| Understanding our Stats Gear is more than just covering our privates, it's the stats that make it so important. If you want to understand more about what Warlocks go for, have a look at the information posts inside! |
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Published by Kusasi
July 21, 2008 |
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July 21, 2008, 04:44 AM
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#1 (permalink) |
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Character Info
Kusasi 80 Undead Warlock Nordrassil Euro PvE Guild: Simia Infinata Profile: Blizzard Armory Talent Spec: 0/40/31 |
Math and Spell Mechanics
PvE: Spell Damage Probably the most basic but intriguing stat there is for spellcasters. You'll see this on 90% of level 70 gear I reckon. Some items have bonus damage for specific schools of magic such as Orb of the Soul-Eater but most items increase damage to all schools. The effect of this stat is in fact specific to the cast time of each individual spell every class has which I'll get onto in a moment. Say you had 1000 bonus damage and the base damage of a spell was 1000, the expected damage the spell would cause won't necessarily be 2000. This is because each spell has it's own attribute known as the spell co-efficient. Quite simply, every spell/ability available to a class has a percentage of bonus damage added onto it. For instance, the Corruption dot spell has a spell co-efficient of 93.6%. At rank 8 its base damage is 900. If you had 1000 bonus damage for instance, this would mean it would deal 900 + (1000 x 93.6%) = 900 + 936 = 1836. Spell damage co-efficients can be increased through talents. These talents as far as I'm aware will relate to specific spells only. Typically they'll be called 'Empowered [spell]'. Warlocks have a talent in the Affliction tree called 'Empowered Corruption' which will increase the spell co-efficient of Corruption to 129.6% at 3/3 points. Shadow Bolts can also have their spell co-efficient increased via the Shadow & Flame talent in the Destruction tree (from 85.71% to 105.71%). Rather than designating a specific spell co-efficient to each spell (which would be hideously complex to balance), Blizzard has a rule to calculate the co-efficient of each spell which is very simple, but to which there are a fair few exceptions. Simply, the spell co-efficient is determined by the cast time divided by a fixed value of 3.5. So a warlocks shadowbolt with a cast time of 3 seconds would give 3/3.5 = 0.8571 which as a percentage is 85.71. It is very important to note here that talents which reduce the cast time of spells have no effect on the spell coefficient. Only talents that specify a bonus from "your bonus spell damage effects" will increase the spell co-efficient. So in the case of a shadowbolt, the tier 2 destruction talent Bane which reduces the cast time by 0.5s at 5/5 will have no effect whereas further down, the Shadow and Flame talent will. For spells with a cast time longer than 7 seconds, the damage coefficient is capped at 200%. Instant cast spells are treated as 1.5 second casts. The general rule for damage over time spells is the duration of the spell divided by 15 to give the co-efficient in decimal form. So a Priest's Renew spell for instance has 15 seconds duration. And 15/15 = 1 therefore the spell co-efficient is 100%. But because us warlocks are so special, just about all of our dots are exceptions to this rule. Spells that steal health from a target (such as Drain Life, Siphon Life, Death Coil) have their spell co-efficient halved after using the normal equations. Same goes for AoE spells and I believe other channeled spells such as Drain Soul also. There is also a mechanic known as the "AoE Cap" which involves limiting the potential damage of an AoE spell across a large number of targets. Visit the Elitist Jerks site for more on this. Note: The next part becomes a lot more involved mathematically and is only more detail on how the equations work. So feel free to move onto the next section if you wish. Hybrid spells are a special situation. The co-efficient is split between the direct damage and dot components of the spell. This is proportional to the base damage of each of these components. This means the equations will involve factors of the equations used to calculate spell co-efficients of independent direct damage and dot spells. To explain this part I'm using the spell co-efficients page on Elitist Jerks. The derivation of the equations is actually quite simple. Because the spell co-efficient is split between the DD and DoT components, you need to know what fraction of the total damage each component receives. This is simply done by dividing the base damage of that component by the total base damage of the overall spell. So we'll call the base damage from the DD component X and the base damage from the DoT component Y. For each component the equations will be: Fraction of DD component = X / (X + Y) Fraction of DoT component = Y / (X + Y) Now you calculate the spell co-effecient for each component like you do with regular DDs and DoTs. Then you multiply those results by the relevant fractions to work out the co-efficient for that component. So we'll use Immolate as an example, with a 2s cast time and a 15s DoT. At rank 9, DD co-efficient = (2 / 3.5) * (327 / (327 + 615) = 0.5714 * 0.3471 = 0.1983 DoT co-efficient = (15 / 15) * (615 / (327 + 615) = 1 * 0.6529 = 0.6529 Another thing to note is that direct damage spells such as Shadowbolt are tooltipped to do x - y damage. Now what is certain is that the average damage it will do will be (x + y)/2 which would have to mean there is an equal chance of the spell dealing damage equal to all values within that range inclusive. Perhaps the public can elaborate on this for me. |
