Attack Level and Defense Level Demystified

Asterelle - Sanctuary_1381265973

The latest entry in the popular Demystified series: Attack Level and Defense Level

Please check this PWI WIKI article for a comprehensive guide to Attack/Defense levels and all other game mechanics.

TL; DR Formula
If Attack Level > Defense Level:
damage = damage dealt * (1 + (A - D)/100)
else
damage = damage dealt / (1 + 1.2 * (D - A)/100)

Background:

Alright so there was some confusion about the effects of combining attack level and defense level. There were two theories...

1) damage = damage dealt * (1 + (A - D)/100)
2) damage = damage dealt * (1.01)^A * (0.99)^D

where A is attacker attack level and D is defender defense level

Test:
Feel free to skip this section. I tested on a target, Linnkotsu, in fb19 with a combination of lvl 10 Frenzy and the Dominance Blessing. My normal test dummy, Quilue, was unavailable. This was a duel using only punches which deal a fixed physical damage.

Raw damage in a duel using punches 
with dominance blessing and frenzy.

          ATT+00 ATT+10  ATT+20  ATT+30
         _______________________________

+00DEF |   141    155     169     183
+10DEF |   126    141     155     169

Dividing out by the base damage 141 and keeping 3 significant figures:

Normalized Damage
          ATT+00 ATT+10  ATT+20  ATT+30
         _______________________________

DEF+00 |   1.00   1.10    1.20    1.30
DEF+10 |   0.90   1.00    1.10    1.20

Values Predicted by (1.01^A * 0.99^D)
          ATT+00 ATT+10  ATT+20  ATT+30
         _______________________________

DEF+00 |   1.000  1.105   1.220   1.348
DEF+10 |   0.904  0.999   1.104   1.219

This exactly matches: (1 + (A - D)/100) and disproves 1.01^A * 0.99^D.

Looking at Higher Defense Levels:
After my initial results I was told that the formula doesnt hold for higher defense levels and collected data to test this. For this I used unarmed attacks against a psychic with varying defense levels.

ATT	DEF	DAM	DEC% 	ATT-DEF
0	0	1227	0	0
0	41.8	822	-33.00	-41.8
0	36.3	856	-30.23	-36.3
20	41.8	980	-20.13	-21.8
20	36.3	1029	-16.13	-16.3
0	5.5	1157	-5.70	-5.5
20	5	1411	14.99	15
20	0	1472	19.96	20

(1+(A-D)/100) matches exactly for positive values of (A-D) but not negative negative.
azukaya was able to find a matching formula in this post:
http://pwi-forum.perfectworld.com/showpost.php?p=9805402&postcount=110

For D > A: 1/(1 + 1.2(D - A)/100)

Effect of Full Sharding:
Let's see the effect on the effective enemy HP with full 24 stone sharding in addition to +8 attendance blessings.

Effective HP is how much damage an enemy can absorb before dying:

effective HP = base HP / defense reduction

          ATT+00 ATT+24 ATT+32 
         ____________________

DEF+00 |   1.000  0.806  0.758
DEF+24 |   1.288  1.000  0.926
DEF+48 |   1.576  1.288  1.192
DEF+56 |   1.672  1.384  1.288

If you have a ATT+32 advantage they are 24.2% easier to kill.
If enemy has a DEF+24 advantage they are 28.8% harder to kill.
If enemy has a DEF+48 advantage they are 57.6% harder to kill.
If enemy has a DEF+56 advantage they are 67.2% harder to kill.


Here's a chart showing the effectiveness of defense level sharding versus various attack levels

http://imgur.com/w81Eh.png

The blue line is for an attacker with attack level = 0 and corresponds to PVE pretty much.
The red line (attack level = 15) is for someone wearing the anniversary blessing.
The yellow (attack level for someone wearing Jones blessing.
The green is someone DoT Sharded with attack level = 45

You can see that defense sharding actually becomes more effective after you get more defense level then their attack level.


