Stoutwood
17-07-2006, 06:37
Introduction
One of the most confusing aspects of Diablo II is the "-XX% Target Defense" mod. It shows up on different weapons and skills, and the fact that the skill version and weapon version work differently only causes more misinformation to spread across the internet. Another mod, called "Ignore Target Defense" sounds similar, thus causing many people to assume that both mods work in a similar fashion. "Ignore Target Defense" has been shown not to work in PvP, which results in many melee characters wondering if the same could be true of "-XX% Target Defense".
In 1.09, the eth rune not only worked, but was bugged. It would reduce the target's defense to 25% of its original value, making defense all but worthless. When the new patch came, people soon found out that this bug had been patched. This raised a new question, how does it work now?
Conviction
Before I go over the various theories, let me first shed light on how Conviction works. Luckily, Conviction visibly reduces defense on the character screen, making this test considerably easier than the -XX% Target Defense tests. For this test I simply grabbed my Zealot and had a friend throw Conviction on me with his V/T.
FoH paladin Conviction: -86%
Base Defense on Zealot: 3388
Holy Shield ED: 835%
Defense after Holy Shield: 31677
Defense after Holy Shield with Conviction: 28764
So my Zealot has a base defense of 3388, which is multiplied by a holy shield bonus of 835% ED, thus giving him (3388 def * (1 + 8.35) = 31677 defense. Now what conviction does is subtract the 95% directly from his ED bonus, meaning he is actually getting a bonus of 749% ED. This leaves him with (3388 def * (1 + 7.49)) = 28764 defense.
Theory
The Arreat Summit at http://www.battle.net/diablo2exp states that the Chance to Hit formula is:
Chance to Hit: 100 * AR / (AR + DR) * 2 * alvl / (alvl + dlvl)
This means that it is a probability function. If you have taken a Calculus or Statistics course, you know that while each individual hit is a gamble, as the number of hits go to infinity the percentage will approach the probability value. Marcus (MrJ) and I decided on doing 3 tests of 200 hits each, then dividing the number of successful hits by 200 to arrive at the percentage. We also made both characters the same level, simplifying the calculation to:
Chance to Hit: 100 * AR / (AR + DR)
The previous section demonstrates that Conviction functions by taking the percentage directly off of the target's total Enhanced Defense from skills. Because both the skill and the weapon mod bear the title "-XX% Target Defense", it is reasonable to postulate that the two work in the same manner. Thus, in future calculations, I will include a possibility for Conviction.
There are other theories as well. One is that the mod doesn't work at all. This will be easy to prove, since only one calculation is needed. Another is that it works on the total defense at half efficiency, meaning a mod that says -25% Target Defense would actually be applied at -12.5% Target Defense. Some people also claim that it acts at full efficiency, and that will be considered as well.
The final theory that I have heard is that it works on the base defense. That is, if you have a character with 4000 defense multiplied at 800% by a skill, the mod will take the defense off of the 4000, then multiply that number by 800%. This is a cumbersome calculation, so I will address it now and save myself the trouble. The equation for reducing base defense and total defense results in the same answer. Save yourself the confusion and just say that it takes off of the total.
Test
MrJ and I ran the test on Open, since the builds we needed had to be made-to-order. Here are the stats:
Attacking Character:
Attack Rating: 19999
Defending Character:
Base Defense: 12308
Enhanced Defense from Defiance: +550%
Total Defense: 80002
Anyway, the defending character only wore armor. He had no shield, so block wasn't a factor in this test. The attacking character used normal attack, and received all of his AR from the weapon. The increments of -XX% Target Defense used were -25%, -50%, -100%, and -200%. We tallied the number of hits and recorded them.
Melee attacks will never have less than 5% or more than 95% chance to hit.
