Armor Analysis and it's impact on Damage Reduction

[GoodSyntax]

So, I'm not sure why it is, but I got curious about Damage Reduction after reading a thread that referenced the following statement by one of the Devs: Armor Value * (Armor Modifier by level of attack mob) = Damage Reduction
See post here: http://www.spacetimestudios.com/showthread.php?79913-Known-Issue-with-Passive-Abilities&p=902866&viewfull=1#post902866

Armed with this knowledge and the obvious unknown of what the modifier value is, I figured I could back-calculate what this value is for an Elite Tindirin mob. I chose the first, unmasked spearman in Elite Jagged Trail for my testing purposes. All testing was done without a pet, and I didn't attack the mob after initial aggro to avoid any possibility of buffs or debuffs.

I tested at various armor levels, to determine if damage reduction is indeed linear as the Developer's post implies.

I recorded 30 non-critical hits by the mob, and below is the summary of the data recorded (I personally favor Geomean as opposed to straight average):
102044

Chart of Damage Received vs Armor Values:
102045
What is interesting to note in this chart is that we see a clear plateau of damage received between 1k armor and 1198 armor (about 200 armor difference). We see the same plateau between 1444 armor and 1600 armor (again, about 150 armor difference). This seems to imply that the incremental addition of nearly 200 and 150 armor, respectively, yield very little in terms of a reduction of damage.

Chart of Damage Reduction Percent vs. Armor Values:
102046
Once again, we see the same plateaus between 1k and 1198 armor, and again at 1444 and 1.6k armor. Based on these results, there are some obvious peaks and valleys, and the reduction is clearly not linear as the formula above says it should be.

Conclusion:
It is difficult to see exactly where these plateaus of efficiency come from, but if I had to guess, it seems that the damage reduction formula is either banded (based on the data I have, it seems banded at 400 armor intervals), or is spline based. This implies that incremental armor within the same band yields only a marginal improvement in damage reduction; therefore, if the difference in builds can put you into the next damage reduction band, go for it otherwise, it would seem better to focus in other areas (such as DMG or HP).

Now, being that it is difficult for Rogues to get much beyond 1.9k armor at this point, I can only assume that we will encounter another plateau beyond this 1.9k armor level. I may try testing with Iron Bite's AA to get to 2k, but that will have to wait for another day.

In the meantime, if a Dev could point out what the actual damage reduction formula is, I would greatly appreciate it, because from my testing, the mob modifier is not a fixed value, and seems to be based on the armor stat.

[Kreasadriii]

Nice analysist..
but, can damage reduction stack? elix + pet?

[Anarchial]

So basically then, singe damage reduction of 4% is equivalent to a hella lot of armor :O

[GoodSyntax]

Not sure.....was trying to figure out how armor affects damage reduction. It isn't working like the formula says it should.

So, I'm just trying to nail down what the actual formula is.

[GoodSyntax]

So basically then, singe damage reduction of 4% is equivalent to a hella lot of armor :O

Yes, based on what I've been seeing, 4% damage reduction from a pet would be equivalent to a lot of armor.

[FluffNStuff]

Here is what I know about the subject, including that specific mob (Love him for testing):
1) Armor Value for Same Level attacks is 1/Level. (Level 21 = 1/21 = .00047619 in that post)
2) At Level 41 that is 0.00024390243902 in the way you calculated the percentage)
3) That mob hits both normal and skill attacks, so it is possible some groups had higher attacks, so your distribution ~fits~, and even if they were all uniform, it still ~fits~.
4) I have tested that against that mob and found that he has ~2050 armor (IF he is level 41) which is a ~50% reduction.
5) Aim Shot 15% Armor Reduction increases attacks against him by 7.5%.
6) This also shows it 2000 armor as a 15% reduction would give 1740 Armor which now blocks 42.5%.
7) 20% Armor Reduction Increases Damage by 10% against him.

That is what I know.
What I ~DONT~ know is how Level Affects this, and i have tested that extensively. That is where the plateau comes in and the level difference reduction is like X^((Defenders Level - Attackers Level)/4). Note, this can go negative which is where it becomes a damage magnification, and also the reason for those crazy damage values that high level players put out in low levels.

[Madnex]

Nice info we are gathering here. Yes, all normal mobs have two attacks; one normal and one that we could name as skill, which hits ~10% harder. When the skill-like attack involves a red zone, that number is up to even 250% at specific mobs. Then we have mobs like green trolls or shamans which also have a third, defensive skill-like attack (AoE panic, AoE healing) but this is off-topic here.

I mentioned this to kal during the tests but I guess we could repeat without counting the skill-like hits (personally this is not much of a problem since I take small videos to record the hits).

