Showing posts with label Theorycrafting. Show all posts
Showing posts with label Theorycrafting. Show all posts

Thursday, January 21, 2010

Gemming

This will be an in-depth guide to gemming, focused specifically on DPS classes (much of the advice will hold for other roles, but not all of it).

Basics
Gems are divided up into 8 types: red, orange, yellow, green, blue, purple, prismatic, meta.  The first 6 are going to be the primary ones used for gemming.  Gem sockets in items are divided into 5 categories: red, yellow, blue, prismatic, meta.

Meta sockets can only take meta gems, and meta gems may only be socketed in meta sockets.  Prismatic sockets will take any color (at present, the only prismatic sockets are the ones from an Eternal Beltbuckle and the Blacksmithing-specific wrist and glove socket modifications).

The colored sockets will take any color of gem (excluding meta), but require a gem of a color corresponding to the socket color in order to count towards the socket bonus.  Socket bonuses are granted if all of the baseline sockets (ie. excluding Blacksmithing sockets and Beltbuckles) are socketed with gems matching their color.  Red, yeloow, and blue gems match only sockets corresponding to their color (though they may be socketed in any socket except a meta socket).  Orange, green, and purple gems match two colors of sockets, red/yellow, yellow/blue, and red/blue respectively.  They will activate a socket of either color if placed in it.

Each of the primary gem colors (red, yellow, blue) has certain stats assigned to it, and gems will have a balance of stats from all colors present.  Red generally has the most direct upgrade stats, yellow tends to have the combat ratings, and blue tends to have the endurance-related stats.  A full list of stats obtainable from each color follows:

Red - Strength, Agility, Attack Power, Expertise, Armor Penetration, Spell Power, Parry, Dodge.
Yellow - Intellect, Resilience, Haste, Hit, Crit, Defense
Blue - Stamina, Spirit, mp5, Spell Penetration

Each meta gem has a certain set of gemming requirements in order to be activated (for example, 2 blue gems, or more yellow gems than red gems, etc.).  For the purposes of these meta requirements, gems that count for multiple colors count for all of those colors at the same time regardless of which slot they are socketed in.  For example, a Relentless Earthsiege Diamond requires 1 red, 1 yellow, and 1 blue gem.  Socketing an orange gem will fulfill both the red and yellow gem requirements, even if the orange gem is put into a blue socket.  A Siren's Tear or Nightmare's Tear will fulfill all 3 requirements on it's own.

Metas and Socket Bonuses
Almost all dps classes will use one of two different gems: Relentless Earthsiege Diamond or Chaotic Skyflare Diamond.  Casters will almost universally use a Chaotic Skyflare.  Similarly, agility-based physical dps will almost universally use a Relentless Earthsiege.  Strength-based physical dps may use either, and there are pros and cons to each (explained in detail below in the Advanced section).  Thus nearly all dps classes will require either 1 or 2 blue gems, and 0 or 1 yellow gems.

As stated above, both the blue and the yellow gem requirement for the Relentless Earthsiege may be filled with a single Nightmare's Tear (which will similarly fit any socket (excluding meta) in your gear), and will fill the first of the two blue gem requirements for the Chaotic Skyflare.  The second blue requirement is usually filled with a purple gems, as the red color portion tends to grant a greater benefit than the yellow portion of a green gem (the blue portion will be the same in both cases).

The general rule of thumb for dps classes (see the Advanced section for exceptions) is to socket the minimum number of blue-colored gems needed for your meta gem using your spec's optimal blue gem, which for most is a Nightmare's Tear in one socket and (if a second is needed) a purple gem with Str/Stam, AP/Stam, Agi/Stam, SP/Stam, or SP/Spi, depending on class and spec.  All other slots are filled with your spec's best overall gem (see Advanced).

Advanced Gemming
This section relies rather heavily on having accurate stat weights for your spec.  Ideal places to gather these are from the forums on Elitist Jerks, Rawr's Pawn export, and any simulators being maintained for your class.