-25% Target Defense
CTH if -TD Doesn't Work: 20%
CTH if -TD Works at Full Efficiency: 25%
CTH if -TD Works at Half Efficiency: 22.2%
CTH if -TD Works like Conviction: 20.6%
Test 1: 44/200 = 22%
Test 2: 42/200 = 21%
Test 3: 37/200 = 18.5% - Outlaying Value
-50% Target Defense
CTH if -TD Doesn't Work: 20%
CTH if -TD Works at Full Efficiency: 33.3%
CTH if -TD Works at Half Efficiency: 25%
CTH if -TD Works like Conviction: 20.6%
Test 1: 49/200 = 24.5%
Test 2: 39/200 = 19.5% - Outlaying Value
Test 3: 48/200 = 24%
-100% Target Defense
CTH if -TD Doesn't Work: 20%
CTH if -TD Works at Full Efficiency: 95%
CTH if -TD Works at Half Efficiency: 33.3%
CTH if -TD Works like Conviction: 22.8%
Test 1: 82/200 = 41% - Outlaying Value
Test 2: 61/200 = 30.5%
Test 3: 68/200 = 34%
-200% Target Defense
CTH if -TD Doesn't Work: 20%
CTH if -TD Works at Full Efficiency: 95%
CTH if -TD Works at Half Efficiency: 95%
CTH if -TD Works like Conviction: 26.5%
Test 1: 184/200 = 92%
Test 2: 181/200 = 90.5% - Outlaying Value
Test 3: 184/200 = 92%
Conclusion
As you can see, the numbers indicate that -XX% Target Defense does works in PvP by taking the percentage off of the total defense at half efficiency. The outlaying values can be attributed to the nature of the experiment, with the results staying around the projected value. If you would like more exact numbers, feel free to do tests of 400, 1000, or 1000000 hits. Count me out though.
Special Thanks
Marcus - I couldn't have done this test without you. Thanks for the patience.
Brian - All of the D2 theorizing.
Dave - PMAOing entire games.
Ant - The emo king. Also thanks for showing me Dead Poetic.
Alex/Andrew/Eric - The endless hours of abusing randoms.
Nick - Keeping that channel full of at least one person.
RDS - Without you, I would have no one to prove wrong.
Any Temple members I may have forgotten. Without you, I would have quit this game years ago.
One of the most confusing aspects of Diablo II is the "-XX% Target Defense" mod. It shows up on different weapons and skills, and the fact that the skill version and weapon version work differently only causes more misinformation to spread across the internet. Another mod, called "Ignore Target Defense" sounds similar, thus causing many people to assume that both mods work in a similar fashion. "Ignore Target Defense" has been shown not to work in PvP, which results in many melee characters wondering if the same could be true of "-XX% Target Defense".
In 1.09, the eth rune not only worked, but was bugged. It would reduce the target's defense to 25% of its original value, making defense all but worthless. When the new patch came, people soon found out that this bug had been patched. This raised a new question, how does it work now?
Conviction
Before I go over the various theories, let me first shed light on how Conviction works. Luckily, Conviction visibly reduces defense on the character screen, making this test considerably easier than the -XX% Target Defense tests. For this test I simply grabbed my Zealot and had a friend throw Conviction on me with his V/T.
FoH paladin Conviction: -86%
Base Defense on Zealot: 3388
Holy Shield ED: 835%
Defense after Holy Shield: 31677
Defense after Holy Shield with Conviction: 28764
So my Zealot has a base defense of 3388, which is multiplied by a holy shield bonus of 835% ED, thus giving him (3388 def * (1 + 8.35) = 31677 defense. Now what conviction does is subtract the 95% directly from his ED bonus, meaning he is actually getting a bonus of 749% ED. This leaves him with (3388 def * (1 + 7.49)) = 28764 defense.
Theory
The Arreat Summit at http://www.battle.net/diablo2exp states that the Chance to Hit formula is:
Chance to Hit: 100 * AR / (AR + DR) * 2 * alvl / (alvl + dlvl)
This means that it is a probability function. If you have taken a Calculus or Statistics course, you know that while each individual hit is a gamble, as the number of hits go to infinity the percentage will approach the probability value. Marcus (MrJ) and I decided on doing 3 tests of 200 hits each, then dividing the number of successful hits by 200 to arrive at the percentage. We also made both characters the same level, simplifying the calculation to:
Chance to Hit: 100 * AR / (AR + DR)
The previous section demonstrates that Conviction functions by taking the percentage directly off of the target's total Enhanced Defense from skills. Because both the skill and the weapon mod bear the title "-XX% Target Defense", it is reasonable to postulate that the two work in the same manner. Thus, in future calculations, I will include a possibility for Conviction.
