Blog Articles by keyword: theorycrafting



Simulation: Partial Resists

by Tachyon on Sun. 13. June 2010, 03:13

Filed under: dps, simulation, theorycrafting, fire, resists

The development of the new DPS-simulation engine is progressing as planned, and requires more and more time doing research of the spell mechanics, to find out how the spell effects work in detail. It's very hard to find any fundamental information on that topic, so I had to switch back to experimental mode and find it out myself.

One particular question I wanted to have aswered today:

How much of a spell is partially resisted (absorbed) by boss targets?
Bosses have a built in resistence mechanic that lets them absorb a part of the damage. The common knowledge is that bosses count as maxlvl+3 mobs (in the WotLK version: level 83), and that they gain 5 resistence per additional level (15 overall). But I have noticed before that the resists fluctuate, sometimes more is resisted, sometimes less, and in some cases nothing is resisted at all.

Partial Resists

To test the partial resists, I unequipped any items that have a +Spelldamage proc, and casted Arcane Missiles on a Heroic Training Dummy. To record the data, I used Fraps and viewed the video in slow motion to note down the damage and absorbs for each tick.
Here's an excerpt of the collected data (in brackets: partial resists)
1099 (275), 2147 (275), 2446 (137), 1374, 1236 (137), 1374, 1236 (137), 2684, 1374, 2147 (275), 1236 (137), 1099 (275), 2415 (137) ...
The resists were either 0, 137 or 275. In relation to the damage before resists, this was exactly 0%, 10% and 20%. The spell crit modifier for Arcane Missiles (with CSD and the AM Glyph) is 1.95375, and the critical spell hits show that the resistance happens before the crit factor is applied.

Now I needed more samples to quantify how many spells have 0%, 10% and 20% resists. For that I parsed the combat log from our raid tonight with a total of 487 samples on 3 bosses. Result:
  • 257x 0% resist (~ 1/2)
  • 152x 10% resist (~ 1/3)
  • 87x 20% resist (~ 1/6)
I have yet to verify these observations with other spells, but I assume for now that all spells are affected the same by partial resists.

EDIT 2010-06-14: Interesting side note
Ingite is affected by partial resists as well. Critical fire spells get thus taxed twice (once for the spell, once for the ignite DoT). This effect is known as Double Dipping.

Simulation: DPS Volatility

by Tachyon on Tue. 08. June 2010, 23:20

Filed under: simulation, theorycrafting, dps

Hey folks, it's been a while since my last post, sorry for that. I've been raiding with my new fire specs during the last weeks, and we managed to kill the Lich King in ICC 25, and are now working on the ICC 25 HC bosses (9/12 so far).



I've also been doing some research on stats scaling for the fire spec, but haven't drawn a conclusion yet. Some sources (like Rawr) state that crit rating is the best stat by far, but given the nature of the Ignite mechanics (ignite munching, losing a huge ignite bank when your target dies) I have some sincere doubts. Thaarsis (one of the other mages in my guild) pointed me to Greatschock <For the Horde>'s Armory profile (you remember, the first mage which participated in a 25 HC LK kill) who had replaced all his yellow gems with pure +20 crit rating gems. We both were puzzeled, but by now Greatschock went back to SP/crit gems, seems like too much crit was not that great after all.

Limits of the old simulation

For the Arcane posting series, I used a simulation program I wrote to observe and analyze the most interesting aspects of the arcane spec (spell rotations, the impact of the T10 boni, stats scaling).
Simulating arcane rotations was fairly easy, every spell does direct damage, and stuff procs on sucessful spell casts rather than on inpact, which was easy to model.

But now that I want to observe the Fire spec in detail, I have to rewrite the whole simulation from scratch. Fire has effects that proc on spell impact, so you have to take the flight time into consideration. Some effects even have a life of their own (hello Ignite!), so a radical new approach was necessary.

New simulation

The new casting simulation I'm writing is event driven, which eases dealing with concurrent effects (such as the Ignite proc still ticking, the player casting a new spell when the last spell is still on its flight to the target). Everything in the simulation is an Event, and can be scheduled for execution in the Simulation on a given time. Events can interact with the simulation, spawn and schedule new events and even reschedule themselves. Event execution can even be observed using Listeners, making it easy to modularize aspects of the simulation.

The simulation API is not yet complete, but it's growing more and more mature.
It may be a little late for the fire spec, regarding that the Cataclysm expansion is already in the beta, but when the simulation's done I think it will be quite easy to adapt it to the Cataclysm spell mechanics, so it's well worth developing it.

