Quick and Dirty Fire Guide

by Tachyon on Wed. 14. April 2010, 02:20

Filed under: fire, guide, raiding, spec, talents, featured

First and foremost, Fire was always my least favourite mage tree. Deep in my heart, I still am a Frost mage (/curses Blizzard for completely ruining it as a raid spec), and have fun raiding with an Arcane spec.
But as my guild is stuck in progress at the Lich King, I had to take desperate measures to optimize my contribution to this particular fight. In other words:
I'm raiding with fire and flames at the moment.



According to Kamigami Tools, Fire is now (since 3.3.3.) up to par with Arcane on some ICC 25 fights (especially Professor Putricide and Sindragosa), and even outperforms Arcane on the Lich King fight (and some other fights in heroic ICC too).

This quick and dirty written guide aims at experienced players who want (or have to) give Fire a try. I suggest reading my Arcane Mage Guide also, as all the stuff I don't mention here (gems, enchants, gear planning, faster casting) are mentioned there.

The Spec

I pondered long about the spec, and only after I was convinced that every point sits where it belongs I cross-checked it with the fire specs of high end mages. The fire spec of the first mage participating in the heroic ICC Lich King kill only differs by one point, so I think there's not much room to negotiate

Endgame Fire Raiding Spec:
53/18/0 Fire/Arcane

Stats

As a fire mage, you have no talents to increase your hit rating. If you assume that you have 3% hit from raid buffs, you need to get the missing 14% (or 13% if spacegoats are in your raid) from your gear. That's 367 hit rating, which should not be hard to get.
Stats priority (updated!)
Hit Rating (until cap) > Crit Rating > Spell Power > Haste > Spirit > Int

Spell Priority System

Fire doesn't use dynamic rotations like Arcane. There's not even a fixed rotation, but rather you will decide what spell to use next using a priority system:

• Priority 1: Keep Improved Scorch up
  Improved Scorch lasts 30 seconds, and increases the spell crit chance on the target by 5% for all casters. Warlocks' Improved Shadow Bolt has the same effect, and doesn't stack with Improved Scorch, so if warlocks in your raid have Shadow Bolt in their rotation, you can forget about applying the Scorch debuff.
• Priority 2: Keep Living Bomb up
  Living bomb does great damage on your target, especially when other targets get hit by the splash damage at the end. Remember that the huge damage comes at the end, so when your target is likely to die within 12 seconds, it's not worth (re-)appying it.
• Priority 3: Use your Hot Streak procs
  Hot Streak procs allow you to cast instant Pyros after two subsequent nonperiodic crits with fire spells. The biggest issue here is Ingite Munching, which causes the system to forget to bank the ignite of one spell if two fire spells crit more or less simultanousely. If you have at least two pieces of the Tier10 set, consuming the Hot Streak proc will give your 5 seconds of +12% spell haste (of which 1 global cooldown is wasted, at least 1 second), this makes it worth using at least when the haste buff isn't up. The pyros are mana consuming, if you ever run into mana problems you may want to use the instant pyros less often.
• Priority 4: Fireball chaincasting
  Pretty straightforward.
  

Configuring TellMeWhen

If you use TellMeWhen, you might want to watch for following procs/debuffs/cooldowns:

BUFFS/PROCS:

• Hot Streak: Buff, Player, When present, Timer

TARGET DEBUFFS:

• Improved Scorch: Debuff, Target, When present, Timer
• Living Bomb: Debuff, Target, When present, Timer, only if cast by self
• Ignite: Debuff, Target, When present, Timer, only if cast by self

COOLDOWNS:

• Combustion: Cooldown, Spell or Ability, When usable, Timer

Useful Macros

This macro lets you cast Living Bomb on the target under your mouse pointer, or if nothing there, on your selected target. Very handy to apply Living Bomb on multiple units without having to lose your current target!

#showtooltip Living Bomb
/cast [target=mouseover,harm,exists,nodead] Living Bomb; Living Bomb
Useful Addons

Keeping up Living Bomb on multiple targets isn't that easy, but fortunately there's a nice little addon that helps here:
Living Bomb Tracker shows a little tooltip when hovering with your mouse cursor over a target, showing whether Living Bomb is applied and how much time is left ticking before you can reapply it.

Understanding Ignite

Ignite is a core mechanic you are expected to understand if you raid with fire.
Whenever one of your fire spells crits, it will do 40% of that damage as DoT (Damage over Time). On a single crit, there will be two Ingite ticks, the first after 2sec, the second after 4sec, both doing 20% of the direct damage component of the spell that crit. If other spell crits happen when there's still Ignite damage to tick, the new Ingite damage is added to the amount that is left to tick, and the timer starts anew to tick after 2/4 seconds.

Example 1: Single crit
t=0sec, Fireball crits for 1000 damage. 400 damage (40%) is added to the Ignite bank.
t=2sec, Ignite ticks for 200 damage (half of what's on the bank)
t=4sec, Ignite ticks for 200 damage (the rest), Ignite debuff expires on the target.

Example 2: Multiple crits
t=0sec, Fireball crits for 1000 damage. 400 damage (40%) is added to the Ignite bank.
t=2sec, Ignite ticks for 200 damage (half of what's on the bank)
t=2.5 sec, Pyro crits for 1500 damage. 600 damage (40%) is added to the bank. Ignite timer is reset
t=4.5sec, Ignite ticks for 400 damage (half of what's on the bank)
t=5sec, Fireball crits for 1200 damage. 480 damage (40%) is added to the Ignite bank.
t=6sec, Fireball crits for 1000 damage. 400 damage (40%) is added to the Ignite bank.
t=8sec, Ignite ticks for 640 damage (half of what's on the bank)
t=10sec, Ignite ticks for 640 damage (the rest), Ignite debuff expires on the target.

This effect of banking Ignite damage is called 'Rolling Ignites'. Back in the classic days, there was only one Ignite bank per unit, so fire mages all added to the same pool. If their crit chance or number was high enough, Ignites could roll for a very long time, increasing the size of the ticks and causing aggro problems to the fire mage which caused the last crit. In vanilla WoW, once Ignite was applied it ticked every 2 seconds until it expired. The damage of the first tick was not substracted, but instead each tick was meant to do half of the banked damage. If rolling ignites occurred, the new Ignite damage was banked to the initial damage and the tick timer was reset to 2, so any damage from the first tick could tick again. This bug caused the banked damage to grow to massive dimensions sometimes, and was a hidden damage boost of fire mages. That had been fixed with patch 2.0, giving each player its own ignite bank slot, substracting any damage ticks and resetting the timer when a new crit occured.

What this means for you: be aware that not all your damage is unloaded directly, and subsequent crits can delay the dot damage (theoretically ad infinitum). Any Ignite damage still banked when your target dies is lost, this is part of the reason fire specs are atrocious for levelling or any target that doesn't live long enough (such as the Ice Spheres in the Lich King fight).

I hope you enjoyed this guide. If there's anything you think should be added, drop me a note in the comments. Now go and RELEASE THE BURNING KRAKEN!

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Tier 10 Set Boni from an Arcane Mage's Perspective

by Tachyon on Wed. 09. December 2009, 18:46

Filed under: arcane, spec, talents, sets, patch, 3.3, haste, tier 10

EDIT 2010-01-22: Tested and verified the mechanic of the T10x2 proc, added and corrected a few things in the article.

Patch day, 3.3 went live today in Europe. This time I refrained from summing up the changes (new raidwide 3% crit buff by Arcane mages, Fire and especially Frost get some small buffs) and instead point to WoW.com's patch 3.3 coverage.

Instead, I will focus on the new Tier 10 sets (presumably the last set we get before the next expansion) that are introduced by patch 3.3.

The Tier 10 armor sets come in three flavours, with an item level of 251, 264 and 279 respectively.
The starting set items are bought with Emblems of Frost, and can be upgraded with normal and heroic (Vanquisher's) Marks of Sanctification.

Emblems of Frost
Emblems of Frost can be obtained from the following sources:

• (3) as loot from killing any boss in Icecrown Citadel
• (3) as loot from killing Toravon the Ice Watcher in Archavon's Vault
• (2) as reward for running the first Daily Heroic Random each day (new in 3.3)
• (5) as reward for completing the Weekly Raid Quest (new in 3.3)

Mage Tier 10 Set(s)

Bloodmage's Regalia Set Boni:

• 2 pieces: Your Hot Streak, Missile Barrage, and Brain Freeze talents also grant you 12% haste for 5 sec when the effect of the talent is consumed.
• 4 pieces: Your Mirror Image ability also causes you to deal 18% additional damage for 30 sec.

Mage Tier 10 2-pieces bonus

After each MBarr cast (Arcane Missiles on a Missile Barrage proc), you gain a buff called Pushing the Limit, which increases your haste for the next 5 sec by 12%.
Note that you gain this buff after channeling Arcane Missiles finishes (or is interrupted), so you gain the full 5 seconds for your next casts.