There are other theories as well. One is that the mod doesn't work at all. This will be easy to prove, since only one calculation is needed. Another is that it works on the total defense at half efficiency, meaning a mod that says -25% Target Defense would actually be applied at -12.5% Target Defense. Some people also claim that it acts at full efficiency, and that will be considered as well.
The final theory that I have heard is that it works on the base defense. That is, if you have a character with 4000 defense multiplied at 800% by a skill, the mod will take the defense off of the 4000, then multiply that number by 800%. This is a cumbersome calculation, so I will address it now and save myself the trouble. The equation for reducing base defense and total defense results in the same answer. Save yourself the confusion and just say that it takes off of the total.
Test
MrJ and I ran the test on Open, since the builds we needed had to be made-to-order. Here are the stats:
Attacking Character:
Attack Rating: 19999
Defending Character:
Base Defense: 12308
Enhanced Defense from Defiance: +550%
Total Defense: 80002
Anyway, the defending character only wore armor. He had no shield, so block wasn't a factor in this test. The attacking character used normal attack, and received all of his AR from the weapon. The increments of -XX% Target Defense used were -25%, -50%, -100%, and -200%. We tallied the number of hits and recorded them.
Melee attacks will never have less than 5% or more than 95% chance to hit.
-25% Target Defense
CTH if -TD Doesn't Work: 20%
CTH if -TD Works at Full Efficiency: 25%
CTH if -TD Works at Half Efficiency: 22.2%
CTH if -TD Works like Conviction: 20.6%
Test 1: 44/200 = 22%
Test 2: 42/200 = 21%
Test 3: 37/200 = 18.5% - Outlaying Value
-50% Target Defense
CTH if -TD Doesn't Work: 20%
CTH if -TD Works at Full Efficiency: 33.3%
CTH if -TD Works at Half Efficiency: 25%
CTH if -TD Works like Conviction: 20.6%
Test 1: 49/200 = 24.5%
Test 2: 39/200 = 19.5% - Outlaying Value
Test 3: 48/200 = 24%
-100% Target Defense
CTH if -TD Doesn't Work: 20%
CTH if -TD Works at Full Efficiency: 95%
CTH if -TD Works at Half Efficiency: 33.3%
CTH if -TD Works like Conviction: 22.8%
Test 1: 82/200 = 41% - Outlaying Value
Test 2: 61/200 = 30.5%
Test 3: 68/200 = 34%
-200% Target Defense
CTH if -TD Doesn't Work: 20%
CTH if -TD Works at Full Efficiency: 95%
CTH if -TD Works at Half Efficiency: 95%
CTH if -TD Works like Conviction: 26.5%
Test 1: 184/200 = 92%
Test 2: 181/200 = 90.5% - Outlaying Value
Test 3: 184/200 = 92%
Conclusion
As you can see, the numbers indicate that -XX% Target Defense does works in PvP by taking the percentage off of the total defense at half efficiency. The outlaying values can be attributed to the nature of the experiment, with the results staying around the projected value. If you would like more exact numbers, feel free to do tests of 400, 1000, or 1000000 hits. Count me out though.
Special Thanks
Marcus - I couldn't have done this test without you. Thanks for the patience.
Brian - All of the D2 theorizing.
Dave - PMAOing entire games.
Ant - The emo king. Also thanks for showing me Dead Poetic.
Alex/Andrew/Eric - The endless hours of abusing randoms.
Nick - Keeping that channel full of at least one person.
RDS - Without you, I would have no one to prove wrong.
Any Temple members I may have forgotten. Without you, I would have quit this game years ago.