The simulation also doesn't use a fixed player stat model, but allows to take a character out of the armory, and take all individual stats and talent point distribution as well as glyph choices, raid buffs and temporary powerups into account.

I've only modelled arcane so far (so I can compare the outputs of the old and new simulation), but at least I can share some effects I'm dealing with at the moment, or rather one effect in particular: Volatility.

Volatility

As a great part of the logic and results depends on the RNG (random number generator), say whether your spell hits, crits or misses, and the procs involved, the outcome will vary each time the simulation is run. This variance is significant and tells a lot on how to interpret simulated results.

For testing purpose, I did 10 runs with my mage's stats, using an arcane rotation on a 5min fight (no raid buffs, no AP/IV etc). Here's the DPS numbers that came out:

10 Runs:


Once I had less than 6800 DPS, and another time over 7200 DPS, using the same rotation, same stats and same duration. When the outcome is so volatile, it's nigh impossible to draw any conclusions when you vary input parameters.
Any DPS tests you do ingame (be it on the target dummies, or in a raid) are rendered obsolete, as you just cannot obtain enough samples to observe what happens when you do something different. You could test on a target dummy, swap some gems to a useless stat (e.g. Agility), test again and have an increased DPS result.

I did some more runs with the simulation:

1'000 Runs:


Those of you with a background in statistics recognize a gaussian distribution in the samples, and if we do event more runs the bell shape of the distribution curve is obvious:

100'000 Runs:


Look at the x-scale to see how far the minimum and maximum value are apart!
What this means is that to be able to draw conclusions on the average DPS for a given situation, the simulation has to do serious number crunching and do lots and lots of runs to have a stable outcome.

Fascinating, isnt't it? I hope you just learned to not to trust any observations that are drawn out of a handful of samples

Stay tuned for more articles on the progress of the simulation!

EDIT 2010-06-12: Sorry, forgot to enable comments (was disabled by default), commenting is now allowed

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

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.

3.2.2 Arcane Mage Changes

by Tachyon on Thu. 10. September 2009, 21:04

Filed under: arcane, patch, spell, simulation, theorycrafting



Arcane is facing some cool new changes in the upcoming patch 3.2.2 which can be tested on the PTR since quite some weeks and could go live any moment (or in a couple of weeks, who knows).
EDIT 2009-09-15: The mana cost for subsequent AB casts has been raised to 175%/stack in the latest PTR build (was 130%/stack in the first 3.2.2 build), therefore I updated the numbers and my conclusions.
  • Arcane Blast: The buff from using this ability now stacks up to 4 times (instead of 3), and each application increases mana cost by 175% (instead of 200%).
  • Missile Barrage: The effect from triggering this talent now removes the mana cost of Arcane Missiles. In addition, the chance for Arcane Blast to trigger this talent is now 8/16/24/32/40%. All other listed spells continue to have a 4/8/12/16/20% chance to trigger it.

The overall DPS wasn't increased all that much, but what really sticks out is the mana efficiency which suddenly makes this spec viable for raiding again, and indirectly boosts the DPS by allowing to run the mana exhausting high DPS rotations for a little longer.

Given the new circumstances, you might now wonder what the preferred DPS or DPM rotations will be once the patch goes live.

Once again I will use the simulation program I wrote for the Going Arcane article series ( part 1, part 2 and part 3) for a detailled anaysis and comparison of possible spell rotation strategies.
For the 3.2.2 spell rotation analysis, I slightly modified the base stats used for the simulation:
  • 3000 Spell Power (used to be 2000)
  • Hit capped, (100% Spell Hit, same as before)
  • 20% Spell Haste before talents (used to be 10%)
  • 50% Spell Crit including CSD (used to be 35%)
  • removed 4xT7 set bonus for the calculation

The simulation yields following results for cast sequences:

