For the time being (until the math is more worked out/confirmed/written down/tested), I will put my focus more on commonly accepted playstyles more than anything else without any maths to back to it. This is not an intent on my par to just 'lay-it-down' without proof -- understand the math is rather tedious.
Arcane differs greatly from the other specs in the mentality behind it. It rewards the informed. It rewards properly planning ahead, both from a micro and a macro perspective. Most of the playstyle revolves around managing DPM more than anything else. As such, I will put an extreme focus on DPM values and making sure everyone understands why. A spell always has 2 costs, one of which is the time spent casting it, the other one being the mana spent for it. Arcane, unlike the other specs, needs to take into account mana cost of spells because it can't sustain its max dps cycle. The idea being here, if you can't sustain the max dps rotation, then the next logical step is to maximize the damage you can deal with the mana you have (aka: maximize DPM).
Also, before anyone asks, only specs with 51 arcane points in them apply. There isn't a good 21pt talent that would mandate skipping arcane barrage, or any competing talent really.
(crit multiplier formula listed in the formula section)
57/3/11 - cookie cutter
57/3/11 - what I recommend (3/3 IA, 3/5 pushback protection, 3/3 ice shards, only 3% hit total from spec)
Please be aware that the information below is horribly out of date. It is being kept there for copy/paste purpose for when I update it.
[b]Rotations[/b] [table]cycle|[color=purple]dps[/color]|[color=blue]mps[/color]|[color=darkred]dpm[/color]|[color=grey][size=1]dpm tradeoff (next cycle)[/size][/color]|[color=grey][size=1]dpm tradeoff (cycle 2)[/size][/color]|general use|note AB3+ [mbarr]|[color=purple]5495.957[/color]|[color=blue]387.9541[/color]|[color=darkred]14.17[/color]||[color=grey][size=1]1.85[/size][/color]|mana dump / during AP|cast mbarr only at 3 stack. [color=purple][b]*[/b][/color] see note2 below [b]AB AB AB ([mbarr] [i]or[/i] abarr)[/b]|[b][color=purple]5132.355[/color][/b]|[b][color=blue]190.8791[/color][/b]|[b][color=darkred]26.89[/color][/b]|[color=grey][size=1][b]1.85[/b][/size][/color]||[b]main cycle / during AP[/b]| [b]AB AB AB AM[/b]|[b][color=purple]5070.111[/color][/b]|[b][color=blue]157.7089[/color][/b]|[b][color=darkred]32.15[/color][/b]|[color=grey][size=1][b]1.88[/b][/size][/color]|[color=grey][size=1][b]1.88[/b][/size][/color]|[b]main cycle / during AP[/b]| [b]AB AB ([mbarr] [i]or[/i] AB AM)[/b]|[b][color=purple]5031.662[/color][/b]|[b][color=blue]146.4452[/color][/b]|[b][color=darkred]34.36[/color][/b]|[color=grey][size=1][b]3.41[/b][/size][/color]|[color=grey][size=1][b]2.27[/b][/size][/color]|[b]main cycle[/b]| AB ([AB mbarr] [i]or[/i] abarr)|[color=purple]4760.778[/color]|[color=blue]87.75334[/color]|[color=darkred]54.25[/color]|[color=grey][size=1]4.62[/size][/color]|[color=grey][size=1]3.60[/size][/color]|mana saving|[color=purple][b]*[/b][/color] see note below AB ([mbarr] [i]or[/i] abarr)|[color=purple]4677.5[/color]|[color=blue]74.82857[/color]|[color=darkred]62.51[/color]|[color=grey][size=1]6.44[/size][/color]|[color=grey][size=1]3.92[/size][/color]|mana saving|[color=purple][b]*[/b][/color] see note below AB AM|[color=purple]4184.583[/color]|[color=blue]32.69562[/color]|[color=darkred]127.99[/color]|[color=grey][size=1]11.71[/size][/color]|[color=grey][size=1]5.99[/size][/color]|mana saving| [/table] [size=1]([b][/b] denotes conditional statement. Cast only on missile barrage proc.)[/size] [size=1]([b]example:[/b] [color=purple]AB AB ([mbarr] [i]or[/i] AB AM)[/color] indicates: "AB AB AB AM" (without mbarr proc) and "AB AB mbarr" when mbarr procs)[/size] [size=1]([b]clarification:[/b] [color=purple]AB3+[/color] refers to AB spamming. It also means you must cast at least 3 AB)[/size] note: be aware that (AB abarr) can fail to work if abarr is still on cooldown (this will typically happens during bloodlust + icy veins). You probably want to use a different rotation during haste cooldowns. note 2: as far as I am concerned, the top realistic DPS rotation of an arcane mage is the 2nd rotation. The reason being that you will consume mana faster than before due to the increased AP uptime%. Realistically I don't believe you will end up doing much AB spamming barring really short fights.