My question is, how does one test with 20% armor reduction? You mean 25% from the four-second myth gun proc?

[GoodSyntax]

I appreciate the assistance with testing Madnex!

Fluff, not sure where you got the info about the things that you know, but they are inline with my data.

What I am not understanding is why I am seeing solid evidence of banding. Is it possible that it is an artifact of the level of the gear I was using? Considering that the 1444 armor (upgraded mythic) is lv36, is it possible that average gear level is contributing to the high efficiency of damage reduction in that particular build?

[FluffNStuff]

My question is, how does one test with 20% armor reduction? You mean 25% from the four-second myth gun proc?

Kal is testing the Mob attacking them, in this case I was testing myself attacking the mob, so the armor reduction came from the pet.


I appreciate the assistance with testing Madnex!

Fluff, not sure where you got the info about the things that you know, but they are inline with my data.

What I am not understanding is why I am seeing solid evidence of banding. Is it possible that it is an artifact of the level of the gear I was using? Considering that the 1444 armor (upgraded mythic) is lv36, is it possible that average gear level is contributing to the high efficiency of damage reduction in that particular build?

When I test, I compare max to max and min to min since any kind of mean can be influenced by hi/low streaks. Do you have the min / max for each set?
Another thing to check is the Dodge value of each set. A higher dodge could increase the damage value as it would remove more auto attacks then skill attacks. (While skills can not be dodged per se, dodge does affect the hit/miss of the attacker and can increase the chance of a miss)

[Carapace]

You guys always impress us with your diligence and analytic information! Its great when you do things like this because it can be another perspective on a calculation or the way something works that is incorrect or should be looked at. When it comes to armor, it is not as clear cut a thing to externally test due to the number of variables involved however.

Here's a high level view of % Damage Reduction per point of armor per level.
102054

To be clear, there ARE modifiers tied to level difference, but they are applied as part of the damage value calculated between MIN and MAX values for an enemy ability. The value of armor is never anything but outside of the passive modifiers pointed out in the earlier thread. If you are level 41 and wear level 4 armor, you will receive the damage reduction % coefficient associated with being a level 41 player. In that sense your level 4 character will receive much more benefit from that level 4 armor because you receive a higher amount of damage reduction per point of armor at that level.

an Example of enemy damage may look something like this:
MIN: ((baseDamage*0.65)*(((level-target_level)*0.035)+1))
MAX: ((baseDamage*1.0)*(((level-target_level)*0.035)+1))

Note that this is an example, and not an actual calculation used by any AI in the game, though the idea is the same.
(The Players version is obviously more involved for dishing out damage, utilizing INT, DEX, STR and other factors combined together as part of level difference etc.)

Depending on the mob you are fighting, they may also have a "heavy" attack that does not have a significant visual distinction, and is thrown in randomly every 3-6 basic attacks or so, that would be responsible for some of those quirky values in your chart. Unexpected spikes or reductions in damage dealt from the AI, not the fluctuation of the players armor value and damage reduction.

As for Singe, yes 4% damage reduction is fairly large. Its one of those things that when you're in the know is quite a huge benefit, but without all the knowledge may look like a trivial stat. If your overall damage reduction is 50%, that 4% accounts for about 8% of your total armor. Nothing to scoff at!

I'm not sure if it answers questions specifically, however I hope it sheds some light on the dark object in the corner your trying to see.

-Carapace

[GoodSyntax]

Kal is testing the Mob attacking them, in this case I was testing myself attacking the mob, so the armor reduction came from the pet.



When I test, I compare max to max and min to min since any kind of mean can be influenced by hi/low streaks. Do you have the min / max for each set?
Another thing to check is the Dodge value of each set. A higher dodge could increase the damage value as it would remove more auto attacks then skill attacks. (While skills can not be dodged per se, dodge does affect the hit/miss of the attacker and can increase the chance of a miss)

Yes, I have max and min, but that's exactly why I use Geomean as opposed to Avg. Geomean smooths out the highs and lows for a more consistent value.

[GoodSyntax]

Thanks Carapace!!!! (I'm out of Thanks, but you'll get one from me as soon as it's available)

I knew the armor reduction was not as linear as was stated a long time ago.

So, from the chart, it seems to imply that incremental +Armor has a negligible difference in damage reduction; therefore, HP is the more desirable attribute going forward.

With that being the case, as the next wave of gear is introduced (Gladiator and Planar) isn't it counter-productive to provide ever increasing armor values (like Druid/Spirit)? Wouldn't it be more sensible for end-game to have higher HP, DMG, Crit in their gear?

[Carapace]

Thanks Carapace!!!! (I'm out of Thanks, but you'll get one from me as soon as it's available)

I knew the armor reduction was not as linear as was stated a long time ago.

