Comparison of Zeal and Vengeance
Diablo II Expansion, v. 1.09d
By Tommi Gustafsson
1. Introduction
Among paladins there has been a lot of discussion about choosing between Vengeance
and Zeal as the main attack skill. In this page, I examine the differences in damage
output of these two skills.
Monsters not immune to physical damage
I concentrate on the case of "normal monsters." I provide a formula for calculating
damage/second, and I use it to attain concrete results in an example case. The results
are listed in Section 4.
Monsters immune to physical damage
I do not discuss the case of PIs on this page. I can say that Vengeance is better
than Zeal against monsters immune to physical damage, if you do not normally deal
any elemental damage. However, if you are using a weapon with lots of elemental
damage, such as Baranar's Star, Zeal may prove more mana efficient (in terms of
damage/mana) thanks to its lower mana cost.
2. Comparison of Damage per Second
The following assumptions are made:
- Weapon damage is 100. (The choice has no effect on relative amounts, and I took
this one for clarity.)
- 100% chance to hit. (The choice has no effect on relative amounts, and I took this
one for clarity.)
- Strength is 150. This is close to what paladins normally have (Baranar's star requires
strength of 153).
- Zeal speed is 4 frames.
- Vengeance speed is 8 frames with Fanaticism, 10 frames without it.
- Fanaticism is at level 26 = +475% damage.
- The mercenary's Might is at level 27 = +300% damage.
- Hell difficulty (i.e. 50% physical resistance).
With regard to mercenaries, two cases are considered. In the first case, a high-level
might mercenary (slvl 27 might) is present. In the second case ("No Might Aura")
there is no might mercenary around. The numbers reported below are damage per second.
Its formula is available at the end of this report.
|
Against monsters
not immune to
fire, cold or lightning (e.g. cows)
|
|
Attack type
|
With Might (slvl 27)
|
No Might Aura
|
|
Zeal
+ Fanaticism (slvl 26)
|
3203
(all physical)
|
2266
(all physical)
|
|
Vengeance (slvl 28)
+ Fanaticism (slvl 26)
|
3777
(1602 physical, 2175 elemental)
|
3308
(1133 physical, 2175 elemental)
|
|
Vengeance (slvl 28)
+ Conviction (slvl 15+)
|
4168
(688 physical, 3480 elemental)
|
3793
(313 physical, 3480 elemental)
|
|
Vengeance (slvl 28)
+ Conviction (slvl 15+)
+ Fanaticism (slvl 26)
|
5952
(1602 physical, 4350 elemental)
|
5483
(1133 physical, 4350 elemental)
|
|
Against monsters immune to one element
(fire, cold or lightning)
|
|
Attack type
|
With Might (slvl 27)
|
No Might Aura
|
|
Zeal
+ Fanaticism (slvl 26)
|
3203
(all physical)
|
2266
(all physical)
|
|
Vengeance (slvl 28)
+ Fanaticism (slvl 26)
|
3052
(1602 physical, 1450 elemental)
|
2583
(1133 physical, 1450 elemental)
|
|
Vengeance (slvl 28)
+ Conviction (slvl 15+)
|
3008
(688 physical, 2320 elemental)
|
2633
(313 physical, 2320 elemental)
|
|
Vengeance (slvl 28)
+ Conviction (slvl 15+)
+ Fanaticism (slvl 26)
|
4502
(1602 physical, 2900 elemental)
|
4033
(1133 physical, 2900 elemental)
|
It seems that a high level Vengeance beats Zeal in all but two comparisons.
Flashing Fanaticism and Conviction
When you use both Conviction and Fanaticism with Vengeance, you have now and then to change to Conviction for 3 seconds that it gets reapplied. When you keep both auras constantly active, you lose the benefits of Fanaticism for about 40% of time.
Other considerations
Amplify damage
If monsters' physical resistance is reduced (e.g. due to amplify damage curse), Zeal may become better than Vengeance in terms of damage. In hell, you triple the physical portion of damage if amplify damage takes effect (because physical resistance is reduced from 50% to -50%).
Elemental damage
If one has additional elemental damage from equipment, Zeal makes a better use of them, because it hits twice as often as Vengeance.
Deadly strike
Deadly strike and critical strike affect only physical damage. Therefore, they are naturally more efficient when used with Zeal. To take deadly strike into account, you multiply the physical damage by (1 + DeadlyStrike / 100). For example, with 100% deadly strike (available on, e.g., Headstriker, the unique battle sword), Zeal damage goes up to 6206 per second (with Might) and 4532 per second (without Might). Vengeance damages are affected too, but to a lesser extent, because their physical damage portion is smaller.