RotationDamageTimeDPSManaDPMMana/sec
ABx18195.0001.9844130.280215.00038.120108.360
ABx217866.0003.9684502.230806.00022.170203.112
ABx315962.0005.9522681.6201773.0009.000297.864
ABx432270.0007.9374066.0203116.00010.360392.616
ABx555730.0009.9215617.5804836.00011.520487.469
ABx10109847.00019.8415536.29013436.0008.180677.174
ABx1000001151280132.000198412.6985802.450171996236.0006.690866.861
ABarr6673.0001.1905605.320553.00012.070464.520
ABx1, ABarr12527.0003.1753946.000768.00016.310241.920
ABx2, ABarr22859.0005.1594431.1301359.00016.820263.437
ABx3, ABarr21616.0007.1433026.2402326.0009.290325.640
ABx4, ABarr47434.0009.1275197.1203669.00012.930401.995
ABx5, ABarr45677.00011.1114110.9305389.0008.480485.010
Mbarr16758.0001.9848446.0300.000&#8734;0.000
ABx1, Mbarr14630.0003.9683686.760215.00068.05054.180
ABx2, Mbarr40658.0005.9526830.540806.00050.440135.408
ABx3, Mbarr51134.0007.9376442.8801773.00028.840223.398
ABx4, Mbarr70458.0009.9217102.1703116.00022.610314.093
ABx5, Mbarr76519.00011.9056427.6004836.00015.820406.224
AM16758.0003.9684223.020952.00017.600239.904
ABx1, AM27970.0005.9524698.9601167.00023.970196.056
ABx2, AM36972.0007.9374658.4701758.00021.030221.508
ABx3, AM34185.0009.9213445.8502725.00012.540274.680
ABx4, AM70458.00011.9055918.4704068.00017.320341.712
ABx5, AM73864.00013.8895318.2105788.00012.760416.736

3.2.2 Spell Rotations

For the spell rotation strategy, the same generic model as pre-3.2.2 was used:
  • 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

The following data is the result of running the simulation with 1'000'000 casts for each casting strategy (A, B):

.A=0A=1A=2A=3A=4A=5
B=0 4941 DPS
14.19 DPM
-10.89% DPS
-16.92% DPM		 4864 DPS
16.19 DPM
-12.29% DPS
-5.21% DPM		 4904 DPS
16.34 DPM
-11.55% DPS
-4.33% DPM		 5031 DPS
15.4 DPM
-9.27% DPS
-9.84% DPM		 5217 DPS
13.37 DPM
-5.91% DPS
-21.72% DPM		 5278 DPS
11.98 DPM
-4.80% DPS
-29.86% DPM
B=1 4836 DPS
32.92 DPM
-12.78% DPS
+92.74% DPM		4821 DPS
33.41 DPM
-13.05% DPS
+95.61% DPM		 4891 DPS
27.79 DPM
-11.79% DPS
+62.70% DPM		 5038 DPS
21.98 DPM
-9.14% DPS
+28.69% DPM		 5241 DPS
17.41 DPM
-5.48% DPS
+1.93% DPM		 5317 DPS
13.73 DPM
-4.11% DPS
-19.61% DPM
B=25031 DPS
32.83 DPM
-9.28% DPS
+92.21% DPM		5017 DPS
32.99 DPM
-9.52% DPS
+93.15% DPM		 5037 DPS
28.89 DPM
-9.16% DPS
+69.15% DPM		 5173 DPS
22.17 DPM
-6.71% DPS
+29.80% DPM		 5363 DPS
17.5 DPM
-3.27% DPS
+2.46% DPM		 5429 DPS
13.76 DPM
-2.10% DPS
-19.44% DPM
B=35216 DPS
29.13 DPM
-5.92% DPS
+70.55% DPM		5203 DPS
29.2 DPM
-6.16% DPS
+70.96% DPM		 5195 DPS
26.82 DPM
-6.32% DPS
+57.03% DPM		 5293 DPS
21.8 DPM
-4.54% DPS
+27.63% DPM		 5469 DPS
17.23 DPM
-1.37% DPS
+0.88% DPM		 5524 DPS
13.57 DPM
-0.38% DPS
-20.55% DPM
B=45364 DPS
26.24 DPM
-3.26% DPS
+53.63% DPM		5356 DPS
26.24 DPM
-3.41% DPS
+53.63% DPM		 5332 DPS
24.83 DPM
-3.84% DPS
+45.37% DPM		 5394 DPS
20.94 DPM
-2.72% DPS
+22.60% DPM		 5548 DPS
17.09 DPM
+0.00% DPS
+0.00% DPM		 5589 DPS
13.44 DPM
+0.79% DPS
-21.31% DPM
B=55442 DPS
24.11 DPM
-1.86% DPS
+41.16% DPM		5441 DPS
24.23 DPM
-1.87% DPS
+41.86% DPM		 5409 DPS
23.19 DPM
-2.45% DPS
+35.77% DPM		 5461 DPS
20.11 DPM
-1.51% DPS
+17.74% DPM		5601 DPS
16.76 DPM
+1.01% DPS
-1.87% DPM		 5587 DPS
13.44 DPM
+0.77% DPS
-21.31% DPM
B=65493 DPS
23.17 DPM
-0.94% DPS
+35.66% DPM		5491 DPS
23.16 DPM
-0.98% DPS
+35.60% DPM		 5451 DPS
22.37 DPM
-1.69% DPS
+30.97% DPM		 5497 DPS
19.69 DPM
-0.86% DPS
+15.28% DPM		5628 DPS
16.56 DPM
+1.50% DPS
-3.04% DPM		 5631 DPS
13.35 DPM
+1.55% DPS
-21.84% DPM
B=75524 DPS
22.57 DPM
-0.37% DPS
+32.14% DPM		5518 DPS
22.6 DPM
-0.48% DPS
+32.32% DPM		 5477 DPS
21.92 DPM
-1.22% DPS
+28.34% DPM		 5518 DPS
19.45 DPM
-0.48% DPS
+13.88% DPM		5647 DPS
16.48 DPM
+1.83% DPS
-3.51% DPM		 5656 DPS
13.31 DPM
+2.00% DPS
-22.07% DPM
B=85537 DPS
22.3 DPM
-0.15% DPS
+30.56% DPM		5536 DPS
22.33 DPM
-0.15% DPS
+30.74% DPM		 5499 DPS
21.72 DPM
-0.83% DPS
+27.17% DPM		 5529 DPS
19.29 DPM
-0.29% DPS
+12.94% DPM		5658 DPS
16.4 DPM
+2.04% DPS
-3.98% DPM		5669 DPS
13.28 DPM
+2.23% DPS
-22.25% DPM
B=infinite5560 DPS
21.88 DPM
+0.27% DPS
+28.10% DPM		5561 DPS
21.94 DPM
+0.29% DPS
+28.45% DPM		 5519 DPS
21.28 DPM
-0.46% DPS
+24.59% DPM		 5549 DPS
19.1 DPM
+0.07% DPS
+11.83% DPM		5669 DPS
16.3 DPM
+2.24% DPS
-4.57% DPM		5689 DPS
13.24 DPM
+2.60% DPS
-22.48% DPM