For all examples in this section, I will be using the following stat weight scale (which comes from Kahorie's DK Simulator from the EJ forums, using my current gear and spec).  I've specifically excluded Hit and Expertise rating, as I always gem for the cap for those stats, so their effective weight is approximately identical to strength (the stat that I'd be replacing, though in reality, hit is worth slightly less then strength on gear and slightly more than strength on gems because the additional yellow gems allow me to get socket bonuses that otherwise would not be worth socketing for the bonus).

Strength - 2.88
Agility - 1.59
Crit - 2.24
Haste - 1.32
ArP - 2.58

To find the ideal gem of each color for your spec, simply add the total overall value of the stats for each eligible gem and pick the one with the highest total value.  For example, a 20 strength gem using the above scale would be worth 20 * 2.88 = 57.6 points, while a 10 strength / 10 crit gem would be worth 10 * 2.88 + 10 * 2.24 = 51.2 points, so the 20 strength one would be the superior gem for a red socket color.  For a yellow socket, strength is my most valuable stat (so the ideal gem will be an orange Str/- gem, rather than a pure yellow), and crit is the more valuable of the two secondary stats, so Str/Crit is my ideal gem.  However, Str/Hit technically ranks higher so long as at least 7 of the hit rating is pre-melee cap.

Evaluating meta gems (for strength-based plate, at least) is somewhat more complex, but not a great deal more difficult.  Since the secondary (non-stat) portion of both the Relentless Earthsiege and the Chaotic Skyflare are the same, the only value I need to take into account is the difference between agility and crit.  Using the above scale, the Relentless Earthsiege is worth 21 * 1.59 = 33.39 while the Chaotic Skyflare is worth 21 * 2.24 = 47.04.

However, the Relentless Earthsiege requires a single blue gem to activate, while the Chaotic Skyflare requires two.  Thus the value for the Relentless Earthsiege must also include the value for the half of the gem that would otherwise be blue.  Since that socket will without fail turn into a 20 Strength gem (all blue sockets except those needed for the meta are socketed pure Strength for me, as there's not a socket bonus yet in existence powerful enough to overrule 10 strength), the half that would normally be blue being 10 strength, the Relentless Earthsiege effectively gains an additional 28.8 value, totaling 62.19.  Thus for the Chaotic Skyflare to be better, I must have a second item requiring a blue socket with a socket bonus equal in value to at least the difference between the metas, or 15.15 points.  This equates to a minimum of 6 strength, 6 ArP, or 7 Crit.  If the item with the blue socket also requires one or more yellow gem sockets, the socket bonus value would need to be increased by 6.4 points per yellow socket, or a minimum of 8 strength for a single yellow socket, and it's impossible to out-value if the meta bonus is crit, ArP, or requires more than 1 yellow or blue socket.

This same technique can be applied to items that only require red and yellow sockets (or even just yellow ones).  Since pure red gems are almost universally better for dps classes than orange ones, the value of the socket bonus can be used to calculate whether it is worthwhile to socket pure red gems or socket orange gems in yellow slots to gain the socket bonus.  For example, my gloves require a single yellow socket for a +4 Strength bonus.  The value of the socket bonus is 4 * 2.88 = 11.52.  The value of socketing it with a red 20 Str gem would be just the value of the red gem: 57.6 points.  The value of socketing it with an orange 10 Str/10 Crit gem would be the value of the gem (51.2) plus the value of the socket bonus, totaling 62.72.  Thus I gain more dps benefit from socketing a less powerful Str/Crit gem to gain the socket bonus than I would from socketing the more power pure Str gem and ignoring the socket bonus.

To generalize, the value of the socket bonus must equal a minimum of the difference between your most powerful gem overall (in my case, 20 Str) and the value of the gem required to match the socket in question (in my case, 10 Str/10 Crit), times the number of sockets of that color required (in this case, 1).

As an example, the plate dps chestpiece from Emblems of Frost (Castle Breaker's Battleplate) requires 1 red, 1 yellow, and 1 blue socket for a +8 Strength bonus.  The red socket has no value difference if socketed for best overall (pure Str) or for the bonus (also pure Str).  The yellow socket sees a decrease of 57.6 - 51.2 = 6.4 if socketed for the bonus, and the blue socket sees a decrease of 57.6 - 28.8 = 28.8.  Thus the socket bonus must equal at least the value of those two decreases combined for it to be more valuable to socket for the bonus, in this case at least 35.2 points.  The 8 strength socket bonus is worth 23.04, well below the required value, so it is more valuable to socket pure strength and ignore the socket bonus.

