Area of Effect (AoE)
From xenowiki
Coefficients for AOE spells are generally thought to fall into an equation like the following:
Coefficient = ( (Cast Time in Seconds / 3.5) / 3 )
With standard penalties applied for snares etc. When AoE caps (http://forums.worldofwarcraft.com/thread.html?topicId=443123919) were introduced notes often were made in the patch notes about changing coefficients. This warrants investigation!
Using a controlled environment of a duel with a Shammy premade of mine (So I could heal it and have only one target to chase around and cast at) with the shammy wearing tier healing gear, no resil, and no talents to eliminate reduction effects on its side. The Mage was specced around all composite damage increasing talents to get to Dragons Breath, and wearing 728 +fire/arcane damage and 556 +frost damage.
To calculate the coefficients I sought out the min/max values for the spells, since we expect coefficients to follow a pattern of:
Base Damage + (Coefficient * +Damage)
If we know that the base damage of spell A is 100-200, we know that after applying the +damage bonus we should have a 100 damage range (+/- 1 for rounding, as I observed). Therefore, if we are applying 100 +damage to spell A, and observe a damage range of 175-275, we know we have seen the range of the spell and its coefficient is .75.
Here is a dump of the parsing script I wrote to compile the information my addon gathered:
Spell (Blast Wave) observed min/max of (756)/(865) mean of (807.953642384106)
Base min/max of (616)/(724) mean of (670)
Gain on min (140) on max (141) on mean (137.953642384106)
Coefficient by min (0.192307692307692) by max (0.193681318681319) by mean (0.189496761516629)
Spell (Cone of Cold) observed min/max of (525)/(564) mean of (547) Base min/max of (418)/(457) mean of (437.5) Gain on min (107) on max (107) on mean (109.5) Coefficient by min (0.192446043165468) by max (0.192446043165468) by mean (0.196942446043165)
Spell (Arcane Explosion) observed min/max of (533)/(563) mean of (549.84375) Base min/max of (377)/(407) mean of (392) Gain on min (156) on max (156) on mean (157.84375) Coefficient by min (0.214285714285714) by max (0.214285714285714) by mean (0.216818337912088)
Spell (Dragon's Breath) observed min/max of (821)/(931) mean of (875.02994011976) Base min/max of (680)/(790) mean of (735) Gain on min (141) on max (141) on mean (140.02994011976) Coefficient by min (0.193681318681319) by max (0.193681318681319) by mean (0.192348818845825)
Spell (Flame Strike) observed min/max of (652)/(757) mean of (703.842105263158) Base min/max of (480)/(585) mean of (532.5) Gain on min (172) on max (172) on mean (171.342105263158) Coefficient by min (0.236263736263736) by max (0.236263736263736) by mean (0.23536003470214)
To put this in a more useful form, here's a table:
| BW | 0.19231 | 0.19368 | 0.18947 |
| CoC | 0.19245 | 0.19245 | 0.19694 |
| AE | 0.21429 | 0.21429 | 0.21682 |
| DB | 0.19368 | 0.19368 | 0.19235 |
| FS | 0.23626 | 0.23626 | 0.23536 |
Now, as suggested by Lhivera, its possible that the current coefficients have been altered to have a .5 penalty instead of a .33 penalty. Looking at the numbers for AE using that assumption:
(1.5 / 3.5) / 2 = 0.21429
An exact match vs expected, which is nice and pretty. We then apply the .95 known penalty to the AoE spells that apply snares (BW/CoC/DB) and get:
((1.5 / 3.5) / 2) * .95 = 0.20357
This does *not* match up. vs observed. Interestingly enough, Blast Wave exceeded its expected range with 1 point, and bridges the observed difference in coefficient between CoC and DB. More on this later.
Flamestrikes ground DoT generated a 128 damage tick with +damage on, 106 without, giving a 3% per tick coefficient, or 12% total over the 4 ticks. Attempting to predict the coefficient of flamestrike:
(3.0 / 3.5) / 2 = 0.42857
Take 12% away for the ground DoT and you're still left with .30857, about 7% unaccounted for by the formula.
And a quick test of Blizzard gave ticks of 265 over 185 without gear. Totaling to 2120 and 1480 respectively. Giving a gain of 640 / 556 = 1.15108.
