Smite DamageModifiers that do NOT apply to Smite- Weapon's base damage
- +% Enhanced Damage on the weapon
- + to Minimum/Maximum Damage *)
- +% Damage to Demons/Undead
- % Critical/Deadly Strike
- % Life/Mana Stolen per Hit
- Magic, Fire, Lightning, Cold, and Poison Damage
- Cold and poison length
Ref: Basin Wiki, Paladin Combat Skills,
http://wiki.theamazonbasin.com/index.php/Paladin_Combat_Skills#Smite*) including Adds Y-Z Damage (read: +Y to Minimum Damage, +Z to Maximum Damage) whether on the weapon or off-weapon (War Traveler).
How is Smite Damage calculated ?- Take the shield's Smite Damage
Add bonus Smite Damage from Holy Shield (HS)
Add X from Damage +X (Grief, Astreon's Iron Ward, The Redeemer, Stone Crusher) - Add the sum of Enhanced Damage bonuses from the following sources
+% ED from Strength (in a 1:1 ratio, regardless of weapon used)
+% ED from skills (Smite, Might, Concentration, Fanaticism)
+% ED which is off-weapon (e.g. Fortitude)
Smite Damage Formula- Physical Damage = [ ( {Shield_min + HS_min , Shield_max + HS_max} + X ) * ( 1 + Strength/100 + (skill +% ED)/100 + (off-weapon +% ED)/100 ) ]
{,}: minimum and maximum values, [ ]: final values are truncated
Smite Speed Modifiers- Weapon Speed Modifier (WSM), the base weapon speed
- Increased Attack Speed (IAS) from equipment
- Effective IAS (EIAS) from Fanaticism
Ref: Smite FAQ,
http://forums.battle.net/thread.html?topicId=10971909421&sid=3000Which base weapon for Black, Grief, and Last Wish ?- Black (club, hamm, mace)
The fastest of the allowed weapon types with 3-socket potential are Flail, Knout, and Scourge (-10 WSM). We pick the Flail below, as it is usually the easiest to obtain. - Grief (swor, axe)
Phase Blade (-30 WSM) is the fastest base weapon available (and it is even indestructible by default). - Last Wish (swor, hamm, axe)
Phase Blade (-30 WSM), by the same reasoning.
To calculate the Average Damage Taken (the average physical damage inflicted to the Übers after Damage Resist), we summarise the weapon modifiers applying to Smite in the following table,
Code
Weapon Modifier WSM 7 FPA 1) 6 FPA 2) Smite ED HS_min-max
Black 40 % Chance of Crushing Blow + 60 % +129 % / +375 % +77-80
(Flail) +15 % IAS -10 + 34 %
Grief Damage +340-400 + 24 % + 65 % / +375 % +77-80
(Phase Blade) +30-40 % IAS -30 + 7 %
Last Wish 60-70 % Chance of Crushing Blow + 24 % + 65 % / +375 % +77-80
(Phase Blade) Level 17 Might Aura when equipped -30 + 7 %
[+200 to skill +% ED]
Astreon's IW 33 % Chance of Crushing Blow + 60 % +129 % / +405-435 % +(85-93)-(88-96)
(Caduceus) Damage +40-85 -10 + 34 %
+2-4 to Combat Skills (Paladin Only)
+10 % IAS
Heaven's Light 33 % Chance of Crushing Blow + 86 % +180 % / +405-420 % +(85-89)-(88-92)
(Mighty Scepter) +2-3 to Paladin Skill Levels 0 + 52 %
Socketed (1-2)
+20 % IAS
Stormlash 3) 33 % Chance of Crushing Blow + 60 % +129 % / +375 % +77-80
(Scourge) 20 % CtC Level 18 Tornado on striking -10 + 34 %
15 % CtC Level 10 Static Field on striking
+30 % IAS
1) Minimum IAS for 7-frame Smite (7 FPA) without Fanaticism (while running Salvation against Über Mephisto, we want at least 7 FPA)
2) Minimum IAS for 6-frame Smite (6 FPA) without Fanaticism / with Fanaticism: Level 23 (25-26 for Heaven's Light; still +36 % EIAS)
Smite IAS breakpoints based on TitanSeal's Attack Speed Calculator
25 frames = 1 second
3) Level 18 Tornado (unsynergised): 233-253 (ø243) physical damage before Damage Resist (DR)
Über Mephisto: 20 % DR, 110 % LR (immune to lightning). Static Field will have no effect
Pandemonium Diablo, Über Baal: 50 % DR, 75 % LR. Static Field is reduced to 25 % effect
Note: even without Fanaticism and even with the lowest possible IAS on Grief (+30 %), our Smite speed reaches the maximum 6 FPA with a Grief PB, Highlord's Wrath (+20 %), and a +15 % IAS Jewel (Helm or HoZ).
