer! +1

Well, maximum damage will occur as frequent as minimum damage, don't always just think about minimum damage ... but then this, a very intelligent contribution:

AngryBanana, on 29 January 2013 - 12:59 AM, said:

this actually partially makes the minimum damage conspiracy theorists right, because minimum damage will occur more often than expected by the distribution and also more often than max damage because more of the high damage shots are made 'invisible' by killshots

Yes, maximum damage occures less often than minimum damage, because you have a higher propability to kill somebody with max damage shot than with a min damage shot and then you wont see the damage you would have dealt ... haven't thought about that before ...

Edited by MadestCat, 29 January 2013 - 01:20 AM.

[Cobra6]

CptTriggerHappy, on 29 January 2013 - 12:50 AM, said:

You sir, have to much spare time.

But if it's right WG is hereby proven to troll players. Minimum damage hits should be the least frequent hits of all, just like maximum damage hits. Not rake up 1/4 of your shots effectively like it does now.

Negrepping is for offensive posting, not opinions you personally disagree with.


Cobra 6

[sv3rre]

Good work! I will bookmark this thread and forward it to the next person who whines about damage rolls.

[azenjood]

Nice find! That explains why I see so much 563 damage rolls on my ISU :S

I'll guess the same distribution pattern is true for penetration rolls?

[MadestCat]

azenjood, on 30 January 2013 - 12:27 AM, said:

I'll guess the same distribution pattern is true for penetration rolls?

Yes, I really think the penetration is calculated in the same way. Why should they use two different algorithms?

Something like this shows that WG has a certain "don't care attitude", because they did it in the easiest way possible and hoped nobody would notice!


It would be nice to have a statement from WG ...

Edited by MadestCat, 30 January 2013 - 01:06 AM.

[MrCaffeLatte]

Awesome post.

[Terracide]

Does this chart take the amour/angle of impacted tanks into consideration?

(the effective amount of amour the shell needs to penetrate)

[MadestCat]

Terracide, on 30 January 2013 - 11:05 AM, said:

Does this chart take the amour/angle of impacted tanks into consideration?

(the effective amount of amour the shell needs to penetrate)

Armour and damage are independant. This means that angle and amour do not influence the damage you are doing.

[Arpee78]

This is an old Q&A topic Here they answered question about dmg and pen distribution:

fabse:
Follow up question:
To prevent freak accidents (like a shot dealing double the damage, or flying backwards) the probabilty distibution (if it is a normal one) has to be cutoff.

At what relaitve probabilty (relative to the maximum) is this done in the three cases (damage, penetration, dispersion).

Overlord: If I do remember right, 2.5-sigma interval is in use.


Sorry, I stolen your diagarm and reworked it. I copied and mirrored the left side, thereby recover the lost shots(kills). And  I tried to draw a 2.5 sigma line.

Nevertheless, You did great job, respect.

[Platypusbill]

So, uh, the max and min damage rolls are more common than they should be to prevent the game fron calculating damage/ pen rolls above or below +/-25%?

BTW I think the gun in question is a 6 Pounder (57mm), the 17 Pounder (76mm) is only available on the TOG II, AT-15A, Centurion series, Black Prince, and Caernavon.

Edited by Platypusbill, 30 January 2013 - 01:46 PM.

[MadestCat]

Platypusbill, on 30 January 2013 - 01:45 PM, said:

So, uh, the max and min damage rolls are more common than they should be to prevent the game fron calculating damage/ pen rolls above or below +/-25%?

Please read the article, i don't want to repeat what I just wrote

Platypusbill, on 30 January 2013 - 01:45 PM, said:

BTW I think the gun in question is a 6 Pounder (57mm), the 17 Pounder (76mm) is only available on the TOG II, AT-15A, Centurion series, Black Prince, and Caernavon.

Thx, you're right, OP has been edited

[MadestCat]

Arpee78, on 30 January 2013 - 01:30 PM, said:

Forum-Diagramm4.png

This is an old Q&A topic Here they answered question about dmg and pen distribution:

fabse:
Follow up question:
To prevent freak accidents (like a shot dealing double the damage, or flying backwards) the probabilty distibution (if it is a normal one) has to be cutoff.

At what relaitve probabilty (relative to the maximum) is this done in the three cases (damage, penetration, dispersion).

Overlord: If I do remember right, 2.5-sigma interval is in use.


Sorry, I stolen your diagarm and reworked it. I copied and mirrored the left side, thereby recover the lost shots(kills). And  I tried to draw a 2.5 sigma line.

Nevertheless, You did great job, respect.

Interesting, I didn't know that, thanks ...

These are the errors, comparing the normal distribution to the measurements:

Sigma		  2		 3		 2,5
StdAbw		  0,00006	 0,00014	 0,00007
Summe Error^2	  0,16%		 0,44%		 0,20%

So 2,5 sigma and 2 sigma both seem to be ok. But with 2.5 sigma, too few shots would fall below min or above max damage, hmm, still strange.

Should I upload the Excel sheet somewhere?

By the way, this is the diagramm with 2.5 sigma added:

[GehakteMolen]

hmm, interesting, but this seems to match with ingame expierence, 300 and 500 shots with T34 aint that uncommon, but 302, or 496 are very rare :p

[tango_delta]

To be precise that dmg distribution is not normal distribution but a polynomial distribution.

For curve fitting the fitting curve looks more like the black line like this:



And tbh it is not very surprising at all how wg just manages to get this kind of stuff wrong all the time. And yet there are people who say these people could code a rigged dice into wot :D.