So, from the chart, it seems to imply that incremental +Armor has a negligible difference in damage reduction; therefore, HP is the more desirable attribute going forward.

With that being the case, as the next wave of gear is introduced (Gladiator and Planar) isn't it counter-productive to provide ever increasing armor values (like Druid/Spirit)? Wouldn't it be more sensible for end-game to have higher HP, DMG, Crit in their gear?

We definitely have a method to the madness in how the armor is being added to new gear, and while its incremental its value certainly trails off in the long run. This is actually why health as a raw stat is finding its way as a more common stat on things like pets, gems (Elondrian for example) and the like. I would be cautious about neglecting armor, as every little bit does help, however there are certain skills and procs (Like the Glaive) that utilize armor value as part of other calculations that are worth considering depending on your play style.

It also means that as you level up higher, the raw Damage Reduction % stat becomes more valuable, as the amount of raw armor points required goes up.

Also of note, but the health gains from small increases in Dex, Int, and Str as part of better gear becomes more relevant as that level cap rises.

[MoloToha]

Meh, I thought that player always receives attackDamage-armorValue damage points (this scheme is pretty common), looks like I was wrong lol))

[Bigboyblue]

Very interesting information here. Thanks for sharing Carapace!!

[GoodSyntax]

So, I decided to continue digging a bit more and, using the data I already had, and Fluff's remark to track the Max and Min values, I created the following chart:

102491

What is interesting to note is that as armor levels increase, the delta between max and min damage seems to shrink. This implies that with more armor, the damage received by a mob attack becomes more consistent and far less peaky. Note how there is an 800 DMG differential with no armor, and with 1900 armor, this differential is spread by about 270.

Even the differential between 1729 armor and 1900 tells a great deal. The max/min differential at 1729 is 370, and at 1900 is down to 270. This 100 point difference spread over all the hits that you would receive in the average elite Tindirin run would account for dozens of health pots. If your offensive damage outweighs your need for defense, just be mindful of the cost burden this choice brings.

Clearly, a good tank, or a pair of good crowd control sorcerers will help a great deal in the decision to spec for DMG or defense.

I would be curious to see if this max and min value is an individual calculation, or if it is a party based calculation.....anyone up for some testing?

[GoodSyntax]

I've been doing some more research, and I don't think that the pseudo-formula that Carapace listed above is correct (at least it doesn't track anywhere close to the min/max chart above).

So, I did some mathematical vooodoo, and this is the formula I came up with, which tracks nicely with the min/max chart:

MIN: (1 - ((armor / level) * .01)) * baseDamage * (0.8)
MAX: (1 - ((armor / level) * .01)) * baseDamage * (1.2)

Given a mob base damage (in this case the unmasked spearman in Elite Jagged Trail) of 1500, the min/max results for each armor level matches up very nicely with my chart above.

So, what does this mean?

It means, as far as my data shows, that armor level plays an integral role in the calculation of mob min/max damage values.

I'll be performing some tests to see how this scales in party to see where it makes a difference (because I know it does).

[FluffNStuff]

I've been doing some more research, and I don't think that the pseudo-formula that Carapace listed above is correct (at least it doesn't track anywhere close to the min/max chart above).

So, I did some mathematical vooodoo, and this is the formula I came up with, which tracks nicely with the min/max chart:

MIN: (1 - ((armor / level) * .01)) * baseDamage * (0.8)
MAX: (1 - ((armor / level) * .01)) * baseDamage * (1.2)

Given a mob base damage (in this case the unmasked spearman in Elite Jagged Trail) of 1500, the min/max results for each armor level matches up very nicely with my chart above.

So, what does this mean?

It means, as far as my data shows, that armor level plays an integral role in the calculation of mob min/max damage values.

I'll be performing some tests to see how this scales in party to see where it makes a difference (because I know it does).

Quick rewriting based on the way the game actually rolls:
MIN: (1 - ((armor / level) * .01)) * (baseDamage * (0.8) + 0 * (.4) * baseDamage)
MAX: (1 - ((armor / level) * .01)) * (baseDamage * (0.8) + 1 * (.4) * baseDamage)

So difference = (1 - ((armor / level) * .01)) * (.4) * baseDamage

Or to use extremes to show it, assume Armor = Level * 100 | 4,100 here, blocking EVERYTHING. Then the difference between them firing 5000 points of damage and them firing 10 points of damage would be zero.

[GoodSyntax]

I'm still trying to figure out how party size fits into the equation.

I just ran the same test with a max armor tank in party (duo party), and with my 1444 armor, I took on about 12% more damage than what I took on when solo. Not sure where this fits into the equation, but it's missing a variable somewhere that I'm still trying to work out. I'm not sure if the baseDamage is a ratio based on average armor value or if there is simply a static multiplier/divisor based on party size.