Blue gems (including Nightmare's Tears) should be used to gain the most amount of overall stat benefit from gear.  If you have more blue sockets than you need blue gems, calculate the total value of the gems and socket bonus for each item both when socketed with the for the socket bonus with the blue gem and socketed for your best overall gem (ignoring the socket bonus).  Whichever item shows the the smallest decrease in value from when it was gemmed for best overall gems is the one in which you should socket the blue gem.  Generally this will be the item requiring only a single blue socket with the largest amount of your most valuable stat.  If you need a second blue gem, repeat this process with all remaining items with a blue socket, excluding the one you used the first blue gem on.

Extrapolation to Other Areas
These same techniques can be applied to other areas of gear optimization as well.  For example, there are three available glove enchants for melee dps (excluding Engineers): +44 AP, +20 Hit, and +15 Expertise.  Since most melee classes will gem for the hit cap, the value of hit can be weighted the same as Strength.  While technically orange -/Hit gems maybe replaced with other orange gems (-/Crit usually), they will only be so replaced if the socket bonus value exceeds the value of the lost additional red-color stat, and can thus be ignored (although this is why the hit on gems is worth slightly more than strength for me, as it allows me to gain yellow sockets that I otherwise wouldn't, effectively allowing me to gain socket bonuses that require yellow sockets with a gem that weights the same as my best overall gem, a pure red.  Correspondingly, since it decreases the amount of hit I am required to gem for and therefore decreases the socket bonuses I receive, hit on gear and enchants is slightly decreased in value compared to strength).  Thus the 20 hit enchant effectively has a weight of 57.8 points, while the AP enchant has an effective weight of 44 points.

Again, though, a balance point can be found.  If I am currently hitcapped with the 20 hit enchant and have a yellow socket on an item that would grant a socket bonus if filled with an orange gem (but the socket bonus is small enough that it isn't worth gemming for Str/Crit), then it would be superior to gem for the hit and use the 44 AP glove enchant if the socket bonus is worth at least the difference between the enchants, in this case 13.8.  However, since the socket bonus value required for it to be better to gem Str/Crit for me is only 6.4 points, this situation will never occur, as that yellow socket would have already been filled with a Str/Crit gem (in other words, the value loss of swapping the enchants needs to be less than the value loss of swapping from a my best overall gem to my best yellow gem in order for the situation to even be possible).

Procs

Definition
A procs is an effect that has a chance of occurring from certain qualifying events. This includes effects that proc off of physical attacks, spell casts, and certain rare conditions such as being attacked, being crit, or taking a certain type of damage.  Procs are of two general types, static-chance and proc-per-minute (PPM).  Procs may also have what's know as an Internal Cooldown (ICD), which indicates the period of time after a proc occurs in which the proc cannot occur again.  In general, static-chance attacks tend to have ICDs, while PPM effects tend not to.

Proc Per Minute
Effects that run on a PPM, system occur almost exclusively as procs from weapon attacks, and are designed to give approximately the same proc rate regardless of the speed of the weapon.  Each proc is given a specific PPM number (for example, 2 PPM for Rune of the Fallen Crusader).  This number is then multiplied by the base speed of the weapon divided by 60 to give the percentage chance per attack of the proc occurring:

P = Proc chance per swing
M = Proc per minute value
S = Base speed of the weapon


Excluding a few BC-era items, the proc chance is calculated from the weapon's base speed (in other words, the speed listed on the tooltip).  Thus any haste effects will increase the actual proc rate of the effect, as the character will swing more often, but at the same percentage proc chance.

In addition, most PPM attacks are capable of procing off special attacks made by the character, though it may be limited to weapon-based specials (in other words, special attacks that involve using your weapon to attack, such as Heart Strike or Crusader Strike, but not Bloodthirst or Judgement).  In these cases, the special attacks use the same percentage chance as the melee attacks.