Conclusion:
The correct attack level formula is:

If Attack Level > Defense Level:
damage = damage dealt * (1 + (A - D)/100)
else
damage = damage dealt / (1 + 1.2 * (D - A)/100)

Attack level exactly cancels out defense level but attack level has diminishing returns while defense level has constant returns. The full sharding with DEF+1 stones isn't really more effective than Citrine gems or Vit stones for most classes unless they have high base HP. DEF+2 sharding is nice but when comparing them to Vit Gems keep in mind that Vit Gems add to both HP and defense.

Teppeii - Dreamweaver

Impressive. Thank you very much for clearing this up^^

Telarith - Sanctuary

I don't get who was confused. This website itself flat out tells you what the formulas were. In warsoul weapon section, it says 50 ATK lvl is 50% more damage, which let's you know 1 ATK directly equals 1% more damage. On character screen, it tells you it's the difference in ATK lvl or DEF lvl that determines over-all effect of the higher number, which means you subtract them first before applying their effect. The answer was always there since they made the Warsoul guide.

Asterelle - Sanctuary_1381265973

Telarith - Sanctuary wrote: »

I don't get who was confused. This website itself flat out tells you what the formulas were. In warsoul weapon section, it says 50 ATK lvl is 50% more damage, which let's you know 1 ATK directly equals 1% more damage. On character screen, it tells you it's the difference in ATK lvl or DEF lvl that determines over-all effect of the higher number, which means you subtract them first before applying their effect. The answer was always there since they made the Warsoul guide.

There was confusion and descriptions are not always reliable.

Olba - Sanctuary

Pardon me, but am I the only one who's thinking Ast might be a tsundere?

Furries - Dreamweaver

Nice guide, but i don't see how this was a mystery. Doesn't it specially say that in game?

what is a mystery to me is how the game calculates drop reduction rates in a sqaud

Smobo - Heavens Tear

The comparing HP shards to def shards thing seems to be lacking one fundimental thing, the fact you can heal in this game. You can't forget that as long as you don't hit your cap on HP, that a source of healing also gets thrown into the formula you mentioned. So:

effective healing = base healing / (1 + (A - D)/100)

So long as you don't get healed to full HP.

People seem to like to focus on HP a lot, and not overly care too much about defense. Your real goal is to have your healing over time be higher than your opponents damage over time, and have a sufficient buffer that your hp doesn't spike down to 0 before your healing sets in.

Asterelle - Sanctuary_1381265973

I can't believe you guys are disputing that not everyone knows how attack level works or how they combine. In other news these posts never existed:

Chezedude - Dreamweaver wrote: »

the actual damage you take when you have X defense lvl is:

normal damage * (0.99)^X

Illyana - Dreamweaver wrote: »

Adding a bit of anecdotal and second hand evidence here...

From what I can tell without doing too many formal tests, attack level has increasing returns and defense levels have diminishing returns.

Specifically, damage modified by attack level is Dmg * 1.01^Atk Lvl

and Defense level is modified by Dmg Dealt * .99 ^ Def Lvl

Chezedude - Dreamweaver wrote: »

constant returns. any additional increase in atk or def lvl provide constant % increase to current damage.

Michael_dark - Lost City wrote: »

I'm still not convinced that it's based solely on a percentage... (even though that would make sense) as when you are attacking/defending against creatures significantly higher or lower, the penalties would seem to be more than just 1% per level.

Admittedly, I haven't done any strict or methodological testing, but just from observation, there would seem to be other factors involved.

WaffleChan - Sanctuary wrote: »

i have a theory about attack level, that its not so much a %, but the game treating you like youre x levels higher.

