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 Attack Level and Defense Level Demystified

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DivineMyst
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PostSubject: Attack Level and Defense Level Demystified   Fri Jan 20, 2012 9:23 pm

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)

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

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.

Code:
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:

Code:
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

Code:
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.

Code:

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

Code:

          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
Spoiler:
 
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.


Stolen from: http://pwi-forum.perfectworld.com/showthread.php?p=7770212

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