Color legend:
  • Black: Base rotation used as reference: ABx4, (MBarr|ABarr)
  • Gray: Rotation for which another rotation with better DPS and DPM exists
  • Blue: Rotation with more DPS than base rotation.
  • Green: Rotation with more DPM than base rotation.
  • Blue-green: Rotation with more DPS and more DPM than base rotation.
  • Red: Bad rotation, worse DPS and DPM than base rotation
Optimal DPM rotations ( green, blue-green)

In the table above, the most efficient rotations mana-wise are those with A=0-1 and B=2..infinity. The Mana burn ratio (which is DPS/DPM) is about 254 Mana/sec*, which should be sustainable in a raid scenario.

For B=2, A=0..1 (use ABarr to clear the AB stack if MBarr didn't proc after 2xAB, and use the MBarr as soon as it procs) you can increase the Damage per Mana by over 90% at the cost of only ~9.5% less DPS compared to the base rotation. The Mana burn ratio is about 154Mana/sec*, which can be kept up even for long fights.
If you never use ABarr to clear the AB stack but just cast AM until MBarr procs and then use MBarr as soon as possible, you still have a very efficient DPS/DPM rotation.

Recommended optimal rotation: A=0, B->Infinity
Spam Arcane Blast, use Missile Barrage as soon as it procs

Recommended DPM/recovery rotation: A=0, B->2..5
Spam Arcane Blast, use Missile Barrage as soon as it procs. If no procs occur after 2..5 AB stacks, clear the stack with Arcane Barrage.

High/Burst DPS rotations ( blue)

The best DPS rotations are found when saving the MBarr proc until you have AB fully stacked (4 stacks). The later you give up fishing for a proc and clear the stack with ABarr (or AM), the higher the DPS, but the higher the mana cost. With A=4, B->Infinity, the Mana burn ratio is about 350 Mana/sec* which is rather high, but with Evocation every 2 minutes you should hardly run into mana problems.

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).

* = Mana/sec values without taking Clearcast or Arcane Power into account

All in all we can be very happy with the arcane changes, for once Blizzard managed to boost them for PvE only without making them overpowered in PvP (not that we wouldn't need that, though).

If you have any questions, or want to share your experiences with the new arcane rotations, please drop me a comment, I'd appreciate that.