To find out how much the 2-pieces bonus is worth, I adapted the Casting Simulation acordingly and ran it again with the same parameters as before (3000 Spell Power, Hit Capped, 20% Spell Haste before talents, 50% Spell Crit including CSD). Here are the results:

.	A=0	A=1	A=2	A=3	A=4	A=5
B=0	5261 DPS 14.21 DPM -10.47% DPS -16.80% DPM	5153 DPS 16.19 DPM -12.31% DPS -5.21% DPM	5173 DPS 16.37 DPM -11.97% DPS -4.16% DPM	5257 DPS 15.4 DPM -10.54% DPS -9.84% DPM	5417 DPS 13.39 DPM -7.81% DPS -21.60% DPM	5459 DPS 11.98 DPM -7.11% DPS -29.86% DPM
B=1	5186 DPS 32.99 DPM -11.75% DPS +93.15% DPM	5161 DPS 33.43 DPM -12.16% DPS +95.73% DPM	5195 DPS 27.76 DPM -11.59% DPS +62.53% DPM	5315 DPS 21.96 DPM -9.55% DPS +28.57% DPM	5485 DPS 17.42 DPM -6.65% DPS +1.99% DPM	5532 DPS 13.75 DPM -5.86% DPS -19.50% DPM
B=2	5401 DPS 32.77 DPM -8.08% DPS +91.86% DPM	5378 DPS 33.02 DPM -8.48% DPS +93.33% DPM	5395 DPS 28.96 DPM -8.19% DPS +69.56% DPM	5499 DPS 22.17 DPM -6.42% DPS +29.80% DPM	5642 DPS 17.5 DPM -3.98% DPS +2.46% DPM	5664 DPS 13.78 DPM -3.60% DPS -19.32% DPM
B=3	5597 DPS 29.15 DPM -4.75% DPS +70.67% DPM	5578 DPS 29.2 DPM -5.07% DPS +70.96% DPM	5566 DPS 26.8 DPM -5.28% DPS +56.91% DPM	5648 DPS 21.78 DPM -3.89% DPS +27.52% DPM	5776 DPS 17.24 DPM -1.70% DPS +0.94% DPM	5774 DPS 13.58 DPM -1.74% DPS -20.49% DPM
B=4	5760 DPS 26.16 DPM -1.97% DPS +53.16% DPM	5750 DPS 26.22 DPM -2.15% DPS +53.51% DPM	5728 DPS 24.78 DPM -2.52% DPS +45.08% DPM	5783 DPS 20.96 DPM -1.59% DPS +22.72% DPM	5873 DPS 17.08 DPM +0.00% DPS +0.00% DPM	5863 DPS 13.44 DPM -0.23% DPS -21.31% DPM
B=5	5857 DPS 24.1 DPM -0.33% DPS +41.10% DPM	5850 DPS 24.18 DPM -0.45% DPS +41.57% DPM	5818 DPS 23.2 DPM -0.99% DPS +35.83% DPM	5861 DPS 20.1 DPM -0.27% DPS +17.68% DPM	5939 DPS 16.75 DPM +1.07% DPS -1.93% DPM	5858 DPS 13.44 DPM -0.31% DPS -21.31% DPM
B=6	5904 DPS 23.15 DPM +0.48% DPS +35.54% DPM	5903 DPS 23.12 DPM +0.46% DPS +35.36% DPM	5869 DPS 22.39 DPM -0.12% DPS +31.09% DPM	5903 DPS 19.63 DPM +0.46% DPS +14.93% DPM	5980 DPS 16.57 DPM +1.76% DPS -2.99% DPM	5915 DPS 13.36 DPM +0.66% DPS -21.78% DPM
B=7	5936 DPS 22.53 DPM +1.01% DPS +31.91% DPM	5933 DPS 22.65 DPM +0.97% DPS +32.61% DPM	5902 DPS 21.96 DPM +0.45% DPS +28.57% DPM	5932 DPS 19.45 DPM +0.95% DPS +13.88% DPM	5997 DPS 16.47 DPM +2.05% DPS -3.57% DPM	5940 DPS 13.31 DPM +1.09% DPS -22.07% DPM
B=8	5954 DPS 22.26 DPM +1.33% DPS +30.33% DPM	5951 DPS 22.25 DPM +1.27% DPS +30.27% DPM	5916 DPS 21.64 DPM +0.68% DPS +26.70% DPM	5942 DPS 19.31 DPM +1.13% DPS +13.06% DPM	6008 DPS 16.39 DPM +2.25% DPS -4.04% DPM	5958 DPS 13.28 DPM +1.40% DPS -22.25% DPM
B=infinite	5977 DPS 21.83 DPM +1.72% DPS +27.81% DPM	5979 DPS 21.84 DPM +1.74% DPS +27.87% DPM	5939 DPS 21.37 DPM +1.07% DPS +25.12% DPM	5970 DPS 19.08 DPM +1.60% DPS +11.71% DPM	6031 DPS 16.3 DPM +2.63% DPS -4.57% DPM	5991 DPS 13.25 DPM +1.96% DPS -22.42% DPM

The best spell rotations when having the 2pT10 bonus are the A=0|1, B->Infinite rotations (lower left corner in the table above). They even have higher DPS than Arcane Blast spamming (which has 5788.37 DPS @ 6.68 DPM), so it's also the preferred rotation for burst phases.

The A=4, B->Infinite rotation that is the current 'state of the art' shouldn't be used anymore with the 2pT10 bonus, as it yields marginally lower DPS and way worse DPM compared to the A=0|1, B->Infinite rotations.

Recommended 2pT10 rotation: A=0|1, B->Infinity
Spam Arcane Blast, use Missile Barrage immediately or after the next Arcane Blast cast.

But now much is the DPS boost with the set bonus?
A=0, B->Infinite:
Without set bonus: 5560 DPS @ 21.88 DPM, 254.11 mana/sec
With 2pT10 Bonus: 5977 DPS (+7.50%) @ 21.83 DPM (-0.23%), 273.8 mana/sec (+7.75%),

The 2pT10 bonus here gives a plain +7.5% DPS boost, that's pretty massive!

The A=0, B->Infinite rotation with 2pT10 yields 5.43% more DPS compared to the A=4, B->Infinity rotation without the bonus (5669 DPS @ 16.30 DPM), that's the effective DPS increase as we are also swapping our main spell rotation.

New peak haste cap!

The haste peak is defined by:

• 1% per 32.79 haste rating on your gear
• 6% from Talents
• 5% from Wrath of Air Totem
• 3% from Swift Retribution or Improved Moonkin Form
• 20% when Icy Veins is active
• 30% when Bloodlust or Heroism is active
• 12% from 2pT10 procs after casting MBarr

The haste peak cap is reached when your spells (Arcane Blast and Missile Barrage + Arcane Missiles, both having a 2.5 sec base cast time) have an effective cast time of 1 sec (subsequent spells can't be cast any faster).

The haste% factors scale multiplicatively, so your haste peak cap now is at:
(2.5 / (1.06*1.05*1.03*1.2*1.3*1.12) - 1) * 3279 = 814 (813.337) haste rating.

Please note that I ignored the effect of Speed Potions and on-proc haste Trinkets; if we take those into account the haste peak cap would be even lower.

Black Magic

Also note that the weapon enchant for Black Magic has been changed in patch 3.3, and can now proc 250 haste for 10 seconds (proc chance: 35%, 30 sec assumend internal cooldown). When you're at 564 haste or above, Enchant Weapon - Mighty Spellpower might still be the better choice though.
For PvP though, Black Magic is godsend!

Mage Tier 10 4-pieces bonus

The 4-pieces bonus is really nice and works like second Arcane Power (and yes, it stacks), giving mages an even higher burst potential. With a 30 sec duration and 3 min cooldown, the average uptime on a fight with infinite duration is 1/6, which is a plain 3% damage boost. The shorter the fight duration, the larger the uptime, when we keep Mirror Images on cooldown. If we assume randomly distributed fight durations between 1 min and 10 min, the average uptime is 22%, which is almost a 4% damage boost. If you use it along with your other cooldowns such as Arcane Power, Icy Veins, Bloodlust/Heroism and Trinkets, the bonus is worth much more.

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Arcane Mage: Stats contribution

by Tachyon on Wed. 23. September 2009, 20:47

Filed under: arcane, spec, theorycrafting, analysis

In the previous article, we derived the formulas to calculate the DPS (Damage per Second) and DPM (Damage per Mana) for the two suggested new arcane rotations (covered in this article).

The formulas are based on the mage's spellpower, crit chance, hit chance and haste. In this article, we want to further split up those variables and show how they are calculated from your mage's stats (intellect, spirit, spellpower, crit/hit/haste rating), talents and glyphs (for arcane mages: Glyph of Molten Armor, Glyph of Arcane Blast, Glyph of Arcane Missiles).
Given those refined formulas, we can then investigate how much each stat contributes to the new spell rotations' DPS.

Stats conversion

Intellect
Intellect is increased by 15% by the Arcane Mind (5/5) talent:
effectiveIntellect := intellect * 1.15
Spirit
Spirit is increased by 10% by the Student of the Mind (3/3) talent:
effectiveSpirit := spirit * 1.1
Spellpower
Spellpower is increased by 15% of your intellect by the MindMastery 5/5 talent:
effectiveSpellpower := spellpower + effectiveIntellect * 0.15
Crit%
The base class crit chance for mages is 0.91%. Intellect will also increase your crit chance (by 1% every 166 2/3 int). The rest of your crit chance is determined by your crit rating (1% per 45.91 crit rating), whereas you get 55% of your spirit as additional crit rating if you use Molten Armor with its glyph (with 2pT9 bonus it would be even more). Crit% is capped at 100%, for obvious reasons.
crit% := min (1, 0.0091 + effectiveIntellect * 3 / 50000 + (critRating + spirit * 0.55) / 4591)
Hit%
Against boss targets (who are considered lvl 83), you have a 17% chance to miss with spells. Arcane Focus (3/3) increases your hit chance by 3%, and in any reasonable raiding scenario an additional 3% is contributed by a Shadow Priest (Misery debuff) or Balance Druid (Improved Faerie Fire debuff). Additional hit rating will grant you 1% hit per 26.23 rating, or 17% for 446 rating. Hit% is also capped at 100%.
hit%:= min(1, 0.83 + hitRating * 0.17 / 446 + 0.03 + 0.03)
Haste%
32.79 haste rating grants 1% haste, and from Netherwind Presence (3/3) you get an additional 6% haste.
haste%:= hasteRating / 3279 + 0.06

DPS per stat: Graphical analysis

To find out how much additional stats contribute to the DPS, we can start with a base set of stat values, calculate the base DPS for that stat combination using the DPS formulas, and calculate the relative DPS increase that results from increasing any of the stats individually. Details on the spell rotation used here can be found in this article.