Thus, while running Salvation against Über Mephisto, we lose only the skill +% ED from Fanaticism when using Grief.
The other weapons suffer a minor loss of speed, dropping from 6 FPA (4.16 attacks per second) to 7 FPA (3.57 attacks per second), given sufficient IAS. Even a Heaven's Light can easily reach 7 FPA (+86 % IAS) thanks to the 2 sockets. Once Mephisto is no more, we switch to Fanaticism and maintain a 6-frame Smite with either weapon.
Crushing Blow (CB) + Average Damage Taken (ADT)CB and OW odds, ADT, and Smite speed values are given in the table below. Indicated weapon stats used. Assuming +15 % off-weapon ED on Duress (Grief).
Code
Full equipment
Chance of Crushing Blow (CB %), Chance of Open Wounds (OW %), and Average Damage Taken (ADT)
Herald of Zakarum (Gilded Shield)
Weapon Stats CB % 4) OW % Strength Physical Damage DR ADT FPA 4)
Black 100 25 170 916-1020 20 % 774 7
(Flail) 1327-1478 50 % 701 6
Grief +370 75 58 170 3082-3154 20 % 2494 6
(Phase Blade) 5062-5181 50 % 2560 6
Last Wish 65+ % 100 25 185 1125-1252 20 % 950 7
(Phase Blade) 1536-1710 50 % 811 6
Astreon's IW +62,3 100 35 170 1692-1801 20 % 1397 7
(Caduceus) 2417-2573 50 % 1247 6
Heaven's Light +3 100 35 170 1079-1188 20 % 906 7
(Mighty Scepter) 1596-1758 50 % 838 6
Stormlash 100 35 170 916-1020 20 % 774 7
(Scourge) 1327-1478 50 % 701 6
Herald of Zakarum (Zakarum Shield)
Weapon Stats CB % 4) OW % Strength Physical Damage DR ADT FPA 4)
Black 100 25 170 1162-1190 20 % 940 7
(Flail) 1683-1724 50 % 851 6
Grief +370 75 58 170 3253-3273 20 % 2610 6
(Phase Blade) 5344-5376 50 % 2680 6
Last Wish 65+ % 100 25 185 1426-1461 20 % 1154 7
(Phase Blade) 1948-1995 50 % 985 6
Astreon's IW +62,3 100 35 170 1950-1980 20 % 1572 7
(Caduceus) 2785-2828 50 % 1403 6
Heaven's Light +3 100 35 170 1336-1366 20 % 1080 7
(Mighty Scepter) 1977-2021 50 % 999 6
Stormlash 100 35 170 1162-1190 20 % 940 7
(Scourge) 1683-1724 50 % 851 6
4) Required use of sockets for 100 % Chance of Crushing Blow and a 7-frame Smite without Fanaticism,
Guillaume's Face: +15 % IAS
Astreon's IW: 'Ber'
Heaven's Light: 'ShaelBer'
Stormlash: 'Ber'
Herald of Zakarum: +15 % IAS (required for Black, Astreon's IW, and Heaven's Light)
Using Fortitude with either weapon except Grief (Guillaume's Face + Duress + Goblin Toe: 75 % CB)
Mind the low weapon range when using Heaven's Light (rangeadder 0):
http://wiki.theamazonbasin.com/index.php/Melee_range , as Smite will miss if the target is out of range.
Crushing Blowhttp://classic.battle.net/diablo2exp/items/magic.shtml#sma (scroll down)
A Crushing Blow (CB) is a
fixed percentage modification of a unit's current Hit Points (Static Field is basically the lightning version of Crushing Blow). The more HP a unit has left, the greater the loss of HP from the next CB. Since the Übers initially have ~ 655k HP each, we are interested in knowing just how effective CB is.