Still need more data to figure out how it works with parties.

[Jirikjurasek]

This should be armor reduction on lvl 41 via Carapace chart:
102979

Hard data:
Armor Blue Red Green
0 0.00% 0.00% 0.00%
100 2.30% 2.16% 2.43%
200 4.59% 4.32% 4.86%
300 6.89% 6.49% 7.30%
400 9.19% 8.65% 9.73%
500 11.49% 10.81% 12.16%
600 13.78% 12.97% 14.59%
700 16.08% 15.14% 17.03%
800 18.38% 17.30% 19.46%
900 20.68% 19.46% 21.89%
1000 22.97% 21.62% 24.32%
1100 25.27% 23.78% 26.76%
1200 27.57% 25.95% 29.19%
1300 29.86% 28.11% 31.62%
1400 32.16% 30.27% 34.05%
1500 34.46% 32.43% 36.49%
1600 36.76% 34.59% 38.92%
1700 39.05% 36.76% 41.35%
1800 41.35% 38.92% 43.78%
1900 43.65% 41.08% 46.22%
2000 45.95% 43.24% 48.65%
2100 48.24% 45.41% 51.08%
2200 50.54% 47.57% 53.51%
2300 52.84% 49.73% 55.95%
2400 55.14% 51.89% 58.38%
2500 57.43% 54.05% 60.81%
2600 59.73% 56.22% 63.24%
2700 62.03% 58.38% 65.68%
2800 64.32% 60.54% 68.11%
2900 66.62% 62.70% 70.54%
3000 68.92% 64.86% 72.97%

Column1 = Armor
Column2 = 2,297*10^-4 reduction per point of armor (this should be correct value) (Blue)
Column3 = 2,162*10^-4 reduction per point of armor (tolerance for 1 pixel mistake) (Red)
Column4 = 2,432*10^-4 reduction per point of armor (tolerance for 1 pixel mistake) (Green)

Value "2,297*10^-4 reduction per point of armor" has been read by pixel position of level 41 point in Carapace chart

[Jirikjurasek]

Just for comparison (Kalizza & Carapace) in one chart
103008

[Jirikjurasek]

... Armor Value * (Armor Modifier by level of attack mob) = Damage Reduction...

102044



As was said, creep dmg modifier is level based. Its impossible to calculate that modifier, because you can't measure dmg with and without it. However creep dmg modifier is useless for us, players, because we just need to know dmg reduction per point of armor.

Thanks for your thread and Carapace chart :-)

[Carapace]

The factor for parties you are not able to account for is a small variance in additional stats for mobs as part of playing with multiple players. Games like Diablo 2/3 do this, they just call it out when a player joins the world stating "Another hero has joined the game, Hell's minions grow stronger".

We do something similar to keep the challenge more or less normalized within reasonable amounts. Exceptional players will still plow through with this modifier in place, but it helps preserve the integrity of the experience.

[FluffNStuff]

The factor for parties you are not able to account for is a small variance in additional stats for mobs as part of playing with multiple players. Games like Diablo 2/3 do this, they just call it out when a player joins the world stating "Another hero has joined the game, Hell's minions grow stronger".

We do something similar to keep the challenge more or less normalized within reasonable amounts. Exceptional players will still plow through with this modifier in place, but it helps preserve the integrity of the experience.

The big question that seems to be on everyone's mind is whether that modifier is simply a function based on the number of players or does it take into account anything about the players other then just their level (armor/damage/rarity are some of the theories that have popped up)?

[Carapace]

while the specifics I cannot disclose, it is based on the number of players and not items/stats of the players involved in the party.

[Serancha]

Still doesn't explain why runs are so much more difficult with a maxed warrior present. When the majority of dps players agree with this, it's not a hallucination. We're also experienced enough not to believe it "just seems harder" due to their lack of damage or dps. And we're comparing a run of 4 dps to 3 dps + fatty - so it's not the number of players either.

[FluffNStuff]

while the specifics I cannot disclose, it is based on the number of players and not items/stats of the players involved in the party.


Can you disclose if the percent increase in stats is derived from the current mob stat or the original mob (Basicly, is it a compound rate or a simple rate).

An example would be health. Elite Mobs have about 10K health. If stats increased by 50% per player then after you add one player, it would go up by 5K to 15K.
Now the question is when the third player enters, does the stats go up by 50% of the original 10K or 50% of the current 15K.
The Differences would be:




Solo
Two Players
Three Players
Four Players


Simple 50%
10K
15K
20K
25K


Compound 50%
10K
15K
22.5K
33.75K