This means that for PPM effects, the chance per swing from white attacks is irrespective of weapon swing, but the proc chance per special increases as base weapon speed increases.  Assuming two players, one with a fast weapon, one with a slow weapon, with the same amount of haste from buffs and gear, using the same number of procable special attacks per period time, the player with the slower weapon will experience more procs on average over a given interval due to the higher proc chance per special attack.

Static Chance
Static chance procs function just as they sound:  they have a fixed percentage chance per qualifying attack to proc.  Otherwise, they function just as PPM effects.

Uptime and Time Between Procs
Calculating the uptime (for a duration proc) or time between procs (for instant effect procs, such as damage), the method is strikingly similar.  One needs to know 4 values: the duration of the proc (only applicable to procs with duration.  Instant effects have an effective duration of 1 second), the internal cooldown (if any), the chance to proc (either static or the percentage calculated from PPM), and the average time between procable attacks.  These are noted as follows in all following formulae:

U = Percentage uptime
D = Proc duration (D = 1 if the effect is instant)
T = Time between procable attacks
P = Proc chance per attack
I = Internal Cooldown

The following formulae will give the uptime for any duration proc.  If seeking the time between procs, whether for an instant effect or duration proc, simply take D / U (remember, D = 1 for instantaneous effects).

Instant Effects and Long-ICD Effects
If the effect has an ICD at least as long as the duration or if the effect is instantaneous (most trinkets), the uptime is as follows:


As an example, the ability to use Deep Freeze for a frost mage has a 15% proc per cast, and an effective internal cooldown of 30 seconds (the cooldown on Deep Freeze).  Assuming the mage has an average net haste of 15%, the mage will be casting a Frost Bolt every 2 seconds.  Based on the above, the mage will then have an average time between Deep Freezes of 43.3 seconds.

No-ICD Duration Effects
Duration procs without an internal cooldown function differently, as overlapping procs will reduce uptime below what one would expect intuitively.  Uptime for a proc without an internal cooldown is as follows:

As an example, Fallen Crusader with a 3.0 speed polearm has precisely a 10% chance to proc per swing, with a 15 second duration and no ICD.  Assuming no haste and no special attacks, FC will show a 41% uptime.  Compare this with the 50% uptime one would estimate if one simply took the PPM times the duration and divided by 60.

Short ICD Duration Effects
Procs with an Internal cooldown shorter than their duration use a complex amalgam of these two.  The formula is as follows:

As an example, the Totem of Electrifying Wind has a 70% proc chance per Lightning Bolt, with a 12 second duration and a 6 second ICD.  Assuming 33% overall haste (reduces Lightning Bolt to a 1.5 second cast), and assuming the shaman is spamming nothing but Lightning Bolt, the totem will have an uptime of 99.6%.

Friday, January 8, 2010

Bryntroll Update 2

Spent some time this morning testing Bryntroll since the hotfix:

  • It can still proc from BCB strikes.
  • It CAN still apply from Icy Touch.
  • It CAN still double-proc from Plague Strike
  • It doesn't seem to be able to proc off the shadow portion of Scourge Strike.
  • Refreshing diseases with Pestilence via Glyph of Disease does not seem to proc it.
  • It CAN, however, proc off of spreading diseases with Pestilence, even apparently on targets out of melee range (had it proc against a target dummy ~9 yards laterally away from me), and on the primary target (so long as Pestilence hits more than one target, that is).

Assuming this is the way it stays, this adds 36.55 dps and 60.92 AEP to the above for non-GoD Unholy (total 330.61 dps, 551.02 total AEP) and 37.54 dps and 62.57 AEP for non-GoD Blood (total 377.10 dps, 628.50 AEP).

The procing from spreading of diseases and applying them via IT or PS seems like it may be removed as well, though, in which case the AEP would drop to my prior calculated value.

Bryntroll Update

Blizzard released a modification tonight to Bryntroll's proc, labeling it is a 'bug fix'.

We have found a bug with Bryntroll where it procs too often for Retribution paladins or Unholy DKs. For example both portions of Scourge Strike could cause a proc, which is unintended.


Bryntroll seems to account for about ~3-4% of dps for a typical Icecrown Fury warrior. That's more of where it should be for other melee.