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July 25, 2008, 08:25 PM
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#2 (permalink) |
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Character Info
Kusasi 80 Undead Warlock Nordrassil Euro PvE Guild: Simia Infinata Profile: Blizzard Armory Talent Spec: 0/40/31 |
Re: Math and Spell Mechanics
Spell Critical Strike Rating When Burning Crusade was released, Blizzard introduced a new rating system for the calculation of spell critical strike chance (and other stats too). The reason for this was that percentage based increases would scale astronomically with gear by level 70. When working with raw values this problem is eliminated. Spell Critical Strike Chance increases your chance to critically strike (no way!) with spells on top of your base critical strike chance which is determined by the amount of intellect you have. So firstly, base critical strike chance via intellect varies per class. At level 70, a Warlock requires 81.92 points of intellect for an increase of 1% in spell critical strike chance where as all other casters require a nice round 80, except for Paladins where it is 80.05. Then, for all casters, 22.08 points of spell critical strike rating equates to an increase of 1% in spell critical strike chance. Remember that a rating is a raw value and chance is a percentage. Finally, each class has it's own specific constant (a percentage) which is added on to give the overall critical strike chance. Note that there are many talents which will increase crit chance for specific spells. Note also that dots cannot crit at all. Even Curse of Doom. The initial damage of Immolate however, can. To take an example, a Warlock has 400 intellect and 200 spell critical strike rating. The base crit rating would be 400/81.92 = 4.883. The bonus crit rating would be 200/22.08 = 9.058. Then add onto this the class specific constant, which for warlocks is 1.701 to give, 4.883 + 9.058 + 1.701 = 15.642% spell critical strike chance. Then you add onto this the chance for specific spells which may have an increase via talents. It may as well be noted here that Blizzard calculates to 4 significant figures. The damage increase from a critical strike is 150% for all classes. Yet again this can be increased through talents to 200%. The warlock talent is called Ruin in the destruction tree. |
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July 25, 2008, 08:25 PM
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#3 (permalink) |
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Character Info
Kusasi 80 Undead Warlock Nordrassil Euro PvE Guild: Simia Infinata Profile: Blizzard Armory Talent Spec: 0/40/31 |
Re: Math and Spell Mechanics
Spell Hit Rating This is an uber important stat for any class particularly when it comes to raiding. I know Warlocks and I bet for any class that where you are undercapped, an increase of 1 hit rating will result in a much higher dps output than an increase of 1 bonus damage. WoWWiki states that "for most casters, 1% of additional spell hit amounts to 1% additional damage in the long run." This means that your dps will increase by a factor of your bonus spell damage per percentage increase in spell hit rating. Spell Hit rating as it indicates, increases your chance to hit with spells. This is the melee equivalent of a hit and miss with a weapon. If you 'miss' with a spell it will appear in game as a resist but it is actually due your spell missing its target. Why it appears as a resist I don't know. But the true 'resist' of a spell is determined by resistances of a target and the casters spell penetration which I'll get onto soon. Spell hit chance has a base value which is determined by the level and level difference of a player and target. The chance is different between a player target (PVP) and an npc target (PVE). All Burning Crusade bosses are considered level 73. The base chance to hit for all classes at level 70 on a level 73 mob is 83%. This is then increased through spell hit rating enhancements. The chance to hit is capped at 99% meaning that no matter how much spell hit rating you stack, there will always be a 1% chance your spell will miss. At level 70, 12.62 points of spell hit rating equals 1% of spell hit chance. It may be of interest to know that melee hit rating is slightly different. 