For a basic poor mages' stat combination, I chose the following values:
500 intellect, 200 spirit, 1500 spellpower, 0 crit/hit/haste rating.

Chart: Relative DPS increase per additional stat value, A=0/B->Infinity rotation:


As you can see, hit rating proves to be the most important stat until the hit cap is reached; after that point it ceases to provide any more DPS.
We can now calculate the Spell Power Equivalent (SPE) value for each stat, which allows us to compare how much each stat is worth compared to 1 spellpower:

1 hit rating = 1.2280 spellpower
1 crit rating = 0.4917 spellpower
1 haste rating = 0.8250 spellpower
1 intellect = 0.3269 spellpower
1 spirit = 0.2975 spellpower

Those values vary depending on the given stat combination, but using the formulas above you should be able to do the math to find out the SPE values for your current gear.

Once you reach the hit cap, and your stats get better, the chart and SPE values will look a little different. As an example, here's the results for my current gear:
1170 intellect, 634 spirit, 2411 spellpower, 370 hit rating, 582 crit rating, 481 haste rating.

Chart: Relative DPS increase per additional stat value, A=0/B->Infinity rotation:


1 hit rating = 0.0000 spellpower
1 crit rating = 0.5659 spellpower
1 haste rating = 0.9828 spellpower
1 intellect = 0.3559 spellpower
1 spirit = 0.3424 spellpower

The chart for a A=4/B->Infinity rotation looks almost the same:

Chart: Relative DPS increase per additional stat value, A=4/B->Infinity rotation:


1 hit rating = 0.0000 spellpower
1 crit rating = 0.5663 spellpower
1 haste rating = 0.9983 spellpower
1 intellect = 0.3560 spellpower
1 spirit = 0.3426 spellpower

Here, additional hit rating is completely worthless, and haste rating has become worth as much as spellpower (in fact it will even become worth more that spellpower the better your overall stats are).

For more accurate results, you can try to take all raid buffs into account and inject them in the formulas, or use your raid buffed stats as an input.
The aim of the formulas is to give you a tool to do some quick analyses and comparisons, but keep in mind that they cannot be as accurate as a simulated scenario which also takes raid buff uptimes, trinkets, movement, lag, input delay and different encounter lengths into account.

Oh, and thanks to Google for their wonderful and well-documented Chart API, which I used for the charts here and intend to use from now on whenever suitable

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Arcane 3.2.2 Theorycrafting

by Tachyon on Wed. 23. September 2009, 00:58

Filed under: arcane, spec, theorycrafting

Last time we analyzed the impact that the patch 3.2.2 Arcane Mage Changes have on the spell rotations with the help of a simulation program I wrote. The simulation casts spells, rolls dice and can do dynamic decisions on what spell to cast next based on a casting strategy.
Using a simulation to gain numerical results of different casting strategies is like employing Monte Carlo Integration to integrate multidimensional functions: it's plain simple, reliable and leads to accurate results, but takes a long time.

The simulation provides only numerical solutions, so you'd have to test different scenarios one-by-one, which isn't very efficient.

In this article, we will derive the theorycrafting formulas to calculate the DPS and DPM for the two recommended spell rotations I introduced in the last article, to be able to calculate the DPS and DPM for any scenario directly. This not only saves us time (direct calculation vs. approximating using simulation), but gives you a tool to do the calculations yourself without me having to publish my simulation program. Furthermore, we can use the formulas to observe the results we get when tweaking with the input (in fact that will be the topic of the next article, where we observe how much the mage's stats contribute to the DPS and DPM for those rotations).

Just for completeness, here are the two recommended spell rotations for 3.2.2+:

• Recommended optimal rotation: A=0, B->Infinity
  Spam Arcane Blast, use Missile Barrage as soon as it procs
• Recommended high/burst DPS rotation: A=4, B->Infinity
  Spam Arcane Blast, use Missile Barrage when it procs and AB is fully stacked (4 stacks).

Both rotations only consist of a sequence of AB (Arcane Blast) casts followed by Arcane Missiles on a MBarr (Missile Barrage) proc. This simplifies things a lot, as there are only two spells we have to investigate: AM and MBarr.

Average damage per spell

The noncrit damage of a spell is the average base damage plus the spellpower times the spell power coefficient, times any spell multipliers:
dmgNoncrit := (( baseDmgMin + baseDmgMax) / 2 + spellpower * coefficient ) * multiplier
The average damage is the chance of a notcrit-hit times the noncrit damage plus the chance of a crit times the crit damage. The crit damage is the noncrit damage times the crit multiplier:
avgDmg := hit% * ((1 - crit%) * noncritDmg + crit% * noncritDmg * critMultiplier
When we combine the formulas and simplify them, we get:
avgDmg := hit% * ((( baseDmgMin + baseDmgMax) / 2 + spellpower * coefficient ) * multiplier* (1 + crit% (critMultiplier -1)))
The multiplier for all arcane spells is 1.03 * 1.12 (3% from Arcane Instability and 12% from Torment The Weak). Spellpower, Hit% and Haste% are equal for both spells, only the Crit% is different as AB gets an additional 6% from Incineration 3/3.

The base damage, cast time, mana and spell power coefficient are spell-specific:

Arcane Blast:

• Base Damage: 1185-1377
• Cast Time: 2.5 sec
• Mana: 215
• Spell Power Coefficient: 2.5/3.5+0.09 = 80.42857143%
• Crit Multiplier: 1+(((1.5*1.03)-1)*(1+0.5)) = 1.8175 (with CSD metagem)

Missile Barrage (Arcane Missiles):

• Base Damage: 360-361 x 5
• Cast Time: 2.5 sec (half the time of AM)
• Mana: 0 (free AM on MBarr proc)
• Spell Power Coefficient: 5/3.5+0.45 = 187.8571429%
• Crit Multiplier: 1+(((1.5*(1+0.03))-1)*(1+0.5+0.25)) = 1.95375 (with CSD metagem & AM glyph)

Missile Barrage proc chance

Arcane Blast has a chance of 40% to proc Missile Barrage, which lets you cast your next Arcane Missiles in half the casttime. The chance that it didn't proc is therefore 60%, and the chance that it procs on your next AB is 40% of that, which is 60%*40%=24%. The probability that it doesn't proc after ABxN is 0.6^n, and for each subsequent AB the chances are split again in this 40%/60% ratio.
The MBarr proc chance on the n-th AB cast are therefore:
procChance(n):=0.4*(1-0.4)^(n-1), for n>0, with procChance(0):=0
ABxN-MBarr cast sequences

For a cast sequence that consist of n x Arcane Blast followed by Missile Barrage, we get following formulas for the damage, cast time and mana cost:

damage(n) := sum(dmgAB*(1+0.18*min(x, 4)), x=0..n-1)+dmgMBarr*(1+0.18*min(n, 4))
casttime(n) := n*casttimeAB+casttimeMBarr
mana(n) := sum(manaAB*(1+1.75*min(x, 4)), x=0..n-1)+manaMBarr

For the damage calculation, we took the Arcane Blast glyph into account, which increases the damage for the next arcane spell by another 3% (from 15% to 18%) per AB stack.

Weighting the rotations

We've now got the formulas to calcuate the average damage for AB and MBarr, and we can even calculate the total damage, mana and casttime for a given ABxNMBarr rotation. The number of ABs we cast before we cast MBarr is very dynamic, as both suggested rotations cast an unlimited number of Arcane Blasts in a row until Missile Barrage procs. To calculate the overall DPS and DPM, we have to calculate the DPS and DPM for any possible ABxNMBarr rotation and weight them with the probability they occur:

A=0, B->Infinity rotation (optimal DPS/DPM):DPS := sum(damage(n)*procChance(n), n=1..infinity)/sum(casttime(n)*procChance(n), n=1..infinity)

DPM := sum(damage(n)*procChance(n), n=1..infinity)/sum(mana(n)*procChance(n), n=1..infinity)
As the terms for larger values of n quickly become insignificant (for n>26 its under 1:1000000, for n>39 under 1:1000000000), we can approximate the sums with a large non-finite value (I used 100, which more than suffices) to simplify the formulas significantly. Approximated formulas:
DPS := (3.08752*dmgAB+1.39168*dmgMBarr)/(2.5*casttimeAB+casttimeMBarr)
DPM := (3.08752*dmgAB+1.39168*dmgMBarr)/(8.212*manaAB)
A=4, B->Infinity rotation (high DPS):DPS := (damage(4)*sum(procChance(n), n=1..4)+sum(damage(n)*procChance(n), n=5..infinity))/(casttime(4)*sum(procChance(n), n=1..4)+sum(casttime(n)*procChance(n), n=5..infinity))

DPM := (damage(4)*sum(procChance(n), n=1..4)+sum(damage(n)*procChance(n), n=5..infinity))/(mana(4)*sum(procChance(n), n=1..4)+sum(mana(n)*procChance(n), n=5..infinity))
Approximated formulas:
DPS := (5.63728*dmgAB+1.72*dmgMBarr)/(4.324*casttimeAB+casttimeMBarr)
DPM := (5.63728*dmgAB+1.72*dmgMBarr)/(17.092*manaAB)

Given any combination of spellpower, hit%, crit% and haste% we're now able to calculate the DPS, DPM and Mana/sec (which is DPS divided by DPM) for both rotations. I intentionally refrained from cramming all the individual formulas into the final DPS/DPM formulas to keep them plain and simple.