Arcane Rotations - Numbers updated for 3.2

by Tachyon on Wed. 22. July 2009, 18:14

Filed under: arcane, theorycrafting, simulation

I didn't blog for quite some time now (due to summer vacations and me generally don't playing my mage so much apart from the Ulduar raids, which I try to participate in as much as my time allows), so I thought I owe you at least an update to my arcane theorycrafting stuff for the minor changes that brings the new 3.2 patch. I got some other articles in the queue (equiment planning tips), that I intend to publish in the near future.

The upcoming content patch 3.2 will reduce the mana cost of Arcane Blast from 8% to 7% of your base mana (that's a plain 12.5% reduction).

Whilst this doesn't affect the DPS directly, indirectly Arcane becomes more viable in mana-demainding encounters, and in all other situations we can afford the higher DPS/mana rotations a little easier to crank up our DPS.

To update the arcane spell rotation tables I adapted and run the simulation once more. Here are the results for patch 3.2:
RotationDamageTimeDPSManaDPMMana/sec
ABx14968.0002.1552305.150215.00023.11099.760
ABx210830.0004.3102512.560860.00012.590199.520
ABx317586.0006.4662719.9701935.0009.090299.280
ABx425236.0008.6212927.3803440.0007.340399.040
ABx532886.00010.7763051.8204945.0006.650458.896
ABx1071136.00021.5523300.71012470.0005.700578.608
ABx100000764994636.000215517.2413549.580150497420.0005.080698.308
ABx0, ABarr3762.0001.2932909.280553.0006.800427.653
ABx1, ABarr9407.0003.4482728.030768.00012.250222.720
ABx2, ABarr15946.0005.6032845.7501413.00011.290252.166
ABx3, ABarr23379.0007.7593013.2902488.0009.400320.676
ABx4, ABarr31029.0009.9143129.8803993.0007.770402.772
ABx5, ABarr38679.00012.0693204.8305498.0007.040455.549
ABx0, Mbarr8812.0002.1554088.770952.0009.260441.728
ABx1, Mbarr15367.0004.3103565.1401167.00013.170270.744
ABx2, Mbarr22815.0006.4663528.7201812.00012.590280.256
ABx3, Mbarr31157.0008.6213614.2102887.00010.790334.892
ABx4, Mbarr38807.00010.7763601.2904392.0008.840407.578
ABx5, Mbarr46457.00012.9313592.6705897.0007.880456.035
ABx0, AM8812.0004.3102044.380952.0009.260220.864
ABx1, AM15367.0006.4662376.7601167.00013.170180.496
ABx2, AM22815.0008.6212646.5401812.00012.590210.192
ABx3, AM31157.00010.7762891.3702887.00010.790267.914
ABx4, AM38807.00012.9313001.0704392.0008.840339.648
ABx5, AM46457.00015.0863079.4405897.0007.880390.887

Dynamic Arcane Rotations:

Just for completeness (the details can be found in Going Arcane Part 3 - Spell Rotations), here's the generic pattern of spell rotations I suggested:
  • 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

.A=0A=1A=2A=3A=4A=5
B=0 -4.38% DPS
-27.09% DPM		 -5.35% DPS
-14.72% DPM		 -3.92% DPS
-10.70% DPM		 -1.13% DPS
-13.25% DPM		 -0.26% DPS
-21.00% DPM		 +0.43% DPS
-26.01% DPM
B=1 -9.61% DPS
+17.86% DPM		 -9.59% DPS
+23.85% DPM		 -7.63% DPS
+21.98% DPM		 -4.56% DPS
+11.19% DPM		 -3.34% DPS
-3.93% DPM		 -2.37% DPS
-13.05% DPM
B=2 -6.40% DPS
+14.33% DPM		 -6.56% DPS
+17.57% DPM		 -5.53% DPS
+17.08% DPM		 -2.68% DPS
+7.75% DPM		 -1.67% DPS
-6.18% DPM		 -0.84% DPS
-14.72% DPM
B=3 -2.15% DPS
+2.26% DPM		 -2.32% DPS
+4.12% DPM		 -1.92% DPS
+4.81% DPM		+0.00% DPS
+0.00% DPM		 +0.75% DPS
-11.48% DPM		 +1.32% DPS
-18.74% DPM
B=4 +0.60% DPS
-9.72% DPM		 +0.40% DPS
-8.54% DPM		 +0.59% DPS
-7.26% DPM		 +2.01% DPS
-9.42% DPM		 +2.44% DPS
-16.98% DPM		 +2.82% DPS
-22.96% DPM
B=5 +2.33% DPS
-15.60% DPM		 +2.15% DPS
-14.72% DPM		 +2.21% DPS
-13.54% DPM		 +3.31% DPS
-14.62% DPM		 +3.58% DPS
-20.31% DPM		 +3.84% DPS
-25.12% DPM
B=6 +3.46% DPS
-19.04% DPM		 +3.33% DPS
-18.45% DPM		 +3.30% DPS
-17.27% DPM		 +4.25% DPS
-17.86% DPM		 +4.40% DPS
-22.47% DPM		 +4.59% DPS
-26.50% DPM