Understanding DPM tradeoffs
A DPM tradeoff represents roughly the extra DPM you get from 1 mana by spending that mana on another cycle.
In other words, it represents the extra damage you will deal from switching rotations (assuming the initial rotation would have ran you OOM). It also indirectly indicates the value of mana, and how much more damage more mana will give you in total. Keep in mind here a very important detail; it also assumes the fight duration will not change for the dpm tradeoff to make sense.
The reason why DPM is misleading and gives you the impression you get a tremendously cheaper rotation is because it totally ignores duration (ie: the dps element). If you had infinite time, then yes, follow exclusively the optimum DPM value to maximize total damage dealt with the mana available. If constrained by time (99.9% of cases), then you want to look at dpm tradeoffs rather than dpm.
Presence of Mind
optimal use: last AB of any rotation
1- POM-AM doesn't work. I mean, its not going to finish your channel in 1.5s. Additionally, I think POM doesn't apply the 30% crit to AM due to the wotlk-beta bug of POM+AM spam (ie: permanent 30% crit).
2- POM-abarr is nice and all, but doing so will not take advantage of the cast-time-reduction element of POM. Only the 30% more crit part. As such it is not recommended. Sure, you do gain 18% more damage over any AB (AB4+ spam), but the cast time reduction is worth more than that 18%.
3- POM-AB is the only other alternative (well, that and FFB, but the math is inconclusive on that). You gain 1s of dps time by reducing the cast time from 2.5->1.5. Thinking about it, the most logical choice for AB would be the last AB of your rotation, because it has the biggest damage multiplier (ie: 30% more crit from POM is better used coupled with the highest damage multiplier).
4- As a general note, I recommend generally to go for one extra AB on your rotation where you cast POM, in a case where you had planned to do some mana dumping at the end of the fight. It makes sense to use an extra 18% more damage on AB.
It is currently not proven whether or not POM-AB during cooldowns (lust/IV) is better than outside of cooldowns. The reason being that reducing 2.5->1.5 is worth a lot more than reducing, for example 1.4->1.0.
most burst: POM/AP/IV/blizzard + flamestrike + blizzard spam (this is counter-intuitive; we use POM for blizzard for the 30% crit, and the instant cast stays on for the following flamestrike (which will not get the 30% crit))
ranged aoe: AP/IV/blizzard + POM/flamestrike
close aoe: same as ranged. do not go in melee range.
The above rotations are what I personally use. I haven't mathed-out to figure which is optimum. As such, there is a possibility the above is not optimum.
Generally you want to delay invisibility as much as possible, because the more you wait, the more effective it becomes.
Based on my personal experience, waiting for the boss to reach 70% hp before using invis will allow you to go all out for the remainder of the fight. Of course, this is only a rule of thumb and assumes that you produce more threat than your tank, and that you will catch up to him. You can play with the number a bit if you can afford to use invis at the end of the fight (ie: finish the fight with >130% threat). It has proven to work well, however, expanded math could give optimum values (if anyone is willing to do it).
for the time being, the information below is out of date. The FFB thread has more updated info although the FFB thread doesnt have the new info on flamestrike and 3.3 recent changes.