The next article will introduce the conversion formulas needed to calculate the spellpower, hit%, crit% and haste% using the mage's stats (spellpower, intellect, spirit, hit/crit/haste rating) and arcane talents, to complete the toolset of arcane theorycrafting formulas.

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Patch 3.1 goes live

by Tachyon on Wed. 15. April 2009, 18:30

Filed under: patch, ulduar, spec, mage

Patch 3.1 - The Secrets of Ulduar - went live today in the US and EU.
Not much has changed since my PTR 3.1 post, and the mage class wasn't affected much by the many changes made in class balance.

The complete 3.1 patch notes can be found here:
http://www.worldofwarcraft.com/patchnotes/

Features in Patch 3.1:

Dual Talent specs

Class trainers now offer the ability to have a second talent spec for 1000 gold.
Each talent spec has its own set of mayor and minor glyphs, and its own set of key bindings. The two talent spec windows can be accessed by pressing 'N', that's also where you'll find the glyph sets now. Switching your talent spec is a 5 second cast (affected by haste!) and can be done everywhere when you're out of combat, except in battlegrounds and arenas. No tome of power is required for applying glyphs anymore.

As a mage, you will most probably want to have a raid-oriented spec, and a PvP/solo/trash spec.

My choice of spec is follows:

• Raid PvE: 56/3/12 Arcane
  http://www.wowhead.com/?talent#of0Vfz0IzxGuMtedcZb...
  That's the spec I'm using now, I'm quite content with it. I decided to keep slow, and placed another point in frost to get 3/3 Ice Shards for superb Blizzard DPS.
• PvP / Solo: 20/0/51 Frost-TTW
  http://www.wowhead.com/?talent#of0ic0McZZAc0fRbu0f...
  Yay, finally back to frost! The 20 points into arcane are mandatory for PvP to get Torment The Weak and Improved Counterspell. That leaves too few points left to get all the goodies in frost, so I had to make tradeoff decisions between DPS/utility/cooldowns.

Ulduar / T8

The new raid instance, Ulduar, is the main focus of the 3.1 content patch.

My guild will venture into that place starting tonight, and I'm really looking forward to learning new encounters with my guild mates (unlike the T7 dungeons, where I got piggybacked through more or less, which was rather challenging for me as everyone except me was already quite used to the encounters).

MMO-Champion already reports severaly world first kills of Ulduar bosses by US guilds, seems they managed to use their head start to their advantage (but I'm sure that the EU-Guilds will get the credits for a Yogg-Sharon first kill).

Mage changes

The changes to the mage class are, like, not spectacular. At all.
Despite Blizzard announcing that they intended to make frost viable for raiding again, and fire solid for PvP, neither of that happened.
Frost continues its existance as a pure PvP or trash mob spec for the time being, but thanks to dual speccing, that's not much of an issue.

Out-of-combat mana regeneration was lowered, but that affect more the healing classes, as we mages got compensated for that loss by higher in-combat regeneration, so for us it eves out.

There are only two big changes concerning the mage class:

• Molten Armor and the according glyph now grants its crit chance based on the spirit, and no longer on a fixed value.
  
  Molten Armor used to increase the crit chance by 3% (with the glyph: 5%), and now grants 35% crit rating (55% with glyph) per point in spirit.
  Remember that it takes 45.91 critical strike rating for 1% critical strike chance, so to end up with the same crit chance as before, you'd need to have 394 spirit (without the glyph) or 417 spirit (with the glyph).
  For PvP, this is a huge nerf (for solo play it doesn't matter that much), as you barely got any spirit on your PvP gear. With my current raid gear, I'm at 370 spirit unbuffed, so in a raid scenario my crit chance will be slightly higher than before.
  
  Despite the PvP nerf and despite the fact that spirit is one of the worst stats to get on gear, I think the change is justified, and mages finally scaling with spirit is nice and necessary.
• The Improved Scorch and Winter's Chill crit debuff were lowered to 1/2/3/4/5% (from 2/4/6/8/10%). After a few gazillion sour mage tears, we got compensated with an increased crit chance for Scorch, Fireball and Frostfire Bolt (1/2/3% with Improved Scorch) and Frostbolt (1/2/3% with Winter's Chill).

Argent Tournament

To be honest, I couldn't care less for the Argent Tournamentright now, but hey who knows, I'm sure I'll pass by some day anyway.

I never bothered to read into the details, but if I recall correctly it's a horse mount PvP duel thingy which rewards titles and vanity pets. Whatever.

Miscellaneous

• Mounts now can swim (and dive?)
• Flasks only last 1h (before: 2h). The recipies stay the same, but will yield now two flasks at once. Old flasks were migrated to 'mixtures' which can be transformed to 2 new flasks.
• Curse Gaming and WowInterface.com decided to block WoWMatrix requests. I switched to the curse client to keep my addons up-to-date, works quite well.
• A new boss named Emalon The Stonewatcher has been added to Archavon's Keep in Lake Wintergrasp. The new boss dropps the iLvl 226/232 Furious Gladiator PvP gear.

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Going Arcane, Part 3 - Spell Rotations

by Tachyon on Fri. 20. February 2009, 00:22

Filed under: arcane, spec, raiding, dps, patch, theorycrafting

In part 2 of this series, we introduced the theorycrafting basics to calculate the average DPS for the single target arcane spells, as well as the DPM. Now let's look into possible spell rotations.

The arcane spec allows to dynamically tweak the DPS/DPM depending on how many subsequent Arcane Blasts are cast.

The Arcane Blast debuff

Remember that Arcane Blast applies a stackable debuff (up to 3 times), which increases the damage of the next arcane spell by 15% (18% with the Arcane Blast glyph) per stack, but also increases the mana cost of the next Arcane Blast by 200%.
Casting Arcane Missiles or Arcane Barrage will consume that buff and thus reset the stack. Note also that those spells will profit from the increased damage, but will not get a mana penalty.

• Arcane Blast, 1 stack: increases damage by 18%, next AB costs 3x its base mana
• Arcane Blast, 2 stacks: increases damage by 36%, next AB costs 5x its base mana
• Arcane Blast, 3 stacks: increases damage by 54%, next AB costs 7x its base mana

Being to lazy to do all the calculations in a spreadsheet, I wrote a small simulation program in Java instead. Here's the outcome:

DPS/DPM for arcane cast sequences

Rotation	Damage	Time	DPS	Mana	DPM	Mana/sec
ABx1	4968.000	2.155	2305.150	245.000	20.280	113.680
ABx2	10830.000	4.310	2512.560	980.000	11.050	227.360
ABx3	17586.000	6.466	2719.970	2205.000	7.980	341.040
ABx4	25236.000	8.621	2927.380	3920.000	6.440	454.720
ABx5	32886.000	10.776	3051.820	5635.000	5.840	522.928
ABx10	71136.000	21.552	3300.710	14210.000	5.010	659.344
ABx100000	764994636.000	215517.241	3549.580	171497060.000	4.460	795.746
ABx0, ABarr	3762.000	1.293	2909.280	553.000	6.800	427.653
ABx1, ABarr	9407.000	3.448	2728.030	798.000	11.790	231.420
ABx2, ABarr	15946.000	5.603	2845.750	1533.000	10.400	273.582
ABx3, ABarr	23379.000	7.759	3013.290	2758.000	8.480	355.476
ABx4, ABarr	31029.000	9.914	3129.880	4473.000	6.940	451.190
ABx5, ABarr	38679.000	12.069	3204.830	6188.000	6.250	512.720
ABx0, Mbarr	8812.000	2.155	4088.770	952.000	9.260	441.728
ABx1, Mbarr	15367.000	4.310	3565.140	1197.000	12.840	277.704
ABx2, Mbarr	22815.000	6.466	3528.720	1932.000	11.810	298.816
ABx3, Mbarr	31157.000	8.621	3614.210	3157.000	9.870	366.212
ABx4, Mbarr	38807.000	10.776	3601.290	4872.000	7.970	452.122
ABx5, Mbarr	46457.000	12.931	3592.670	6587.000	7.050	509.395
ABx0, AM	8812.000	4.310	2044.380	952.000	9.260	220.864
ABx1, AM	15367.000	6.466	2376.760	1197.000	12.840	185.136
ABx2, AM	22815.000	8.621	2646.540	1932.000	11.810	224.112
ABx3, AM	31157.000	10.776	2891.370	3157.000	9.870	292.970
ABx4, AM	38807.000	12.931	3001.070	4872.000	7.970	376.768
ABx5, AM	46457.000	15.086	3079.440	6587.000	7.050	436.624

(AB = Arcane Blast, ABxN = N subsequent AB casts (max. 3 stacks), ABarr = Arcane Barrage, AM = Arcane Missiles, MBarr = AM cast on Missile Barrage)

A first approach towards a new cast sequence

According to these results, you get the highest DPS cycle when using Missile Barrage procs as early as possible. Arcane Missiles however should never be cast without Missile Barrage procs, the DPS is just not competitive without it.