Assuming they simply remove the ability for disease, Righteous Vengeance, Deep Wounds, and similar DoT refreshes or applications to proc the effect, this is a noticeable nerf to Unholy, Fury, Arms, and Ret, and a mild nerf to Blood.  Blood will lose 6 procable attacks per minute, Unholy will lose 12, and Ret, Arms, and Fury lose an amount dependent on their haste, crit, and skill at maximizing GCDs, though all 3 will likely lose 12 or more.

For those looking for numbers, this reduces the DPS / AEP for DKs down to 294.0 dps / 490.10 for Unholy and 340.0 dps / 565.93 for Blood at raid baseline (Windfury, Swift Retribution, zero haste rating).

Monday, December 14, 2009

Bryntroll



I recently was lucky enough to get my hands on one of the more powerful (and cooler looking) weapons out of ICC, namely Bryntroll, the Bone Arbiter.  The theorycrafting on this potent weapon is still rather sparse, so I spent several hours testing the limits of the proc and it's dps contribution.  First off, the basics:

  • The 264 version proc has an average damage of 2250, while the 277 version has an average of 2538.
  • The damage does not scale with any character stats (though the dps does, more on that below).
  • The damage does scale with any percentage damage increases that affect spell damage, such as Avenging Wrath, Curse of Elements, Blood Presence, etc.
  • The drain can proc off of any weapon attack, as well as some odd events such as applying or refreshing effects such as deathknight diseases or the paladin talent Righteous Vengeance.  However, any of the odd events that can proc it require you to be in melee range and facing the target (in other word, in a position such that your character would swing the axe at the target if you turned on auto-attack) in order for the drain to be able to proc.
  • The drain has a base proc rate of 2 procs-per-minute, or 11.3333% chance per swing, and has no internal cooldown.
  • The drain can proc multiple times per attack, provided there's are more than one weapon event for the attack.  For example, the drain can multi-proc off the following:
    • On any or all of the multiple targets of Cleave, Whirlwind, Divine Storm, Heart Strike, or Sweeping Strikes.
    • From a melee (or special) and it's subsequent seal proc, Blood-Caked Blade proc, or Windfury proc (though why a shaman would be using it...).
    • From both the physical and shadow portions of Scourge Strike.
  • The drain can not proc from any spells, excluding the odd events mentioned above.
  • The drain is incapable of critting, functions on the spell hit table, and can be partially resisted.
Now, with a 2 PPM baseline, the weapon will deal 2 procs a minute before any waste or special attacks or talents are factored in, giving it a minimum dps of 75.  The wonderful thing about the proc rate, though, is that it scales linearly with haste buffs.  The more haste your character has, the more dps the proc provides and the higher it's equivalent AP value.  In practice, the proc will usually provide between 200 and 400 dps, depending on the character's haste rating, spec and rotation (and therefore number of procable attacks per second), spell hit chance, and +damage buffs present.  A good estimate is that it will provide approximately 4-8% of a character's dps.

For many classes, this means the proc is worth the equivalent of between 400 and 800 additional attack power, though it's place on the best-in-slot list is strongly dependent class, spec, haste rating, and rotation.  In general is can be assumed to be near the top of the list, however, as the proc itself provides a fairly respectable amount of dps while also making it easier for the healers to keep you alive through miscellaneous raid damage.


References
Melee/BCB Doubleproc
Scourge Strike Doubleproc
Heart Strike Doubleproc
PPM Recount Parse
Bryntroll on DK Forums

Monday, December 7, 2009

3.3: Area Damage Caps

Patch 3.3 is changing the way Area Damage Caps function, but AoE Caps are a fairly poorly understood mechanic to begin with for most players.  Thus I will explain how the current capping mechanics works, how the new 3.3 mechanics works, and the advantages and disadvantages of the new system.

Currently, the cap on an AoE spell is set by and only by the spell's rank.  3 spells with known caps are Arcane Explosion, Howling Blast, and Blood Boil, all three of which have a cap at max rank (rank 10 for AE, rank 4 for HB and BB) of 37500 damage.  Each spell has a designation for how much damage it does per target, and this is the maximum damage per target it can do, but not the minimum.  The AoE cap comes into play when the total damage being done reaches said cap.  At that point, instead of doing the damage stated by the spell per target, it does damage to each target equal to the damage cap divided by the number of targets.  Thus once you are at the cap, adding more targets reduces the amount of damage per target done, keeping the total damage done constant.  Note that this damage cap applies before critical effect damage is factored in, so an AoE spell can in fact to more damage than the cap if some of the strikes crit.