15.76 points of hit rating equals 1% of hit chance. So if the chance to hit any mob is capped at 99%, and the base chance to hit a level 73 (boss) mob is 83%, this means a caster requires an increase of 16% chance to hit. As just mentioned, this can be obtained through spell hit rating, and like crit chance and spell co-efficients, through talents as well. If 12.62 points of spell hit rating equals 1% increases chance to hit and we require 16%, then 12.62 x 16 = 201.92. Then round this to our magic number of 202. Remember it is always better to be overcapped than to be just undercapped as each point under the cap can mean a fairly large decrease in damage, relatively speaking. Just about every class has a talent or 2 or even 3 that can increase your spell hit chance for either all spells or particular spells only. Warlocks for example have a tier 1 talent in the affliction tree called Suppression which increases spell hit chance by 2% per point to a maximum of 10% for affliction spells only. This would mean that only a player would require only 6% more to reach the cap. 12.62 x 6 = 75.72 rounded to 76. This is why Affliction specs are the best way to go for new level 70s as this Suppression talent will give them a great head start to make up for the lack of hit rating on gear and allow them also to focus on stacking bonus damage which is what the affliction tree is all about. Now as for PVP it's slightly different, and easier. At level 70, the base chance to hit a player of the same level is 96%. Meaning you need a mere 3% to reach the cap which equates to only 37.86 points rounded up to 38. This allows you to focus on much more important stats such as resilience which I'll get onto soon. |
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July 25, 2008, 08:25 PM
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#4 (permalink) |
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Character Info
Kusasi 80 Undead Warlock Nordrassil Euro PvE Guild: Simia Infinata Profile: Blizzard Armory Talent Spec: 0/40/31 |
Re: Math and Spell Mechanics
Spell Haste Rating Spell Haste reduces casting time of all spells and also your Global Cooldown to a minimum of 1 second. Spell Haste rating stacks together additively, and Spell Haste percentages are multiplied. So all haste rating on gear will be totaled, converted to a percentage and then this will stack multiplicatively with effects such as trinkets, Bloodlust, Drums etc.# For channeled spells this stat will reduce time channeled, resulting in higher dps. The damage itself won't be effected. So each "tick" lets say, will occur at shorter intervals. At level 70, 15.7 points of Spell Haste Rating equals 1%. To calculate your cast time you first need to work out your spell haste as a percentage through the following formula: Spell Haste % = (Total Spell Haste Rating / 15.7) / 100 or for a slightly more simple formula: = (Total Spell Haste Rating) / 1570 Note: The result of the above formula is your spell haste percentage in decimal form. You need to keep it like this for the purposes of the next formula. Next we need to use a formula to calculate your new cast time. Note that the cast time is not before talents. So 5/5 Bane will reduce your Shadowbolt cast time to 2.5 seconds. You use this value as the current cast time. New cast time = Current cast time / (1 + spell haste %) So for an example, lets take a warlock with a 2.5 shadowbolt with 0 haste rating on gear. They gain Bloodlust which is a 30% increase, which, in decimal form is 0.3. Punch that into the formula and you get: New cast time = 2.5 / (1 + 0.3) = 2.5 / 1.3 = 1.923s They're then also buffed by Drums of Battle which as you can see increases Spell Haste Rating by 80. Firstly we need to convert 80 haste into a percentage decimal. 80 / 1570 = 0.051 Then work out the new cast time: 1.923 / (1 + 0.051) = 1.923 / 1.051 = 1.83 |
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July 25, 2008, 08:25 PM
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#5 (permalink) |
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Character Info
Kusasi 80 Undead Warlock Nordrassil Euro PvE Guild: Simia Infinata Profile: Blizzard Armory Talent Spec: 0/40/31 |
Re: Math and Spell Mechanics
Resistance I've left this stat last in the PvE bit because it is slightly more complex that the other stats in that it is dependant on all stats just mentioned. When a spell is cast the game takes into account whether the spell will hit the target based on hit rating. If it does then it will need to decide how much damage it will do based on resistances and resilience for critical strikes and DoTs specifically. To my knowledge, whether the game uses a 1 roll or 2 roll system hasn't been confirmed. Firstly, the game needs to know how much of your own resistance will be effective against a caster's spell on you. This is determined by your base resistance value, level difference, and spell penetration. The formula (from WoWWiki) is this: Code:
effective resistance value = Rb + max((Lt - Lc) * 5, 0) - min(P, Rb) Rb - target base resistance (as advertised on the character sheet) Lt - target level Lc - caster level P - caster spell penetration So punch these values in and you get the following: effective resistance value = 380 + max((70 - 73) * 5, 0) - min(0, 380) The max and min functions take the max and min values (respectively) within the brackets. So to simplify a little more: 380 + 0 + 0 = 380. Meaning that my effective resistance value is 380. However it's not quite as simple as that for what is actually a simple reason. Now that the effective resistance value is determined you can calculate what percentage of damage reduction your resistance will give you. This is given by the following formula: Code:
Damage reduction percentage = (effective resistance value / (caster level * 5)) * 75 The next thing to be considered is the type of spell being resisted. There are two different kinds of spell, a damage dealing spell (such as Shadowbolt) and a Binary spell such as Frost Nova which deals damage but can also cause a movement debuff. The resistance of both the spells is iterative. Take for example me tanking Leo, where 365 of my resistance is effective. His only cast on me in this phase is Chaos Blast which is a binary spell as it deals damage and a debuff. Lets say that in this phase he casts 20 Chaos Blasts on me. On average I will resist 75% (15) of these whereas 5 will hit me. [Be warned that the following paragraph is potentially the most confusing one of the whole article. ;)] For general damage dealing spells it works slightly differently. These spells succumb to partial resists. Lets say a mage with 0 spell penetration is casting Fireballs at me. Regardless of your resistances, there is always a chance that each Fireball will deal either 0%, 25%, 50%, 75% or 100% damage. However, your damage reduction percentage (based on effective resistance value) determines the chance of each individual partial resist percentage. In an effort to explain this better we'll take yet another example. For a target with 75% damage reduction (365 resistance), there is a 25% chance that they will resist 100% of the damage of a spell. For a target with 60% damage reduction (292 resistance) there is only an 11% chance to resist 100% of the damage of that spell. For damage over time spells this mechanic applies to each individual tick. When I said that resistance of both spells is iterative, I mean that through all partial resists, at 75% damage reduction, the damage received will average out at 75% of the maximum theoretical damage. |
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July 25, 2008, 08:25 PM
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#6 (permalink) |
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Character Info
Kusasi 80 Undead Warlock Nordrassil Euro PvE Guild: Simia Infinata Profile: Blizzard Armory Talent Spec: 0/40/31 |
Re: Math and Spell Mechanics
PvP: Spell Penetration It may as well be said from the get go that spell penetration has virtually no use in PvE. Spell Penetration is a stat that works against resistances, and very few mobs and raid bosses will have a significant amount of resistance to overcome. There are some however but it certainly isn't worth sacrificing other stats for this unless the whole raid does it together. If there is any resistance on mobs or bosses, this can generally be negated through a Warlocks Curse of Elements spell. In some cases they may have complete immunity but that isn't quite the same as having full resistance. PvE targets have a base resistance of 2% per level difference and this cannot be overcome through spell penetration. Therefore, this stat is only of real interest in PvP. The equations of spell penetration are very simple and basically work out as 1 point of spell penetration to ignore 1 point of resistance of a target to a minimum of 0. A target's resistance cannot be lowered beyond 0. This also means that the required amount of spell penetration is more dependant on your playstyle. For casual battleground play you're generally only going to come across targets with resistances from racial abilities. Druids with Mark of the Wild will have 40 however and some classes such as Paladins with their aura will have 70 to certain magic schools. It can be quite difficult to find the right balance as there aren't a lot of ways to obtain this stat and you can't really tell how much of it you're always going to need. The top teams in the world such as Frag Dominant, Nihilum, SK Gaming etc all have a tree form druid meaning they'll have MotW for instance. |
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July 26, 2008, 08:45 AM
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#7 (permalink) |
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Character Info
Kusasi 80 Undead Warlock Nordrassil Euro PvE Guild: Simia Infinata Profile: Blizzard Armory Talent Spec: 0/40/31 |
Math and Spell Mechanics