So my first approach (Rotation_Tachyon)was following:

• Cast AM when MBarr procs, no mater how many stacks of AB you have
• Otherwise cast AB, stack maximally to 3, then use ABarr if MBarr didn't proc

Running the simulation with this rotation (1'000'000 spells cast) resulted in:
Rotation_Tachyon: 3279.46 DPS, 9.58 DPM

Then I wanted to compare this to the classic rotation:

• Cast AB until you have 3 stacks
• Cast AM if MBarr procced, otherwise cast ABarr

Rotation_Classic: 3351.04 DPS, 9.27 DPM

To my surprise, the classic rotation still had slightly more DPS. This is confusing, as the rotation involved less MBarr procs than the first rotation. I'd have expected to see higher DPS when using more of the high DPS sequences, but obviously that was not the case. To explain this effect, it's crucial to know how to calculate the DPS/DPM of mixed rotations.

Spell rotation: DPS/DPM of mixed cast sequences

The best cast sequence above, ABx0,Mbarr is only sustained for a very short time, so it contributes less to the overall DPS than other rotations which have a longer run time.

The total DPS contribution of a cast sequence is therefore to be weighted by the length of the sequence, the DPS during that lenght, and the probability you are casting it.
DPS := sum(DPS[i]*t[i]*p[i]) / sum(t[i]*p[i])
where DPS[i] is the DPS of Sequence_i, t[i] is the cast time of Sequence_i, and p is the probability (or percentage of times) we use Sequence_i.

To determine the probabilities, the simulation comes to aid again. Results:
RotationTachyon:
ABx3, ABarr 46.5139%
ABx1, MBarr 18.0682%
ABx2, MBarr 14.4659%
ABx3, MBarr 11.6308%
ABx0, MBarr 9.3213%
RotationClassic:
ABx3, MBarr: 53.5976%
ABx3, ABarr: 46.4024%
The calculated weighted DPS matches the results of the simulated DPS, so you can take that formula along with the probabilities as given fact for your own theorycrafting calculations.

In conclusion, the best approach is to use the longest cast sequences that give you good DPS without wasting too much mana, as they often contribute more to the effective DPS than short cast sequences with slightly higher DPS.

Generic pattern of arcane rotations

Basically, every arcane rotation follows the same pattern:

• If Missile Barrage procced, use it after at least A subsequent Arcane Blast casts
• If Missile Barrage didn't proc after B subsequent Arcane Blast casts, cast Arcane Barrage instead

There are two paramenters in there, A and B. My suggested rotation was A=0,B=3, while the classic rotation is A=3,B=3.

Using the simulation, I calculated the DPS and DPM for the configurations A=0..6, B=0..6, and here's the result:

.	A=0	A=1	A=2	A=3	A=4	A=5
B=0	3204 DPS 7.43 DPM	3171 DPS 8.62 DPM	3219 DPS 8.86 DPM	3312 DPS 8.44 DPM	3343 DPS 7.55 DPM	3366 DPS 6.98 DPM
B=1	3028 DPS 11.66 DPM	3029 DPS 12.21 DPM	3095 DPS 11.8 DPM	3196 DPS 10.56 DPM	3238 DPS 8.99 DPM	3271 DPS 8.06 DPM
B=2	3136 DPS 10.93 DPM	3132 DPS 11.23 DPM	3165 DPS 11.09 DPM	3262 DPS 10.08 DPM	3296 DPS 8.67 DPM	3321 DPS 7.84 DPM
B=3	3278 DPS 9.58 DPM	3272 DPS 9.75 DPM	3286 DPS 9.78 DPM	3351 DPS 9.27 DPM	3374 DPS 8.13 DPM	3394 DPS 7.43 DPM
B=4	3371 DPS 8.36 DPM	3363 DPS 8.47 DPM	3370 DPS 8.56 DPM	3417 DPS 8.34 DPM	3432 DPS 7.6 DPM	3445 DPS 7.02 DPM
B=5	3428 DPS 7.78 DPM	3422 DPS 7.85 DPM	3425 DPS 7.96 DPM	3462 DPS 7.83 DPM	3470 DPS 7.27 DPM	3479 DPS 6.82 DPM
B=6	3467 DPS 7.44 DPM	3462 DPS 7.49 DPM	3462 DPS 7.59 DPM	3493 DPS 7.52 DPM	3498 DPS 7.07 DPM	3503 DPS 6.68 DPM
B=7	3493 DPS 7.22 DPM	3489 DPS 7.26 DPM	3488 DPS 7.36 DPM	3516 DPS 7.32 DPM	3518 DPS 6.92 DPM	3521 DPS 6.58 DPM
B=8	3513 DPS 7.08 DPM	3510 DPS 7.1 DPM	3508 DPS 7.21 DPM	3532 DPS 7.17 DPM	3534 DPS 6.83 DPM	3535 DPS 6.51 DPM
B=9	3527 DPS 6.97 DPM	3525 DPS 6.99 DPM	3521 DPS 7.08 DPM	3545 DPS 7.06 DPM	3546 DPS 6.76 DPM	3546 DPS 6.46 DPM

In the table above, I grayed out every rotation for which there is a better (more DPS and more DPM) alternative rotation in the table. The remaining rotations have either better DPS or better DPM than any other rotation in the table.

To put the result in a more relative context, let's take the classic rotation (A=3, B=3) as a base (100%) and compare the relative differences:

.	A=0	A=1	A=2	A=3	A=4	A=5
B=0	-4.4% DPS -19.8% DPM	-5.4% DPS -7.0% DPM	-3.9% DPS -4.4% DPM	-1.2% DPS -9.0% DPM	-0.2% DPS -18.6% DPM	+0.5% DPS -24.7% DPM
B=1	-9.6% DPS +25.8% DPM	-9.6% DPS +31.7% DPM	-7.6% DPS +27.3% DPM	-4.6% DPS +13.9% DPM	-3.3% DPS -3.0% DPM	-2.4% DPS -13.1% DPM
B=2	-6.4% DPS +17.9% DPM	-6.5% DPS +21.1% DPM	-5.5% DPS +19.6% DPM	-2.6% DPS +8.7% DPM	-1.6% DPS -6.5% DPM	-0.9% DPS -15.4% DPM
B=3	-2.2% DPS +3.3% DPM	-2.4% DPS +5.2% DPM	-1.9% DPS +5.5% DPM	+0.0% DPS +0.0% DPM	+0.7% DPS -12.3% DPM	+1.3% DPS -19.8% DPM
B=4	+0.6% DPS -9.8% DPM	+0.4% DPS -8.6% DPM	+0.6% DPS -7.7% DPM	+2.0% DPS -10.0% DPM	+2.4% DPS -18.0% DPM	+2.8% DPS -24.3% DPM
B=5	+2.3% DPS -16.1% DPM	+2.1% DPS -15.3% DPM	+2.2% DPS -14.1% DPM	+3.3% DPS -15.5% DPM	+3.6% DPS -21.6% DPM	+3.8% DPS -26.4% DPM
B=6	+3.5% DPS -19.7% DPM	+3.3% DPS -19.2% DPM	+3.3% DPS -18.1% DPM	+4.3% DPS -18.9% DPM	+4.4% DPS -23.7% DPM	+4.5% DPS -27.9% DPM
B=7	+4.3% DPS -22.1% DPM	+4.1% DPS -21.7% DPM	+4.1% DPS -20.6% DPM	+5.0% DPS -21.0% DPM	+5.0% DPS -25.4% DPM	+5.1% DPS -29.0% DPM
B=8	+4.9% DPS -23.6% DPM	+4.8% DPS -23.4% DPM	+4.7% DPS -22.2% DPM	+5.4% DPS -22.7% DPM	+5.5% DPS -26.3% DPM	+5.5% DPS -29.8% DPM
B=9	+5.3% DPS -24.8% DPM	+5.2% DPS -24.6% DPM	+5.1% DPS -23.6% DPM	+5.8% DPS -23.8% DPM	+5.8% DPS -27.1% DPM	+5.8% DPS -30.3% DPM

Again, the grayed out rotations are to be avoided since there is a better alternative rotation with higher DPS and DPM.
The blue colored rotations are the ones with higher DPS, and the green colored rotations have a higher DPM ratio that the classic rotation. The red ones have less DPS and less DPM, so they should be avoided at any cost.

As a comparison, that's what you get with chain-spamming Arcane Blasts: 3549.58 DPS, 4.46 DPM.


Looks like the optimal path is to use the Missile Barrage proc only with the maximum Arcane Blast (3) stack, and to cast at least one Arcane Blast before using Arcane Barrage. The more subsequent Arcane Blast casts you can afford to wait hoping for a Missile Barrage proc, the higher the DPS, but the lower the DPM.
This path is always efficient, because there is no other alternative path that would yield more DPS for a higher DPM ratio.

So here's my recommended rotation:

DPS/Burst:

• If Missile Barrage procced, use it only with a full Arcane Blast (3) stack
• Otherwise keep casting Arcane Blast, hoping for a Missile Barrage proc. Use Arcane Barrage to reset your stack as soon as you think you're using too much mana.

DPM/Recovering:

• If Missile Barrage procced, use it not before having stacked the Arcane Blast debuff to 2-3
• Cast no more than 3 subsequent Arcane Blasts. Reset the stack with Arcane Barrage if Missile Barrage don't procs.