The suggested strategy remains more or less the same:
  • If Missile Barrage procs, use it when you have 2-3 stacks of the Arcane Blast debuff. If you have the 4xT8 set bonus, you probably want to already cast MBarr with 2 stacks, so your procs can occurr more often (gotta test that)
  • Arcane Barrage is used to clear the AB debuff when MBarr doesn't proc after 2 (mana saving), 3 or 4+ (more DPS) subsequent Arcane Blast casts.


Oh, and big /love to l2dps.com and wow.com (they got new hidden class guides sections, thanks Utada for the hint) for linking my site and feeding me some readers, I really appreciate that!

Going Arcane, Part 3 - Spell Rotations

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

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

UPDATE FOR 3.2.2:
For an updated spell rotation analysis for patch 3.2.2+ see 3.2.2 Arcane Mage Changes or Tachyon's Arcane Mage Guide for 3.2.2.
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
RotationDamageTimeDPSManaDPMMana/sec
ABx14968.0002.1552305.150245.00020.280113.680
ABx210830.0004.3102512.560980.00011.050227.360
ABx317586.0006.4662719.9702205.0007.980341.040
ABx425236.0008.6212927.3803920.0006.440454.720
ABx532886.00010.7763051.8205635.0005.840522.928
ABx1071136.00021.5523300.71014210.0005.010659.344
ABx100000764994636.000215517.2413549.580171497060.0004.460795.746
ABx0, ABarr3762.0001.2932909.280553.0006.800427.653
ABx1, ABarr9407.0003.4482728.030798.00011.790231.420
ABx2, ABarr15946.0005.6032845.7501533.00010.400273.582
ABx3, ABarr23379.0007.7593013.2902758.0008.480355.476
ABx4, ABarr31029.0009.9143129.8804473.0006.940451.190
ABx5, ABarr38679.00012.0693204.8306188.0006.250512.720
ABx0, Mbarr8812.0002.1554088.770952.0009.260441.728
ABx1, Mbarr15367.0004.3103565.1401197.00012.840277.704
ABx2, Mbarr22815.0006.4663528.7201932.00011.810298.816
ABx3, Mbarr31157.0008.6213614.2103157.0009.870366.212
ABx4, Mbarr38807.00010.7763601.2904872.0007.970452.122
ABx5, Mbarr46457.00012.9313592.6706587.0007.050509.395
ABx0, AM8812.0004.3102044.380952.0009.260220.864
ABx1, AM15367.0006.4662376.7601197.00012.840185.136
ABx2, AM22815.0008.6212646.5401932.00011.810224.112
ABx3, AM31157.00010.7762891.3703157.0009.870292.970
ABx4, AM38807.00012.9313001.0704872.0007.970376.768
ABx5, AM46457.00015.0863079.4406587.0007.050436.624

(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 (RotationTachyon)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:
RotationTachyon: 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
RotationClassic: 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 Sequencei, t[i] is the cast time of Sequencei, and p is the probability (or percentage of times) we use Sequencei.

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=0A=1A=2A=3A=4A=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=43371 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=0A=1A=2A=3A=4A=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

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 BlastArcane BarrageArcane MissilesMissile Barrage
Dmg Avg135810401807.51807.5
Mana26158810131013
Mana /w talents245.34552.72952.22952.22
Cast Time2.501.505.002.50
Cast Time /w haste2.1551.2934.312.155
Coefficient /w talents80.429%71.429%187.857%187.857%
Dmg Avg2966.572468.575564.645564.64
Dmg Avg /w talents3233.562542.635731.585731.58
+Torment the Weak3621.592847.746419.376419.37

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 BlastArcane BarrageArcane MissilesMissile Barrage
Crit Multiplier1.844751.844751.9811.981
Crit Dmg6680.935253.3812716.7812716.78

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 BlastArcane BarrageArcane MissilesMissile Barrage
Avg Dmg4967.703761.888812.398812.39
DPS2305.012909.192044.474088.95
DPM20.256.819.259.25

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

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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