For example, at approximately 305 spell power, Arcane Explosion does 625 damage per target.  On up to 60 targets, the spell will continue to deal 625 damage per target (before resists and crits).  After 60 targets, however, the damage per target begins to drop as the cap of 37500 damage has been hit.  In this mage upgraded their gear to approximately 3250 spell power, their AE would then be doing 1250 damage per target.  On up to 30 targets, this would continue to hold true, but beyond 30 targets, the damage per target would again begin to diminish, and once at or past 60 targets, both mages would be doing the exact same damage per target.

The new system radically changes the manner in which this cap is calculated.  Instead of there being a static cap imposed by the spell rank, the cap on any AoE spell is equal to ten times the non-crit single target damage it deals.  In the above example, the first mage would have a cap of 6250 damage, while the second would have a cap of 12500 damage.  If up against 20 targets, the first mage would be dealing 312-313 damage per target, while the second would be dealing 625.  Both of these caps are significantly lower than the prior 37500 cap, but there are advantages to the system as well.

One of the largest advantages is scaling.  Currently, improving your gear will improve your AoE output only while below the damage cap, and increasing that output means that it takes less and less targets to reach that cap as you get better and better gear.  In the above example, the mage improved his spell power from 305 to 3250.  In doing so, his damage per cast below the cap doubled below the cap, but the number of targets necessary to cap out his AE also halved.  In the 3.3 system, this is no longer the case.  All AoE spells by definition now cap out at 10 targets.  However, since the cap itself is based on the scaling damage done by the spell, the damage a spell does even beyond that cap is proportion to the damage done under the cap.  In the above example, the first mage will do half the damage of the second while under the cap...and continue to do half the damage of the second mage while over the cap.  In other words, you are no longer penalized on AoE damage for improving your gear.

The other thing to note about these new mechanics is that they only apply when you are damaging more than 10 targets.  On 10 or fewer targets, all spells, regardless of their potency, will deal full damage to all targets (again, before crits and resists are factored in).  This is especially relevant for higher damage abilities such as Howling Blast which can easily reach the AoE cap in as few as 4 targets in a raid setting (at very high gear levels, of course).  In my current gear in a 10-man raid (and this is against targets without the spell damage debuff), my Howling Blasts average a bit over 5000 damage, and can cap out at almost 10000 damage due to AP procs (and these are non-crits).  This means that it takes between 4 and 8 targets to cap out the damage on HB, much much less than the 20-30 it takes for a mage to cap out AE in similar gear.  With the new 3.3 mechanics, HB will guaranteed full damage against up to 10 targets, giving me a potential cap of up to 100000 damage, a nearly 3-fold increase in maximum damage.

An easy way to illustrate the advantages of this change is to relate it to the testing I did to determine the HB cap.  Against the 33 Converted Heroes gathered up by Frostbound, my HB was dealing 1136 damage a piece, for a total of ~37500 damage done.  Given the new system, and assuming maximum procs in a raid setting, I would be dealing a touch over 3000 damage per target, almost 3 times as much damage per cast as before.

There is a minimum in which this change is valuable, though, and it varies per spell.  In the case of Howling Blast, it takes a touch over 8000 AP for HB to have a cap more than 37500 damage on 10 targets (in other words, for the change to be a buff), which is relatively easy to achieve with a single of the many procs available in a raid setting in high-end raiding gear, but otherwise fairly out-of-reach.  For AE, the necessary spell power is absolutely ludicrous, requiring 12595 spell power to reach a cap of 37500 damage against 10 target, and that's for a mage with full points in Arcane Instability, Spell Impact, and World in Flames, a net 16% increase in damage to AE.

Still, on the whole this change is a good thing as it allows one of the few true damage caps in game to scale with gear.  I'm especially pleased as it means I'll no longer be seeing crits down around the 4-5k mark from HB against packs like the Exploding Lashlings on Freya.