[b]Formulas[/b] base formula for all mage spells (thx to Zaldinar for corrections) [quote][b]avg_damage_per_cast_noncrit[/b] = [i](avg_cast_base_dmg + (spell_coefficient + empowered_fire + empowered_frostbolt + arcane_empowerment) * final_spell_dmg) * (firepower + ffb_glyph + spell_impact) * pwf * piercing_ice * coe * arcane_instability [* frostbolt_glyph] [* arcane_blast_buff] [* arcane_power] [* molten_fury] [* ferocious_inspiration] [* tricks_of_the_trade][/i] [b]spell_coefficient[/b] = [color=gray][size=1](see table below for appropriate coefficients)[/size][/color] [b]avg_damage_per_cast[/b] = [i]avg_damage_per_cast_noncrit * (1 + final_crit% * (crit_multiplier - 1))[/i] [b]final_cast_time[/b] = [i]talented_cast_time / (1 + total_haste_rating / haste_rating_per_percent / 100) / netherwind_presence / wrath_of_air [/ retribution_aura or imp_moonkin_aura] [/ bloodlust or power_infusion] [/ icy veins] [/ berserking][/i] [b]spell_dps[/b] = [i]avg_damage_per_cast * chance_to_hit% / final_cast_time[/i] [color=purple]ex: frostfire bolt -- molten fury + berserking(20%) + bloodlust + icy veins + 4pct7 + CSD included, 2000 spelldmg, 55% crit, 500 haste rating[/color] avg_damage_per_cast_noncrit = ( (722+838)/2 + (3/3.5 + 0.15) * 2000 spelldmg) * (1.1 + 0.02) * 1.03 * 1.06 * 1.13 [* 1.12] [i]=[/i] 4324.43 avg_damage_per_cast = 4324.43 * (1 + 0.55 * (3.34565 - 1)) = 9903.41 final_cast_time = 3 / (1 + 500/32.78998947/100) / 1.05 / 1.03 / 1.3 / 1.2 / 1.2 = 1.29 spell_dps = 9903.41 * 1 / 1.29 = 7677.06 dps [color=purple]ex: arcane barrage(2.5/3.5 coef) -- ab_glyph(3%) + 3_stack_ab_buff + arcane power(20%) + torment the weak + berserking(20%) + bloodlust + icy veins + 4pct7 + CSD included, 2000 spelldmg, 55% crit, 500 haste rating[/color] avg_damage_per_cast_noncrit = ( (936+1144)/2 + (2.5/3.5) * 2000 spelldmg) * (1.06) * 1.13 * 1.03 * 1.54 [* 1.2] [i]=[/i] 5628.20 avg_damage_per_cast = 5628.20 * (1 + 0.55 * (1.84475 - 1)) = 8243.13 final_cast_time = 1.5 / (1 + 500/32.78998947/100) / 1.06 / 1.05 / 1.03 / 1.3 / 1.2 / 1.2 = 0.61 spell_dps = 8243.13 * 1 / 0.61 = 13513.33 dps [color=gray][size=1](ignoring GCD cap)[/size][/color][/quote] notes/gotchas: ffb glyph and spell impact are applied a very odd way, as shown in the formula above. Some frost calculations are not 100% known, given they give sometimes results outside of predicted values. As such, this should be only used to get a rough idea. The above list is simplified and doesn't lists every possible non-stacking buffs. For a proper list, check the FFB thread or [url=http://raidcomp.mmo-champion.com/]MMO-Champion RaidComp[/url] . For example, 'coe' refers to any of (Ebon Plaguebringer/Curse of the Elements+Malediction/Earth and Moon). crit multiplier formula [quote][b]crit_multiplier[/b] = [i](1 + ( ((1.5 [* CSD]) - 1) * (1 [+ ice_shards] [+ burnout] [+ spell_power] [+ 4pct7] [+ am_glyph]) )) [* ignite][/i] [color=purple]ex: frostfire bolt -- ignite + burnout + ice shards + CSD + 4pct7[/color] crit_multiplier = (1 + ( ((1.5 * 1.03) - 1) * (1 + 1 + 0.5 + 0.05) )) * 1.4 = 334.565%[/quote] Base mana [table]Class|Level 70|[color=blue]Level 80[/color] Mage|2241|[color=blue]3268[/color] Druid|2370|3496 Warlock|2871|3856 Priest|2620|3863 Paladin|2953|4394 Shaman|3457|4396 Hunter|3383|5046[/table] [table]Spell|Coefficient|Base damage|Talents affecting the dot|Mana cost %|Mana cost (lvl 80)|Notes [url=http://www.wowhead.com/?spell=47610]Frostfire Bolt[/url]|3.0/3.5|722-838 + 90/9s|pwf, firepower, arcane instability, piercing ice|14%|457|1 tick / 3s [url=http://www.wowhead.com/?spell=55360]Living Bomb[/url]|0.80/12s + 0.40|1380/12s + 690|pwf ([b]not[/b] firepower)|22%|718|1 tick / 3s [url=http://www.wowhead.com/?spell=42891]Pyroblast[/url]|1.15 + 0.20/12s|1210-1531 + 452/12s|pwf, firepower, arcane instability|22%|718|1 tick / 3s [url=http://www.wowhead.com/?spell=42859]Scorch[/url]|1.5/3.5|382-451||8%|261| [url=http://www.wowhead.com/?spell=42833]Fireball[/url]|3.5/3.5|898-1143 + 116/8s|pwf, firepower, arcane instability|19%|620|1 tick / 2s [url=http://www.wowhead.com/?spell=42873]Fire Blast[/url]|1.5/3.5|925-1095||21%|686| [url=http://www.wowhead.com/?spell=42926]Flamestrike[/url]|0.2427 + 0.1220 (per tick)|876-1071 + 780/8s|pwf, firepower, arcane instability|30%|980|1 tick / 2s [url=http://www.wowhead.com/?spell=42925]Flamestrike (rank 8)[/url]|0.2427 + 0.1220 (per tick)|699-854 + 620/8s|pwf, firepower, arcane instability|30%|980|1 tick / 2s [url=http://www.wowhead.com/?spell=42940]Blizzard[/url]|8.0/3.5/2 /8s|3408/8s||74%|2418|1 tick / s [url=http://www.wowhead.com/?spell=42931]Cone of Cold[/url]|1.5/3.5/2|709-776||29%|947| [url=http://www.wowhead.com/?spell=42950]Dragon's Breath[/url]|1.5/3.5/2*0.90|1101-1279||31%|1013| [url=http://www.wowhead.com/?spell=42945]Blast Wave[/url]|1.5/3.5/2*0.90|1047-1233||28%|915 / glyphed: 777| [url=http://www.wowhead.com/?spell=42921]Arcane Explosion[/url]|1.5/3.5/2|538-582||22%|718| [url=http://www.wowhead.com/?spell=42917]Frost Nova[/url]|1.5/3.5/2*0.90|368-419||8%|261| [url=http://www.wowhead.com/?spell=42842]Frostbolt[/url]|3/3.5*0.95|803-866||13%|424| [url=http://www.wowhead.com/?spell=42914]Ice Lance[/url]|1.5/3.5/3|223-258||7%|228| [url=http://www.wowhead.com/?spell=42897]Arcane Blast[/url]|2.5/3.5|1185-1377||8%|261| [url=http://www.wowhead.com/?spell=42846]Arcane Missiles[/url]|5/3.5|~362||31%|1013| [url=http://www.wowhead.com/?spell=44781]Arcane Barrage[/url]|2.5/3.5|936-1144||18%|588| [url=http://www.wowhead.com/?spell=55342]Mirror Image[/url]|-|-||10%|326|30s [url=http://www.wowhead.com/?spell=55342]Mirror Image[/url] - frostbolt|0.10|163-169 [color=purple]*[/color]|150% crits, ~22-25 per cast|-|-| [url=http://www.wowhead.com/?spell=55342]Mirror Image[/url] - fireblast|0.05|88-98 [color=purple]*[/color]|150% crits, ~10-14 per cast|-|-| [url=http://www.wowhead.com/?spell=31687]Water Elemental[/url] - frostbolt|2.5/3.5*0.4|601-673|150% crits, sta/int = 0.3, 5% base crit|16%|522|45-60s [/table] note: there is a discrepancy between the in-game-tooltip values and the ones reported by sites parsing the data files. The values above are taken from in-game-tooltips (except for arcane missiles). [color=purple]*[/color] Based on a limited number of casts (~100 per). [quote][b]base_mana_cost[/b] = [i]rounddown( class_base_mana[player_level] * spell_mana_cost )[/i] [b]final_mana_cost[/b] = [i]rounddown( base_mana_cost [* elemental_precision] [* arcane_focus] [* arcane_power] )[/i] [color=blue]exception case[/color]: [b]ab_mana_cost[/b] = [i]rounddown( round(base_mana_cost [* arcane_focus] [* elemental_precision]) * (1 + ab_stacks * 2 [+ arcane_power] [+ 2pct5]) )[/i] [color=grey][size=1](Arcane_blast is different than the rest because the first part of the mana cost can be rounded up, whereas every other spell can only be rounded down. So even though it seems like the formulas are the same, they need to be treated separately.)[/size][/color] [color=purple]ex: arcane barrage -- 3/3 elemental precision + 3/3 arcane focus + arcane power(20%)[/color] base_mana_cost = rounddown( 3268 * 0.18 ) = 588 final_mana_cost = rounddown( 588 * 0.97 * 0.97 * 1.2 ) = 663 [color=purple]ex: arcane blast (3 stacks already up) -- 3/3 arcane focus + 3/3 elemental precision + arcane power(20%) + 2pct5[/color] base_mana_cost = rounddown( 3268 * 0.08 ) = 261 ab_mana_cost = rounddown( round(261 * 0.97 * 0.97) * (1 + 3 * 2 + 0.20 + 0.05) ) = 1783[/quote]
If you're just doing the equivalence for Arcane Blast (and not a mixed rotation [...]), the calculations are extremely straightforward.
m is the average base damage (ex: arcane blast: (1185+1377)/2 = 1281)
r is the spell power coefficient (see table above for spell coefficients)
d is your spell power.
b is the critical strike bonus. (see table above for crit multiplier)
c is your crit chance.
z is the bonus to your casting speed from gear-based haste.
h is your hit chance.
crit_rate_from_int = 0.9075 + final_int / 166.6666709
note: 0.9075 applies only to lvl 80 ? currently unknown
ManaRegen(SPI, INT, LEVEL) = roundup( (0.001+SPI*BASE_REGEN[LEVEL]*(INT^0.5) *0.60 )*5 )
* applies only to 3.10
Professions / Racials
1- AB mana cost tables
3- Added Professions / Racials
4- Added threat management
5- Added AB mana cost formula
Points of contention
1- Which talents are the best to cut when going from 57 to 51 pt in arcane?
2- Is is worth taking the last 2 points in Arcane Stability (conc. aura being a possibility)?
3- If yes, then what talent to sacrifice?
1- <many many many things here>
(as a temporary thing, if you want to have a rough idea of the calculations of arcane spells, check the ffb thread for the spreadsheet. for some mundane reason I can't re-link on this thread)
type something about arcane debuff being cleanseable
finish spreadsheet according to 'to do' list on ffb thread.
add dpm-affecting buff/debuffs