In order to examine the effect of CB, we discard Physical Damage, Open Wounds, and monster HP regeneration (note that OW eliminates regeneration; see below). Under these conditions,
- 1st Crushing Blow
HP_max is reduced by a factor of 1/8 * (1 - DR%/100), i.e. 1/10th for Über Mephisto (DR% = 20) and 1/16th for his two brothers (DR% = 50) - 2nd Crushing Blow
(HP_max - HP lost from the 1st CB) is reduced by 1/10th or 1/16th - n'th Crushing Blow
(HP_max - HP lost from the previous n-1 CBs) is reduced by 1/10th or 1/16th
Thus, Über Mephisto has 9/10th of HP_max after the 1st CB, 9/10th of (HP_max - HP lost from the 1st CB) after the 2nd CB etc. Formally,
Code
Remaining Hit Points after n CBs *)
HP_1 = 9/10 * HP_max
HP_2 = 9/10 * HP_1 = (9/10)^2 * HP_max
HP_3 = 9/10 * HP_2 = (9/10)^3 * HP_max
.
.
.
HP_n = 9/10 * HP_n-1 = (9/10)^n * HP_max
Cumulative loss of HP from n CBs *)
HP_lost = HP_max - HP_n
= HP_max * {1 - (9/10)^n}
*) For Pandemonium Diablo and Über Baal, replace 9/10 by 15/16
The cumulative loss of HP increases asymptotically (for Über Mephisto: 10 %, 19 %, 27 %, ... of HP_max), tending towards HP_max, while the remaining HP decrease exponentially (90 %, 81 %, 73 %, ... of HP_max). In a mere 10 CB hits, Über Mephisto's initial HP are cut to ~ 33 % (his brothers' HP would be nearly halved). A perfect 7 FPA Smite assault (3.57 attacks per second) with 100 % Chance of CB could ideally achieve this within 3 seconds.
The ideal effect of CB is graphed below (HP_max = 655k), along with a graph representing the HP left after n hits with
no CB and 2.5k ADT (Grief 0 CB). Note that while CB quickly decimates the initial HP, it struggles to finish off the target. Smite Damage becomes increasingly important towards the end.
A few questions remain: How do we estimate the kill speed when both CB and ADT are involved and 0 < Chance of CB < 100 % ? Even with our Helm, Body Armor, and Boots providing CB, for Grief to be competitive, we cannot reach 100 % Chance of CB with Grief. And how about monster HP regeneration ?
Let's deal with the latter first ...
Open Woundshttp://classic.battle.net/diablo2exp/items/magic.shtml#smaOpen Wounds 'Damage' (negative life regeneration) is largely inferior to Physical Damage and CBs. Even at clvl 90, the OW 'damage' inflicted over 8 seconds is comparable to the ADT with Astreon's in the Smite Damage section. Over a time span of 8 seconds (200 frames; ideally 28 hits at 7 FPA or 33 hits at 6 FPA), Physical Damage and CB together can easily apply several hundred times the damage equivalent of OW.
The reason for OW is the fact that the modifier
Prevent Monster Heal (PMH)
does not work against the Übers and we want to eliminate HP regeneration. In
MonStats.txt, the Übers have
twice the regeneration rate of most monsters (according to the
DiabloWiki, standard regeneration is 1.2 % HP/s). Based on 655k HP, this amounts to ~ 16k HP/s (~ 630 HP/frame). Massive regeneration which would decrease our kill speed.
- Open Wounds may be re-applied within the 8 seconds (200 frames)
- Open Wounds 'Damage' doesn't stack; if re-applied, the timer resets
Check the DiabloWiki for the remaining details. For a more technical approach, read
Open Wounds Explained (v1.11b),
http://phrozenkeep.planetdiablo.gamespy.com/forum/viewtopic.php?t=44308Odds of applying Open WoundsFor the estimated kill speed to be fairly accurate, it is imperative that we use at least Dracul's Grasp (25 % Chance of OW) with either weapon. Since we cannot know in advance if a hit applies OW or not, we consider the odds of inflicting OW at least once in n hits. Setting p = 1 - OW%/100, the odds of n consecutive failed OW checks are p^n and so, the chance of at least one OW strike is 1 - p^n, graphed below.
Within a couple of seconds (7-8 hits @ 6-7 FPA), the odds are approximately 90 % with Dracul's Grasp alone and 95-100 % with 35 % Chance of OW or higher.
Based on this, we consider it reasonably safe to ignore regeneration.