Resilience This is basically the PvP version of resistance but don't run away yet because what I'm going to go through here is nowhere near as complicated. The actual damage calculations are very detailed indeed though. Because in PvP you'll be coming up against a whole host of different types of damage (melee, fire, shadow, nature etc), building high resistances to each individual school of magic is impossible and there is no way to 'resist' melee damage except through dodges and parrys although I'm not too familiar with melee mechanics. So Blizzard introduced resilience, a way of reducing damage of all kinds. Resilience reduces chance to be critically hit, reduces the damage if you do receive a crit, reduces damage from dots and reduces mana drained from mana draining spells. It does absolutely nothing to normal attacks. Resistances can work against normal attacks though. More specifically, 1% of resilience will do the following: Reduce the chance to be critically hit by 1% Reduce the extra damage received from a critical strike by 2% Reduce damage from dots by 1% Reduce amount of mana drained through mana draining spells by 2%. The Resilience stat also has a rating like spell hit and spell crit. The amount of rating required for 1% of resilience increases with level. At level 70, 39.4 points of resilience equates to 1% of resilience. As for caps, all of the individual reductions the resilience stat can cause are capped at 25%. As critical strike damage and mana drain drain reductions scale at twice the rate of critical strike chance and dot damage reductions, the former 2 mechanics will be capped first. This means you would need 12.5% resilience (492.5) to reach that 25% cap. And for the other 2 components, you would need 25% (985) resilience, which currently is completely unrealistic. Note: Here is the more detailed bits with equations and calculations. Note this is basically a walkthrough of the Resilience page on WoWWiki but I hope this can make sense a bit easier through the way I express them and use examples step by step. Firstly, I'm going to be a little controversial and challenge the definition of resilience on the WoWWiki page. It states that 1% of resilience reduces the critical strike damage bonus by 2%. The means the extra damage only and not the overall damage they do. However, the equations lower down calculate the effect of resilience on overall critical strike damage, which I believe is correct through some extra research I have done. I hope whilst this article is under public critique that this can be confirmed. Because Resilience affects critical strike chance and critical strike damage, the equations to calculate damage mitigation have to be related to critical strike damage equations to take into account values on the attcker and defender. An equation for average damage is this: Code:
Avg. Damage = [D * (1.0 - C)] + [D * (1.0 + B) * C] A Warlock is fighting a Warlock (when really they should be congratulating each other on such a great character choice), and the attacker does an average of 2000 damage each shadowbolt. Their critical strike chance is 25%. They also have Ruin so their critical strike damage bonus is 100%. Their average damage will be: Average damage = (2000 * (1 - 0.25)) + (2000 * (1 + 1) * 0.25) = (2000 * 0.75) + (2000 * 2 * 0.25) = 1500 + 1000 = 2500. Now we need to work out what effect the defendant's resilience will have on this damage. Lets say the defendant has 400 resilience (R). We need to first convert this into a percentage which is simple. Resilience % = 400 / 39.4 = 10.15% which is 0.1015 as a decimal which is what we'll be needing. Now earlier we learnt that 1% of resilience reduces critical strike chance (C) by 1% and overall critical strike damage by 2%. Note: Percentages in decimal form are generally easier to work with (at least for me) when it comes to doing the mental arithmetic. Although I guess I can equally remember that multiplying by 1% is the same as adding 0.01, so long as the convention is consistent throughout calculations. We can plug these reduction components into the general formula for average damage to see its affect. I'll change the colour of the new parts in the equation to easier describe the affects. Remember that Resilience (R) reduces critical strike chance and overall critical strike damage. (to be confirmed) Avg. Damage = [D * (1.0 - (C - R))] + [D * (1.0 + B) * C * (2 * R)] So plugging in the values we had before and also the 400 resilience rating (0.1015) we get an average damage of: [2000 * (1 - (0.25 - 0.1015))] + [2000 * (1 + 1) * 0.25 * 2 * 0.1015] = [1703] + [203] = 1906
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July 26, 2008, 08:45 AM
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#8 (permalink) |
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Character Info
Kusasi 80 Undead Warlock Nordrassil Euro PvE Guild: Simia Infinata Profile: Blizzard Armory Talent Spec: 0/40/31 |
Math and Spell Mechanics
References WoWWiki Spell damage and healingThe Warlocks Den Elitist Jerks Wowhead
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http://www.myspace.com/markpeskett |
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July 27, 2008, 07:50 AM
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#9 (permalink) |
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Re: Math and Spell Mechanics
/promote!
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