3. Comparison of Other Aspects
Although the damage comparison would suggest using Vengeance, Zeal has some important properties that didn't come apparent in the analysis.
Life stolen per hit
Zeal deals more physical damage than Vengeance and hence leeches back more life, which may help you to survive in tough situations.
Mana consumption and mana stolen per hit
Zeal costs only 2 mana per 5 swings, while Vengeance costs over 10 mana per attack at high levels. You may need lots of mana leech with Vengeance, especially when you use Vengeance without Fanaticism.
Skill points
Zeal: You need to get Zeal only to skill level 4, which gives you 5 hits. +3 to skills is not difficult to get, and usually it is enough to put only 1 skill point into Zeal.
Vengeance and Conviction: Vengeance requires a full investment of 20 skill points and Conviction some 10-15 depending on your equipment.
Ease of play.
Zeal auto-targets, which makes playing easier. Zeal also hits up to five times, which reduces need for clicking and saves your fingers.
Fighting out of a mob
You can more easily fight your way out of a mob with Zeal. With faster attack speed, you have a better chance to making a successful attack before getting hit and going into hit recovery or block animation.
Stunning enemies
Fast hits of Zeal keep enemies with low life amounts stunned more often than hits of slower Vengeance. (Naturally only if Zeal damage exceeds 1/12 of monsters' life.) On the other hand, greater damage of Vengeance may stun also enemies with higher life.
4. Conclusion
Overall, it is not obvious if one skill is superiour to another. Both seem like very good choices to me. Vengeance is probably better in terms of damage, but Zeal, however, may prove handier thanks to its other properties.
Acknowledgements
-
Ophidian for pointing out that it is easier to fight your way out of mobs with Zeal than what it is with slower Vengeance.
Derivation of Damage per Second Results
Zeal
By using zeal, a paladin makes from up to 5 quick hits against enemies. Fundamentally, the zeal speed is twice as fast as the normal attack speed. Attack speed with zeal is capped at 4 frames. There are 25 frames per second.
Vengeance
Vengeance adds each fire, cold and lightning damage to the attack. The addition per element, which is based on the weapon's damage, is +70% at the first level and +6% per level thereafter. Because Vengeance adds three elements, the total elemental damage added is in effect +210% at the first level and +18% per level thereafter. In our example, we use level 28 vengeance, which adds +232% to each of the three elements. That is, +696% total bonus elemental damage. Vengeance's attack speed is normal one, which is capped at 8 frames.
Fanaticism
Fanaticism adds attack speed, attack rating and damage. Fanaticism makes it quite easy to attain attack speed caps. The damage added by fanaticism is 50% at the first level and +17% per level thereafter.
Might
Might aura increases damage by 40% at the first level and +10% per level thereafter. It is available on act 2 mercenaries and can go up to slvl 29 (level 97-99 mercs).
Conviction
Conviction lowers enemy resistances (fire, cold and lightning) and therefore it is useful for enhancing the damage from Vengeance. In Act 5 and the Secret Cow Level, a typical monster has zero resistances to elements it is not immune to. Conviction cannot lower resistances below -100% and cannot affect immunities at all. Below, two cases are considered:
- Monsters have 0% resistance to fire, cold and lightning
- Monsters are immune to one element (fire, cold or lightning) and have 0% resistance
to other elements.
Conviction is assumed to lower resistances (short of immunities) to -100% (i.e. it is level 15+), thus effectively doubling damage from elements.
Damage per second formula
It is assumed that there is a global physical resistance of 50% (that's what it is in hell difficulty), which halves all physical damage. That's why there is 0.50 multiplier in the formula before all physical parts.
The damage per second formula is the following:
DamagePerSecond = WeaponDamage * (0.50 * (1 + Strength / 100 + MightBonus / 100 + FanaticismBonus / 100) + NoOfElements * VengeanceBonus / 100) * 25 / AttackFrames * ChanceToHit / 100
where
WeaponDamage includes the weapon's base damage and modification from enhanced damage (on weapon only) and the effects of +max damage and +min damage equipment.
NoOfElements is 3 when there are no immunities and 2 if a monster is immune to either fire, cold or lightning.
VengeanceBonus is the damage from one element. It is zero when one uses zeal and is doubled when Conviction is in effect.