That's all folks, I hope my calculations aren't too far off, and remember that your mileage may vary, as always

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Going Arcane, Part 2 - Therorycrafting Basics

by Tachyon on Wed. 18. February 2009, 00:57

Filed under: arcane, spec, raiding, dps, patch, theorycrafting

As an arcane mage, your spell arsenal consists of:

• Arcane Blast, Arcane Missiles and Arcane Barrage for single-target damage
• PoM-Flamestrike and Blizzard for AoE (Area of Effect) damage

A good arcane talent spec that gets the optimum out the damage capabilities will put 3 points in fire (for Incineration, as it affects Arcane Blast), at least 11 points in frost to get Icy Veins and the rest in the arcane tree.

Personally I prefer to have 12 points in frost for more AoE damage (3/3 Ice Shards), so my recommended spec is something like this:
56/3/12 Arcane Raid Spec.


Some mages recommend more pushback protection by adding 3-4 points into Arcane Stability, but it's really hard to ditch some points there as it usually hurts other good talents.
Manly from Elitist Jerks even suggests a spec without Slow, and he's right for raiding as you really don't need the talent there, but boy I wouldn't run around without it outside a raid instance, so I'd rather sacrifice that points elsewhere, if at all.

I won't go into details for AoE damage in this article, as with the rotation above (and preferrable Arcane Power), it's straightforward to do massive(!) damage to multiple targets. So let's focus on the single target spells instead.

Arcane Blast - Rank 4
8% of base mana (261 Mana at lvl 80), 30 yd range, 2.5 sec cast
Blasts the target with energy, dealing 1185 to 1377 Arcane damage. Each time you cast Arcane Blast, the damage of all Arcane spells is increased by 15% and mana cost of Arcane Blast is increased by 200%. Effect stacks up to 3 times and lasts 10 sec or until any Arcane damage spell except Arcane Blast is cast.

Glyph of Arcane Blast: Increases the damage from your Arcane Blast buff by 3%. This makes the arcane blast debuff increase the damage by 3% per stack, so it's +18%, +36% and +54% for 1-3 stacks. That glyph is really recommended.

Spell Power Coefficient: 2.5/3.5+0.09 = 80.429%
The coefficient is scaled to the cast time (2.5sec), plus gets 9% from Arcane Empowerment (3/3).

Crit Multiplier (with 4xT7 + CSD): 1+(((1.5*1.03)-1)*(1+0.5+0.05)) = 1.84475
This includes the CSD meta gem (3%), the Spell Power talent (50%), the 4xT7 set bonus (5%). Without the 4xT7 bonus, it would be 1.8175, so it's not much of a difference. The CSD ( Chaotic Skyflare Diamond or Chaotic Skyfire Diamond) however is not negotiable, you're just expected to have it, no way round!

Arcane Missiles - Rank 13
31% of base mana (1013 Mana at lvl 80), 30 yd range, Channeled (5 bolts in 5 sec)
Launches Arcane Missiles at the enemy, causing 360-361 Arcane damage every 1 sec for 5 sec.

Spell Power Coefficient: 5/3.5+0.45 = 187.857%
The coefficient is scaled to the full channel time (5sec), plus gets 45% from Arcane Empowerment (3/3).

Crit Multiplier (with 4xT7 + CSD): 1+(((1.5*(1+0.03))-1)*(1+0.5+0.05+0.25)) = 1.981
This includes the CSD meta gem (3%), the Spell Power talent (50%), the 4xT7 set bonus (5%) and the Glyph of Arcane Missiles (25%). Without the glyph, the coefficient would be 1.84475, so the glyph increases your AM crits by 7.39%

Arcane Missiles become really nice when used on a Missile Barrage proc (20% proc chance after using Arcane Blast or Arcane Barrage), reducing the cast time by 2.5sec and thus doubling the DPS for that spell.

Arcane Barrage - Rank 3
18% of base mana (588 at lvl 80), 30 yd range, Instant cast, 3 sec cooldown
Launches several missiles at the enemy target, causing 936 to 1144 Arcane damage.

Spell Power Coefficient: 2.5/3.5 = 71.429%
This may not seem high, but take into account that this is an instant cast spell. The usual coefficient for instant cast spells will be weighted by the global cooldown time in place of the cast time, so it should be 1.5/3.5 = 42.857%. That's a significant boost, so this spell will scale extremely well with spell damage (66.7% more than compareable spells such as Fire Blast).

Crit Multiplier (with 4xT7 + CSD): 1+(((1.5*1.03)-1)*(1+0.5+0.05)) = 1.84475
This includes the CSD meta gem (3%), the Spell Power (2/2) talent (50%), the 4xT7 set bonus (5%).


Theorycrafting Scenario
For the following scenario, we consider a 57/3/11 standard raid spec with 2000 spell power, 35% crit and 10% haste, hit capped (100%).
Basically we could leave out the haste as well as all talents (Spell Power etc.) or raid buffs/auras that scale the DPS proportionally, as it affects all rotations equally, and your mileage may vary anyway. For comparing the spells and rotations, that scenario suffices well, and if you need exact numbers, just replace the numbers above with whatever works better for your.

Time to start the number crunching!

The average base damage for a spell will be:
avgBaseDmg:= (minDamage+maxDamage)/2
The effective cast time for a spell is the base cast time (or GCD for instant cast spells) divided by the speed multiplier from haste (1+haste). The GCD (Global Cooldown) is also affected by haste, but won't go below 1 sec. For our scenario, we take the 10% haste plus the 6% from talents (Netherwind Presence).
castTime := baseCastTime / (1 + haste)
The average damage is the base damage plus the spellpower times the coefficient, times any talents that multiply the damage (3% from Arcane Instability, +6% for ArcaneBlast with Spell Impact, and 12% in a raid scenario from Torment the Weak)
dmg(hit):= (avgBaseDmg + (spellpower * coefficient)) * multiplier
For the mana costs, we consider -3% from Arcane Focus, and -3% from Precision, but for the time being ignore any Arcane Concentration procs (just substract 10% from the average mana/sec in the end).

Here's what we get so far:

.	Arcane Blast	Arcane Barrage	Arcane Missiles	Missile Barrage
Dmg Avg	1358	1040	1807.5	1807.5
Mana	261	588	1013	1013
Mana /w talents	245.34	552.72	952.22	952.22
Cast Time	2.50	1.50	5.00	2.50
Cast Time /w haste	2.155	1.293	4.31	2.155
Coefficient /w talents	80.429%	71.429%	187.857%	187.857%
Dmg Avg	2966.57	2468.57	5564.64	5564.64
Dmg Avg /w talents	3233.56	2542.63	5731.58	5731.58
+Torment the Weak	3621.59	2847.74	6419.37	6419.37

The average critical damage per spell is just the average damage, multiplied by the crit factor (Arcane Blast gets an extra 6% crit from Incineration):
dmg(crit):= dmg(hit) * critMultiplier

.	Arcane Blast	Arcane Barrage	Arcane Missiles	Missile Barrage
Crit Multiplier	1.84475	1.84475	1.981	1.981
Crit Dmg	6680.93	5253.38	12716.78	12716.78

To find out the average damage, including crits, we'll have to weight that outcomes by the hit, crit and miss probabilities.
p(crit) := critChance * (1 - p(miss))
p(hit) := (1-critChance) * (1 - p(miss))
This leads us to the average damage numbers for our scenario. Divide those by the cast time and you get the DPS, or divide it by the mana cost to get the DPM.

.	Arcane Blast	Arcane Barrage	Arcane Missiles	Missile Barrage
Avg Dmg	4967.70	3761.88	8812.39	8812.39
DPS	2305.01	2909.19	2044.47	4088.95
DPM	20.25	6.81	9.25	9.25

So far so good, we got the basic numbers we need to calculate our spell rotations in Part 3 of this series.

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Going Arcane, Part 1 - Preface

by Tachyon on Wed. 18. February 2009, 00:51

Filed under: arcane, spec, raiding, dps, patch, theorycrafting

Two weeks before, I retired my Frostfire Bolt spec and joined the happy bunch of arcane specced fellows.

I hesitated long before I finally did this step, as this means that my raid will lose yet another scorch debuffer, and will have to run without the 10% crit debuff quite often.
This is a general design flaw by Blizzard, making the arcane tree too attractive compared to the frost or fire tree, causing lots of mages to skip the 10% crit debuff talents (Improved Scorch in the fire tree, Winter's Chill in the frost tree).

Anyway, I'm now Arcane specced, and will probably stay so for the near future. Patch 3.1.0 will bring some improvements for frost, but also the dual specs, so Frost will become an option again, purely for PvP, whilst Arcane will continue to dominate as PvE spec.



The last patches brought quite some nerfs for the Arcane specs, but don't worry, most of it affected the burst damage potential only, and PvE damage stays neraly as effective as it used to be.

The latest patch (3.0.9) reduced the glyphed damage boost of the Arcane Blast debuff (from 5% to 3%), reduced the spell power coefficient of Arcane Barrage (from 3/3.5 to 2.5/3.5), but also introduced an improved Arcane Missiles glyph, which increases the critical damage of the missiles.

When reading the blogs and forums lately, there seems to be a controversy about which spell rotations are now preferred, if Arcane Missiles should be cast even without Missile Barrage, how high to stack the Arcane Blast debuff, and whether using Arcane Barrage is still viable at all.
In the end I gave up on reading recommendations, especially as most of them were based more on claims that on evidence, and did the math for myself.

So that's the whole point of this arcane article series, to guide you through the calculations and considerations towards finding the proper spell rotations for arcane raiding.