Attempting to predict Blizzards coefficient:
(8.0 / 3.5) / 2 = 1.14286
Given my lack of extensive casting to get an average damage output and other testing that has gone on, I'd say this coefficient is locked in by formula. So at this point we have two spells we can predict coefficients for by equation, AE and Blizzard. Still remaining to be explained are CoC/BW/DB and Flamestrike.
Based on what I observed with Pyroblast (http://forums.worldofwarcraft.com/thread.html?topicId=108414447) it's entirely possible that Flamestrike has a defined coefficient that doesn't follow the expected formulas. I plan to go back and re-test BW/CoC/DB with different +damage levels to see if I can recreate these results.
So, for the TL:DR Crowd, heres the two coefficients we know:
Blizzard: 1.1428 Arcane Explosion: .2143
Here is one that we have observed, but can't justify by formula yet:
Flamestrike: .2363 frontend, .12 DoT
And here are three that we have observed, are in somewhat question, and can't be justified by formulas yet:
Dragons Breath: .1937 Cone of Cold: .1925 Blastwave: .1923 - .1937
Any commentary and or formula suggestions are welcome.
Here's how the table stands at present:
| Spell | Avg Base Dmg | Time | Coefficient | Damage Cap | Base Mana | Cooldown |
| Arcane Explosion | 392.0 | 1.5i | 0.2143 | 6,730 | 545 | -- |
| Blast Wave | 670.0 | 1.5i | 0.1357 | 9,440 | 620 | 30 |
| Blizzard | 1476.0 | 8.0 | 1.1429 | 28,950 | 1645 | -- |
| Cone of Cold | 437.5 | 1.5i | 0.1357 | 6,500 | 645 | 10 |
| Dragon's Breath | 735.0 | 1.5i | 0.1357 | 10,100 | 700 | 20 |
| Flamestrike | 725.0 +424 | 3.0 | 0.2363/0.12 | 7,830 | 1175 | -- |
| Frost Nova (rank 1) | 22.5 | 1.5i | 0.0081 | unknown | 55 | 25 |
| Frost Nova (rank 5) | 106.5 | 1.5i | 0.1357 | unknown | 185 | 25 |
| Hellfire | 4590.0 | 15.0 | 2.1429 | unknown | 1665 | -- |
| Rain of Fire | 1212.0 | 8.0 | 0.9520 | unknown | 1480 | -- |
| Seed of Corruption | 1200.0 | 2.0 | 0.2200 | 13,580 | 882 | -- |
| Shadowfury | 670.0 | 0.5 | 0.1950 | unknown | 710 | 20 |
| Spell | Avg Base Dmg | Time | Coefficient | Damage Cap | Base Mana | Cooldown |
| Arcane Explosion | 404.0 | 1.5i | 0.2143 | 6,730 | 545 | -- |
| Blast Wave | 759.0 | 1.5i | 0.1357 | 9,440 | 583 | 30 |
| Blizzard | 1643.0 | 8.0 | 1.1429 | 28,950 | 1356 | -- |
| Cone of Cold | 657.0 | 1.5i | 0.1357 | 6,500 | 532 | 8 |
| Dragon's Breath | 833.0 | 1.5i | 0.1357 | 10,100 | 659 | 20 |
| Flamestrike | 821.0 +480 | 3.0 | 0.2363/0.12 | 7,830 | 1106 | -- |
| Frost Nova (rank 1) | 25.0 | 1.5i | 0.0081 | unknown | 45 | 21 |
| Frost Nova (rank 5) | 118.5 | 1.5i | 0.1357 | unknown | 153 | 21 |
| Hellfire | 5049.0 | 15.0 | 2.1429 | unknown | 1582 | -- |
| Rain of Fire | 1333.0 | 8.0 | 0.9520 | unknown | 1406 | -- |
| Seed of Corruption | 1386.0 | 2.0 | 0.2200 | 13,580 | 882 | -- |
| Shadowfury | 670.0 | 0.5 | 0.1950 | unknown | 675 | 20 |
Cast Time: also applies to channel times. "1.5i" indicates instant + GCD.
Coefficients: mostly taken from wowwiki.com. I tested Blizzard myself on the 2.2 PTR.
Damage Caps: mostly tested by Zandinar ([url]http://forums.worldofwarcraft.com/thread.html?topicId=443123919[/url])
Base Mana: raw mana cost, not counting talents, clearcasting procs, MOE, etc.
Talented Values: assumes the caster is talented for the spell's school, for example Affliction for SoC, or Arcane for Arcane Explosion. |
