[Confirmed] Negative armor has a different effect in DotA2 in comparison to Dota1

[unkie]

According to the mechanics area on playdota.com when having negative armor the following formula is used to calculate the increased damage:

1 - 0.94 ^ (-armor)

with a cap for negative armor of -20. This results in a maximum of 71% increased damage through negative armor.

DotA2 whatsoever seems to use a different coefficient than 0.94 also it seems it is not capped to -20. I did some quick tests with Ogre Magi on level 25 with 6 hots (12 armor) and several items and spells to reduce its armor (melt, dazzle ult, venge wave, slaradar ult, desolator, medalion and AC) resulting in negative armor values of around -44. So in total 12 - 44 = -32. This should result in -71%! The tooltip showed 65% extra damage, so there must be something wrong (or of course playdota.com is wrong on that!)

[shalafi]

Just a wild guess, but it looks like the minimum armour cap (at least in the tooltip) is base armor -20.

Ogre magi has a base armor of 3 + 14 agi /7 ~= 5. So according to my guess, -17 armor would be his minimum, which corresponds to 65.072% increased damage.

You should try to hit him and look at the damage log, to check that it corresponds the tooltip.

[unkie]

So I did some smaller research on this and thing it really is a bug! I again tested with Templar Assasin against a Ogre Magi. Debuffs were: AC, Desolator, Slardar Ult and Medalion of courage. Below is my documenation and the formulas I used.
And yes shalafi you are right, when I substract -20 (cap) from the base armor I end up at the 65.072%!

Ogre base armor:
2.96

Ogre agi total:
51+20

Armor on Hero according to stats panel:
12

Armor on hero calculated from stats:
2.96 + ((14+(25*1.55)+20)/7) = 13.3528571
http://goo.gl/kEHzT

Minus Armor:
-5 AC
-6 Desolator
-6 Medalion
-16 Slardar Ultimate (level 3)

Armor total shown by stats panel:
12-33

Armor total calculate from stats
2.96 + ((14+(25*1.55)+20)/7) + (-5 - 6 -6 -16) = -19.6471429
http://goo.gl/StfuE

Damage gain shown:
54%

Damage gain expected:
(1-0.94^(-((2.96 + ((14+(25*1.55)+20)/7)) + (-5 - 6 -6 -16)))) = 0.703490167
http://goo.gl/GxemR

Lanaya damage:
140+60

Damage expected with "propper" damage gain through negative armor:
(140+60) * (1 + (1-0.94^(-((2.96 + ((14+(25*1.55)+20)/7)) + (-5 - 6 -6 -16))))) = 340.698033
http://goo.gl/Kxa95

Damage expected with implemented damage gain through negative armor:
(140+60) * 1.54 = 308
http://goo.gl/8UukC

Damage dealed according to log:
[22:36.45] Templar Assassin hits Ogre Magi for 310 damage (8771->8461).
[22:37.22] Templar Assassin hits Ogre Magi for 310 damage (8469->8159).
[22:37.85] Templar Assassin hits Ogre Magi for 309 damage (8164->7855).
[22:38.42] Templar Assassin hits Ogre Magi for 310 damage (7861->7551).
[22:39.12] Templar Assassin hits Ogre Magi for 312 damage (7559->7247).
[22:39.75] Templar Assassin hits Ogre Magi for 304 damage (7252->6948).
[22:40.42] Templar Assassin hits Ogre Magi for 307 damage (6956->6649).
[22:41.05] Templar Assassin hits Ogre Magi for 307 damage (6654->6347).
[22:41.68] Templar Assassin hits Ogre Magi for 313 damage (6353->6040).

On a side note and not sure if this is a bug, intentional and how it is with this in dota1:
If using desolator the debuf actually is applied before the projectiles hit the target! This means the first attack already has the additional damage. Same for the meld debuff.

[unkie]

Attached a screenshot of ogremagis statsboard.
I also did some testing on dota1. There it is 340 dmg / 71% dmg gain.

[unkie]

Can anyone please change this to confirmed? Also should be added to the sticky imho.

[iliveoncaffiene]

On a side note and not sure if this is a bug, intentional and how it is with this in dota1:
If using desolator the debuf actually is applied before the projectiles hit the target! This means the first attack already has the additional damage. Same for the meld debuff.

Almost 100% positive this was actually even fixed in WC3, and was either bugfixed once or an intended change in DotA 2.

OT:
This seems like a mechanics bug - and the argument should not be on whether there should/shouldn't be a cap, but whether the -20 cap should factor in base armor (level 1 armor) or not.

[unkie]

Well if the cap is based on the level 1 armor it is different on each hero, making the game unnatrual hard because you have to consider the base armor (not the real level 1 armor, the armor at level 1 if you dont have any agility!) of your enemies if you want to work with -armor rather than with +damage!