Yah noone's ever been confused.

oyamajio

Damn, I hate you now. I'll find it harder to get DoD cheap. I like it better when people are still in the middle of ocean and have no clue which direction to go exactly. ><

Devoted - Lost City

oyamajio wrote: »

Damn, I hate you now. I'll find it harder to get DoD cheap. I like it better when people are still in the middle of ocean and have no clue which direction to go exactly. ><

hehe, that's why buying 30 of them before they were considered anything but trash = win b:thanks

DeathBanana - Heavens Tear

This would do good in General Discussion as well, as other classes can shard attack and defense level shards too b:surrender

Smobo - Heavens Tear

DeathBanana - Heavens Tear wrote: »

This would do good in General Discussion as well, as other classes can shard attack and defense level shards too b:surrender

Too much math and logic in this thread. Anyone who isn't an archer knows to look here if they want math related things. b:chuckle

Asterelle - Sanctuary_1381265973

DeathBanana - Heavens Tear wrote: »

This would do good in General Discussion as well, as other classes can shard attack and defense level shards too b:surrender

General Discussion is a cesspool, **** other classes.
Archer Forums b:kiss

Chezedude - Dreamweaver

the 10 def lvl is too low to tell a difference, 90% damage and 90.4% damage is a difference of maybe 1 damage or less. It possibly shows that attack lvl is A% but for def level it's not enough data.

Since when I punched someone with 46 def lvl it was only reducing about 36%, def definitely doesn't work as D% reduce.

Quilue - Sanctuary

rofl, i cant believe you dragged linn to a dark cave to do damage testing with him.

MagicHamsta - Lost City

Quilue - Sanctuary wrote: »

rofl, i cant believe you dragged linn to a dark cave to do damage testing with him.

Asterelle - Sanctuary wrote: »

My normal test dummy, Quilue, was unavailable.

Quilue be too worn out from the testing of Asterelle
b:surrender
so Asterelle had to drag linn into a dark cave.
>.<'

Hypnos - Raging Tide

I suggest you test it on a Psychic with 66 def lvl to see how it turn out
white voodoo def lvl increase by lvl -> 36.3 - 39.6 - 42.9 - 46.2 - 49.5 -...-66
enough sample ?

DeathBanana - Heavens Tear

Smobo - Heavens Tear wrote: »

Too much math and logic in this thread. Anyone who isn't an archer knows to look here if they want math related things. b:chuckle

<---cleric

Asterelle - Sanctuary_1381265973

Chezedude - Dreamweaver wrote: »

the 10 def lvl is too low to tell a difference, 90% damage and 90.4% damage is a difference of maybe 1 damage or less. It possibly shows that attack lvl is A% but for def level it's not enough data.

Since when I punched someone with 46 def lvl it was only reducing about 36%, def definitely doesn't work as D% reduce.

Yeah I think you're right and +10 DEF level didnt go far enough.

I repeated the test with wingspan to deal greater damage to give more precision. Qui turns out to have a low level psychic which voodoo level 1.

The data does seem to diverge with larger values of DEF:

ATT	DEF	DAM	DEC% 	ATT-DEF
0	0	1227	0	0
0	41.8	822	-33.00	-41.8
0	36.3	856	-30.23	-36.3
20	41.8	980	-20.13	-21.8
20	36.3	1029	-16.13	-16.3
0	5.5	1157	-5.70	-5.5
20	5	1411	14.99	15
20	0	1472	19.96	20

(1+(A-D)/100) matches exactly for positive values of (A-D) but not negative negative. I dont think 0.99^(D-A) quite matches up for that but its close. I need to play with the numbers a bit more to figure it out.

Atm it looks like a stepwise function:

if (A - D > 0)  
    then  (1 + (A-D)/100)
else
    ???  something close to 1.01^(A-D)..

DeathBanana - Heavens Tear

Heh, so much for demystifying

Asterelle - Sanctuary_1381265973

Yeah... I feel so ashamed for being sloppy T_T

I should have thought of investigating larger defense values. Once I fit a better relation to defense levels I'll update the first post. It does seem like the only value that matters is (Attack Level - Defense Level).