Read on in Part 2 of the "Going Arcane" series.

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Frostfire Bolt tested

by Tachyon on Thu. 27. November 2008, 00:47

Filed under: frostfire bolt, elemental, spec, talents, leveling, frostbolt, glyph

I recently dinged level 75, and decided to give the new Frostfire Bolt (FFB) a try. The build I chose is basically a fire build without Improved Fireball, and 18 points in frost to get the full advantage of Shatter: 0/48/18 Frostfire spec.



What I like about this build and Frostfire bolt in general:

• The spec has almost all the talents that make the FFB go *boom* (2 points in Burnout are missing, need lvl 77 to get the full potential of FFB)
• Hot Streak is seksy! This allows to throw out an instant Pyroblast on any two subsequent FFB (or Scorch, Fireblast or Fireball) hits.
• The build still has the full damage potential of Blizzard, thanks to Shatter, Frostbite and Improved Blizzard.
• The maximal range of FFB is larger (40y) than that of Frostbolt (30y, 36y with Arctic Reach), which makes it the perfect spell for pulling (distance + snare = even more distance)
• New fun shatter combo: Frostnova, FFB + Fireblast -> good chance that both crit and thus proc Hot Streak -> say hello to instant Pyro!
• The FFB Glyph actually makes sense (2% more base damage, +2% crit)

What I miss or don't like about it:

• I seriously miss Ice Barrier. Running around without it is like going shopping naked, and generally a bad idea on a PvP server. Ice Barrier gives you the same announcement effect as the blue colored poison dart frogs have: don't mess with the blue dude!
  Of course you don't really need Ice Barrier to survive while levelling, but it usually absorbs enought damage for you to never get hurt. Without it, I constantly lose some HP and have to regenerate more after a few fights, as I get a bad feeling starting a pull with only half of my HP left.
  Ice Barrier is also essential in PvP. As a rule of thumb you can count twice its absorb amout as virtual HP, and with Shattered Barrier you gain essential utility against meele attackers (especially in AoE situations)
• I miss the Water Elemental a little, but just a little. It has undisputed value and contributes a lot to DPS and utility, but hey I could live without it if I get its DPS from elsewhere. I still hate it for not scaling well (it just gets 40% of my Spellpower, but no hot/crit/haste at all) and forget to bring it out regularly (though most of the time I don't need it just for killing 1-3 mobs and then travelling again), but in the end I miss its ranged nova and separate threat pool in instances.
• I loved Deep Freeze for its croud control and mobile burst capabilities (FoF->DF->move and icelance), so I miss it now already.
• The mana consumption is way higher with a FFB or fire build than with frost. If MMOs were a little more realistic, I would pee an ocean every five minutes, I'm reallly just drinking all the time. Hot Streak with an instant Pyro waiting and no mana left = no fun.
• Blastwave is nice, but I can't seem to fall in love with Dragon's Breath. Cone of Cold feels so much better than this 'zomg look I ate chilli!" spell. For AoE I wouldn't use it anyway, for that we have Blizzard now.
• I think I hate Ignite. Sure my FFB and fire spells crit all the time, but the Ignite dot is usually just wasted as mobs tend to die before it starts ticking. When my FFB or Pyro crits and the target has 2k HP left, I could just stand there and wait 4 sec for it to die, but that's so silly and I don't have the nerves to wait, so in the end I put an end to the tragedy with a quick Fireblast before it drives me crazy. Better waste mana and ignite ticks than my sanity.
  Frost is so much more honest, if you crit a nice big number responds to your action, that's instant reward and not the DoT fluff of a critting fire spell where tiny 'me too!' numbers plop up some seconds later.

All in all the FFB spec is not bad, and I'd consider it the preferred spec for instance/raid runs if your mana pool allows it. Former fire mages should love it, pulling with a snare can be so much more fun, but for frost mages it just hasn't the versatility we need.


I'm yet unsure whether I will be raiding with Frost (0/10/61) or Frostfire (0/50/21) once I reach level 80.
If only we could have the promised dual spec right away, then I'd take Frostfire for instances and raiding, and Frost for PvP, but we probably will have to wait for the 3.1 patch before we can have two specs with hopefully also two sets of Glyphs.

My biggest concern for frost is the Frostbolt Glyph. Adding 5% damage is nice for sure, but removing the snare component completely spoils frost for me. I'm playing frost since the vanilla beta, but I can't think of any issue that bothered me as much as the Frostbolt Glyph is now. If I want to be raiding, the +5% damage is a must, but then my Frostbolt is completely screwed for solo and PvP. Seriously, I just won't use that glyph, and no sane frost mage should be forced to use it.

There's only one thing you can do with the Frostbolt Glyph: put it back into the original packaging, return it to Blizzard and claim refunds because it's KAPUT.

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Crowd Control effects explained

by Tachyon on Fri. 03. October 2008, 21:35

Filed under: crowd control, deep freeze, talents, spec, gameplay, pvp

Nobody seems to be familiar with the old terms for different crowd control (CC) effects anymore.
I guess that's why the player community has a hard time comparing different character classes' CC effects, and lately underrate the new Deep Freeze talent, especially now the latest patch stripped the damage component off it.
Back in my DAoC (Dark Age of Camelot) days, we used to distinguish 4 classes of CC effects, which I take the occasion to reintroduce here, from the weakest to the strongest:

Snare
Lowers the movement speed of the affected target, but does not disable them to do anything.

Our arsenal of snare effects resides in the frost tree, where most spells have a snare component built in (Frostbolt, Cone of Cold, Frost/Ice Armor) or can have a snare with special talents (Improved Blizzard).
Arcane mages can have an even stronger snare effect, Slow, which not only affects the movement speed, but also the attack/cast speed. The daze effect of Blast Wave in the fire tree is also a snare (50%), and lasts for 6 seconds.
Snare effects are very effective against meele targets, allowing you to keep your opponent at distance (unless you're also snared). Snaring a non-meele or ranged class is only effective when supporting other meele players in your group, making it harder for the target to escape.
Our strongest snare is Improved Blizzard, which can reduce the movement speed down to 15% if all snare-enhancing talents are taken.

Root
Movement imparing effect that glues the target to the ground for a given amount of time, but does not disable them to do anything but moving.

Again, this is primary useful against meele classes.
Our basic root CC is Frostnova, and the Water Elemental's Water Nova. Frostbite adds a proc to Frostbolt, Cone of Cold, Frostfire Bolt, Improved Blizzard and Frost/Ice Armor which has a 15% chance to root the target.

Mezz
Mesmerizes the target, disabling it to do anything. Effect breaks as soon as the target gets hit.

Polymorph is our primary mezz, but has the annoying sideeffect to heal the target quickly to full health. An other instant mezz spell can be found in the fire tree: Dragon's Breath disorients the target for 3 sec.

Stun
The king of all CC effects: Completely incapacitates the target for a short time, and damage won't break the effect.

The only stun mages had was the Impact talent, which gave fire spells a 10% chance to stun the target for 2 sec.
In patch 3.0 and WotLK, Impact will be able to proc from all spell schools if you can spare 13 points in fire for this talent. That will be interesting for channeled effects such as Arcane Missiles and area effects in general.
And the frost tree gets a new ultimate talent, Deep Freeze, which can stun a 'frozen' target for as long as 5 seconds. For PvP, this is still godsend, although the damaging component was removed in the latest patch.
Hint: if the Fingers of Frost effect is active, you can instant-stun anyone you want, preferrably a healer trying to get a heal off.

While most of the CC effects in WoW fall into one of those categories, some of them have exotic side effects. Druid's Cyclone for example would be a stun, but renders the target invulnerable for its duration. The Warlocks' Fear is something between a mezz and a stun, as it can break on damage. The Priests' Mind Control would also be a stun, but with a much stronger sideeffect which almost qualifies as an own CC category.

The changes to Impact as well as the new Deep Freeze provide us with more stun tools, so from a CC perspective, we can be pretty pleased with patch 3.0/WotLK.

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WoW 3.0 PTR testing and new Frost Spec

by Tachyon on Mon. 22. September 2008, 01:30

Filed under: mage, talents, spec, raiding, wotlk, ptr, deep freeze, patch

This weekend, I did some testing on the public test realm (PTR) with patch 3.0, in order to test the new frost talents, and have some fun with Blizzard now critting (it's about time!)



On visiting the mage class trainer, I was surprised to find new spell ranks for Frostbolt, Fireball and Arcane Missiles at level 70, haven't heard of that before.

• Frostbolt rank 14: 630 to 680 Frost damage
• Fireball rank 14: 717 to 913 Fire damage + 92 Fire damage over 8sec
• Arcane Missiles rank 11: 280 Arcane damage every 1 sec for 5 sec.

Also the new battleground (Strand of the Ancients) is now in the game, though I didn't test it yet, as my addons are quite in a mess due to incompatibilites. I didn't take the time to fiddle with the UI and find out new hotkeys for most of my spells (Bartender3 wouldn't load), so I'd be handicapped for PvP anyway.

I finally decided what frost spec I'd take when 3.0 goes live. My focus is still on raid PvE, but I also took some PvP talents and included meaningful talents for a Blizzard AoE spec.

My new WoW 3.0 spec:
http://wotlk.wowhead.com/?talent=oZZAIccRfu0fdgrst

Improved Frostbolt - Rank 5/5
Reduces the casting time of your Frostbolt spell by 0.5 sec.
Must have talent. Reduces the Frostbolt casting time from 3 to 2.5 sec, which is a 20% DPS increase.