[blash365]

k, adding to sticky.
just to be sure, can you quickly list the heroes, that still have false armor values?

[unkie]

Well I at first thought it might be related to the base armor of the hero but it seems not to. For all heroes I tested I had the same wrong offset regarding the +dmg through negative armor, and they all have different base armor (except for Axe and Anti-Mage).
From the looks (see attachment) there is no cap for negative armor. (also dazzles ultimate stacks! )

[Synth]

Damage Amplification from -armor is uncapped and Algorithm may be wrong.

I would still care for a WC3 test of this, but this involves dota 2 mostly.

It seems that the -20 armor & -71% damage amplification that was hardcoded in dota 1, Doesn't exist in dota 2. Not only is it visual, its also real it seems.
Additionally, it seems that the (1-0.94^n) may be off by a bit.

All taken from the post in the Brainstorming section.

Huh. Always remembered it being +25% damage... Testing this now, and this possibly warrants a bug, since slardar with some massive -armor items, along with a dazzle, could destroy even PL with high armor exceedingly fast. Also going to see what the max damage amplification by unnatural means is, since the HIGHEST possible by one team alone is <-80.

Ok, here it is.

Damage with 8% resistance

Damage with 38% resistance

Maximum Amplification, about -800 armor, -97%. I've been hitting at about this point from now on.

Hit w/o MoM at -97% resistance

and then with.


Using D*Crit*amp*MoM amp, which is 1926*4*1.97*1.3, and substituting/giving when needed.

8% resist(.92 amplification)=7087.68 Very close to what is seen. No issues there.
38% resist(.62 amplification)=4776.48 Also extremely close
-97% resistance(1.97 amp)=15176.88 just under the 15220 seen.
-97% resist with MoM amp=19729.944 also just under the amount seen.

I think the damage amplification from -armor doesn't exist, nor is the exponential calculation of it correct.

Post of the helpful person who also corrected my math and stumbled upon the possibility of the algorithm being wrong

Try doing it with less variables? Also MoM is 1.3 times, not 1.25 times. Perhaps without the MoM active for one trial, to see if that's causing the issues or it is indeed just the armour calc?

I did a few tests on MoM before and found that the only bug with it was with Dispersion (and perhaps other pseudo-evasions) where it wasn't multiplied correctly, as in this thread.

Alright. Actually figured it out, there's no cap on armour, and if you use 1.95 * 1.3 * 4 = 10.14 modifier, so that equals 19530 damage, perhaps just rounding + hero damage fluctuating leading to it being slightly different.

The bug is: Hero -armour is not capped.

EDIT:

also I have no idea why it's "capping" at 94% increased damage (1 - 0.94^n) where n is the absolute value of your negative armour... It should be at +100% damage at -315 armour... Perhaps negative armour is calculated incorrectly? Probably worth an investigation.

[hoveringmover]

I noticed this as well but the thought occurred to me that it may be intentional. Stopping the minus/negative armor at 20 seems odd.

[Wyn-Ryder]

[Confirmed] Negative Armor [armour] is calculated incorrectly

Summary:

Negative armour seems to be amplifying by an amount that is too small in dota 2 (and on a sidenote it is uncapped).

Repro steps:

1) Create any enemy hero
2) Pick/create slardar
3) cast amplify damage on an enemy hero and look at their damage resistance in the UI

Result:

It is higher in dota 1 (unless the cap is reached, in which case it may get closer)

for most noticeable differences get a low armour hero (i.e. doom or something like that)

I am in the process of calculating exactly what equation it uses, but it isn't 1-0.94^x (where x is the absolute value of the negative armour value)

[THIS IS NOT JUST A UI ISSUE, I HAVE CHECKED THE DAMAGE AMOUNTS TOO!]

And props where they are due: http://dev.dota2.com/showthread.php?t=73775

[Wyn-Ryder]

Well this will teach me for not refreshing my list before posting :/ Oops. http://dev.dota2.com/showthread.php?t=73890

[blash365]

added to sticky.

[ThoAppelsin]

(1-0.94^n)

It uses the formula for the positive armors instead; takes the negative armor as if it was positive, grabs the result, and then negates it...
Example;

+ X armor ends up with A% damage reduction?
- X armor ends up with A% damage amplification.

Looks intended, though... I mean, it seems more consistent to my eyes. Probably was something impossible to do on W3 engine, that IceFrog always wanted to change all the time. Positive and negative armor values are acting the same, just on the opposite directions. The armor-amplification/reduction graph is point-symmetrical. What else do we want?
+1 for intended change...



Edit
Srsly guys... Srsly...
https://www.desmos.com/calculator/q4nl5foly9
pls.

If you still did not understand, let me word it out. I was kidding, of course. And this should be fixed like every other thing, including the two third of the whole intended fix list, and maybe even more of it.