DeathBanana - Heavens Tear

I'm not so sure about that; when I fiddle around with it, the first value (the one supposedly close to .99) seems to change with every number set, I suspect either a hidden variable, rounding error, or I'm stupid. Also, from the 5.5 DEF one to the 20 ATK 41.8 DEF, the % added (negative, so reduced) seems to go ever so slightly beyond the positive formula. Again, hidden variable or I'm stupid.

Chezedude - Dreamweaver

this second formula seems a lot closer to what it should be. Otherwise you can make a physic with over 100 def lvl using def shards and voodoo and would be unkillable lol.

Hypnos - Raging Tide

cheze will be the main sponsor in unlockin Atk/Def Level mission YAY

Myerling - Sanctuary

why can't we just fit the negative (A-D) data with some sort of polynomial regression and just see if that works? >.> laziness strikes

Borsuc - Raging Tide

Asterelle - Sanctuary wrote: »

Yeah I think you're right and +10 DEF level didnt go far enough.

I repeated the test with wingspan to deal greater damage to give more precision. Qui turns out to have a low level psychic which voodoo level 1.

The data does seem to diverge with larger values of DEF:

ATT	DEF	DAM	DEC% 	ATT-DEF
0	0	1227	0	0
0	41.8	822	-33.00	-41.8
0	36.3	856	-30.23	-36.3
20	41.8	980	-20.13	-21.8
20	36.3	1029	-16.13	-16.3
0	5.5	1157	-5.70	-5.5
20	5	1411	14.99	15
20	0	1472	19.96	20

(1+(A-D)/100) matches exactly for positive values of (A-D) but not negative negative. I dont think 0.99^(D-A) quite matches up for that but its close. I need to play with the numbers a bit more to figure it out.

Atm it looks like a stepwise function:

if (A - D > 0)  
    then  (1 + (A-D)/100)
else
    ???  something close to 1.01^(A-D)..

The most logical formula, without any "conditional" ifs would be the mathematical one... of course that doesn't mean the devs used it, but it's pretty close to your data anyway. If 100 attack gives you 2x damage then 100 defense should give you half damage, though I don't know how it works in the game.

(1 + A / 100) / (1 + D / 100)

It's not far off from your data, can anyone with White Voodoo please try higher defense values? b:thanks

FitHitDShan - Sanctuary

These data look like a pretty good fit to an exponential curve. Cyanea's theory 3: damage = damage dealt * 1.01^(A-D) is looking like a much stronger explanation as we see the curvature at extreme values.

Illyana - Dreamweaver

Fun topic! I was hoping something about def/atk lvls would prod you into some formal testing. It is much easier to read and comment and pipe in occasionally than it is to do the testing myself

That, and I myself won't have to drag someone into a dark cave for hours of bare fisted action b:chuckle b:chuckle

Asterelle - Sanctuary_1381265973

Punches failed me for this experiment since they didn't deal enough damage to see the trend at higher defense levels. Using wingspan with no weapon will let you do much higher fixed damage than punches.

I'm not happy with the result. The 0.99^(D-A) and 1.01^(A-D) are both off by like 1% at defense level of 40 which makes me think it could be even further off for larger defense levels.

I need to find a high level psychic with maxed tideform and voodoo I think but I'm really not very active in game these days.

FapFapFap - Raging Tide

Too lazy to compare but 68 def lvl reduced the dmg to 47%(+/- 1%) of the dmg with -10 def lvl (Fist BM dmg: ~850->~400).
So basically 78 def lvl reduced the dmg by 53%, maybe it's useful for u pwi-scientists

Asterelle - Sanctuary_1381265973

FapFapFap - Raging Tide wrote: »

Too lazy to compare but 68 def lvl reduced the dmg to 47%(+/- 1%) of the dmg with -10 def lvl (Fist BM dmg: ~850->~400).
So basically 78 def lvl reduced the dmg by 53%, maybe it's useful for u pwi-scientists

Can you do that without any "+/-" or "~"? Easiest would be to take off your armor and duel a weaponless caster before and after voodoo/tideform/blessing. The higher the defense level the better and weaponless attacks always have fixed damage.