Ice Floes - Rank 3/3
Reduces the cooldown of your Frost Nova, Cone of Cold, Ice Block and Icy Veins spells by 20%.
Reduces the Frost Nova cooldown from 24 to 20 sec, Cone of Cold from 10 to 8 sec, Ice Block from 5 to 4 min, and Icy Veins from 3 to 2:24 min.
It's not a must have talent, the only component that makes it wanted for raiding is the reduced cooldown on Icy Veins (to maximize DPS).

Ice Shards - Rank 3/3
Increases the critical strike damage bonus of your Frost spells by 100%.
Must have talent. Makes your frost spells crit for 200% of the normal damage, and with the Chaotic Skyfire Diamond metagem even for 209%.

Frostbite - Rank 3/3
Gives your Chill effects a 15% chance to freeze the target for 5 sec.
Neat for solo/PvP situations, useless for raiding (as boss mobs can't be frozen) - unless you combine it with Improved Blizzard, giving each tick of it the chance to freeze the target, which means superb AoE crit chance with Shatter.

Elemental Precision - Rank 3/3
Reduces the mana cost and increases your chance to hit with Frost and Fire spells by 3%.
Mandatory for PvE. I'm not sure whether the Elemental Precision Ghost Hit (+6% instead of +3% for Frostbolt) still applies in 3.0/WotLK, but I doubt so.
Spell hit chance is no longer capped at 99%, so for raiding situations, you need +17% hit (214 Hit Rating @ lvl70, 446 Hit Rating @ lvl 80), or +14% hit with 3/3 Elemental Precision (176 Hit Rating @ lvl70, 367 Hit Rating @ lvl 80).

Piercing Ice - Rank 3/3
Increases the damage done by your Frost spells by 6%.
Must have talent, no discussion.

Icy Veins - Rank 1/1
Hastens your spellcasting, increasing spell casting speed by 20% and gives you 100% chance to avoid interruption caused by damage while casting. Lasts 20 sec.
Must have talent.

Improved Blizzard - Rank 2/3
Adds a chill effect to your Blizzard spell. This effect lowers the target's movement speed by 50%. Lasts 1.50 sec.
Adds a snare effect to Blizzard, making the affected targets stay longer in the spell's area. The snare allows it also to proc Frostbite, combined with shatter this will turn Blizzard into a crit galore feast!

Arctic Reach - Rank 2/2
Increases the range of your Frostbolt, Ice Lance, Deep Freeze and Blizzard spells and the radius of your Frost Nova and Cone of Cold spells by 20%.
Must have for PvE (Frostbolt) and especially for PvP (Frostnova, Cone of Cold). Too bad it only increases the range of Blizzard and not its radius.

Frost Channeling - Rank 3/3
Reduces the mana cost of all spells by 10% and reduces the threat caused by your Frost spells by 10%.
Must have for PvE, the thread reduction is vital. It's now even better than clearcast, as you get the mana reduction directly, no wasted procs.

Shatter - Rank 3/3
Increases the critical strike chance of all your spells against frozen targets by 50%.
This. Is. SPARTA! The bread and butter of a frost or elemental spec (since patch 1.12 it increases the crit chance also for non-frost spells), mother to all shatter combos, and now also useful in raids, thanks to the Fingers of Frost talent. And it now only costs 3 talent points, and no longer has a prerequisite talent.

Cold Snap - Rank 1/1
When activated, this spell finishes the cooldown on all Frost spells you recently cast.
Allows you to gain more DPS by increasing the Icy Veins and Water Elemental uptime in boss fights, and saves your back in PvP fights by resetting Ice Block / Frostnova.

Cold as Ice - Rank 2/2
Reduces the cooldown of your Cold Snap, Ice Barrier, Deep Freeze and Summon Water Elemental spells by 20%.
Indirectly increases your DPS due to the reduced Cold Snap and Water Elemental cooldown. For two points, a must have, even for PvP, as it reduces the Ice Barrier cooldown from 30 to 24 sec.

Winter's Chill - Rank 3/3
Gives your Frost damage spells a 100% chance to apply the Winter's Chill effect, which increases the chance spells will critically hit the target by 2% for 15 sec. Stacks up to 5 times.
Up to +10% crit, now for all spells. Too bad it doesn't stack with the new Improved Scorch (+10%) or Boomkin aura (+5%). Might help your fellow fire raiding comrades, as they can skip adding Scorch into their spell rotation and just gain the effect from Winter's Chill. Sideeffect in PvP: WC is an additional debuff, making it harder to remove more important ones, such as polymorph.

Shattered Barrier - Rank 2/2
Gives your Ice Barrier spell a 100% chance to freeze all enemies within 10 yds for 8 sec when it is destroyed.
I'd say this is a PvP-only ability, but an incredibly powerful one. Adds a third way to nail your opponent to the ground (besides Frostnova and Frostbite), which helps shattering or deep freezing. It's also good that the effect just freezes the opponents, but doesn't do any damage, so it won't break sheep on any target it hits.
Meele will hate you for this, as soon as they slice away your Ice Barrier, they get frozen, allowing you to gain distance again.

Ice Barrier - Rank 1/1
Instantly shields you, absorbing x damage. Lasts 1 min. While the shield holds, spells will not be interrupted.

• Rank 6 (Level 70) absorbs 1075 damage
• Rank 7 (Level 75) absorbs 2800 damage
• Rank 8 (Level 80) absorbs 3300 damage

Must have, as it's essential for PvP, and helps you survive in PvE in 'oh snap!' situations, or when your healers have a hard time keeping the raid alive.
Never leave the house without it!

Arctic Winds - Rank 5/5
Increases all Frost damage you cause by 5% and reduces the chance melee and ranged attacks will hit you by 5%.
Nice, a plain +5% dmg, take it.

Empowered Frostbolt - Rank 2/2
Increases the damage of your Frostbolt spell by an amount equal to 10% of your spell power and increases the critical strike chance by an additional 4%.
Improves scaleability by adding +10% to your spell power. The crit chance used to be 5% for rank 5 points before patch 3.0, now it's only 4% but only requires to points.

Fingers of Frost - Rank 2/2
Gives your Chill effects a 15% chance to grant you the Fingers of Frost effect, which treats your next 2 spells cast as if the target were Frozen. Lasts 15 sec.
Now that's cool, a 15% proc which allows you to cast 2 spells that profit from shatter, even if the target can't be frozen. That's 2x Frostbolt, or 1x Frostbolt + 1x Deep Freeze with almost guaranteed crits.

Brain Freeze - Rank 2/3
Your Frost damage spells have a 10% chance to cause your next Fireball spell to be instant cast and cost no mana.
This is the most weird talent in the new frost tree. With 3/3 ranks, the proc chance is even higher, 15%. When Brain Freeze procs, you've got 15 sec time to release an instant fireball for free. Untalented fireballs won't do much damage, and only crit for 150% base dmg, but the instant cast (1.5 GDC instead of 3.5 sec casttime) evens this out. Don't expect too much DPS increase from this, the talent only shines because the fireball costs no mana, increasing your overall mana efficiency (DPM).
For PvP this is actually funny, having a little 'PoM Fireball' ready which can be cast while moving, that alone makes it worth taking it.
Might make spell rotations a little tricky, as you don't want to waist the Fingers of Frost proc on a Brain Freeze proc, so watch your procs carefully.

Summon Water Elemental - Rank 1/1
Summon a Water Elemental to fight for the caster for 45 sec.
Squirtle, friend to all frost mages. Will bite nastly rogues into the ankles while they stunlock you, helps you range-shattering with its ranged nova, and add its little share to your raid DPS. Must have.

Improved Water Elemental - Rank 3/3
Increases the duration of your Summon Water Elemental spell by 15 sec and your Water Elemental restores mana to all party or raid members within 100 yds an amount equal to 0.6% of their total mana every 5 secs.
PvE only. Increases WE uptime, and adds a little manareg to the party (for a lvl 70 mage with 10000 mana, it's 60 MP5).

Chilled to the Bone - Rank 5/5
Increases the damage caused by your Frostbolt, Frostfire Bolt and Ice Lance spells by 5% and reduces the movement speed of all chilled targets by an additional 10%.
Another 5% plain damage to your main nukes, and adds an additional snare which comes handy for your Blizzard (with 2/3 Imp. Blizz., it's 60% snare).

Deep Freeze - Rank 1/1
Causes x to y Frost damage and stuns the target for 5 sec. Only usable on Frozen targets.

• Rank 1 (lvl 60): 694 to 806 Frost damage
• Rank 2 (lvl 66): 787 to 913 Frost damage
• Rank 3 (lvl 72): 1018 to 1182 Frost damage
• Rank 4 (lvl 80): 1319 to 1531 Frost damage

Hey, this does significant base damage. And, most important, gives us access to the holy grail of crowd controlling: a stun. The only other stun that mages can have is the Impact talent in the fire tree (10% proc chance).
Stunning your target means totally incapacitating it, so you can do anything to it (paint a moustache on its face, untie its shoelaces or just nuke the living daylights out of it without breaking your CC).
Even better, the freeze effect won't be broken on the target by damage, thus you have 5 sec of shatter opportunity. The Deep Freeze cast will also be affected by shatter, and you enter the global cooldown afterwards as DF is an instant cast spell, so 3.5 sec remain to unleash another Frostbolt/Ice Lance combo, or 3x Ice Lance if you're really quick.
The damage component of Deep Freeze gains 1.5/3.5 = 42.857% of your spell power.

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