Incinerate

Incinerate is a channeling fire spell that launches a torrent of fire from the user's hands, rapidly dealing fire damage. The longer the channel is held, the bigger the damage and area becomes. Releasing the channel launches a wave of fire that deals more fire and ignite damage.

Skill functions and interactions

 * Incinerate gains more damage when cast continuously from one spot, up to a maximum of 200% more damage (25% per stage up to 8 stages maximum, or 10 if you use the helmet enchantment). The next stage is reached after every tick (0.2s). At each stage, the flames become visibly larger and will spread out in a huge cone. If the player is stunned or interrupted in any way while casting incinerate, the spell will come back to stage 1.


 * Damage Effectiveness: The damage effectiveness of Incinerate is a relatively low 30%. However, at the highest stage of Incinerate, flat damage (such as from, , , or , etc.) is added to Incinerate at 90% their normal values because of the 200% more damage modifier.


 * Incinerate cannot be supported by.


 * Traps and Mines: This spell can't be supported by traps or mines, because of its Channeling tag.
 * Spell Totem Support: Totems that use Incinerate will automatically release upon reaching maximum stacks or when the enemy they're targeting dies.

Basic Mathematical Modelling
The following calculation aims towards characters that have a critical strike chance of either 0% or a critical strike multiplier that is strictly 100% (e.g. for characters with the keystones Resolute Technique or Elemental Overload allocated). It can be easily extended to account for critical hits which can be implemented as a multiplicative factor to the skills average base damage.

The additional damage from ignite is assumed to be negligible. Characters that specialise in burning damage are aiming towards the largest ignite damage possible and always want to release at maximum stage if possible.

Under these assumptions, one can calculate the average base damage dealt per second (depending on the current stage n) via

$\begin{align} \text{DPS(n)} = \frac{\text{DMG}_{min} + \text{DMG}_{max} }{2 \cdot \text{CastTime} } \left(1 + \frac{n}{4}\right) \end{align}$

Similarly, the average damage upon release can be calculated to be

$\text{ReleaseDPS} = \frac{\text{DMG}_{min} + \text{DMG}_{max} }{2 \cdot n \cdot \text{CastTime} } \left(6 + \frac{n}{4}\right)$

One also finds

$\begin{align} \text{RampUpDPS} &= \frac{1}{n_{max} + 1 }\frac{\text{DMG}_{min} + \text{DMG}_{max} }{2 \cdot \text{CastTime} } \sum_{k = 0}^{n_{max} }\left(1+\frac{k}{4}\right) \\&= \frac{\text{DMG}_{min} + \text{DMG}_{max} }{2 \cdot \text{CastTime} } \frac{n_{max}+8}{8} \end{align}$

for the average ramp-up DPS when building stages. To calculate the average damage dealt by repeatedly releasing at maximum stages, we have to sum the latter two formulas as follows

$\begin{align} \text{FinalDPSContinuedReleasing} &= \text{RampUpDPS} + \text{ReleaseDPS} \\ &=\frac{\text{DMG}_{min} + \text{DMG}_{max} }{2 \cdot \text{CastTime} } \left[\frac{1}{n_{max} } \left(6 + \frac{n_{max} }{4}\right) + \frac{n_{max} + 8}{8}\right] \\ \text{FinalDPSContinuedFire} &= \frac{\text{DMG}_{min} + \text{DMG}_{max} }{2 \cdot \text{CastTime} } \left[1 + \frac{n_{max} }{4}\right] \end{align}$

For $n_{max} = 8$ both brackets are equal, i.e. there is no difference in DPS. However, for $n_{max} > 8$ it is inefficient to continually release a damaging wave when reaching maximum stages as a simple numerical evaluation of both brackets shows.

Curiously, note that this calculation holds true for arbitrary $n_{\text{Release} }$, which implies a significant increase in DPS the earlier the skill is released. For example, a character that has $n_{max} = 8$, but keeps releasing at $n = 4$, gains an additional 58.3% DPS over a character with identical stats that keeps channeling at 8 stages and never releases.

Version history

 * The visual effects have been improved.


 * Mana Cost at gem level 1 is now 2 (was 3).
 * Mana Cost at gem level 20 is now 4 (was 5).
 * Now gains radius and radius per stage as the gem levels, up to +5 radius per stage (from +4) and +19 radius at max stages at gem level 20 (from +15).
 * Now deals 3 to 5 Fire damage at gem level 1 (unchanged) and 140 to 210 Fire damage at level 20 (from 129 to 194


 * Now deals area-of-effect damage in a cone in front of the caster while channelling, dealing 25% more damage with hits and ailments for each stage. The angle of the cone increases by up to 300% while channelling. When the channeling ends, a final wave is released which deals 500% more damage with hits and Ignite. This final wave always ignites.
 * Now increases fire damage by 1% per 1% quality on the skill gem (previously increased projectile speed by 2% per 1% quality).


 * Added a channelled skill system. Incinerate, and  are now channelled skills.
 * Unlike other skills, which are used once and quickly finish, when you use a channelled skill, it doesn't finish until you release the relevant button/key. You continue performing the same skill.
 * You need to pay mana repeatedly to keep the skill going. The channelled skill's mana cost must be paid again to maintain it with a frequency determined by the cast time. If you can't pay, the skill will end, just as if you'd lifted the button.
 * Dying, being stunned, and other game mechanics that interrupt the use of skills will cause channelling to end as well.
 * Effects which trigger when you use a skill will only trigger when you initially start channelling - regardless of how long you maintain a channelled skill, it's still the same use of the skill. You need to stop channelling if you want to use it again.


 * No longer affected by Spell Echo, as was intended in 2.0.0. Incinerate now only adds 50% more damage for each stage, down from 100% more damage. Incinerate's damage has been increased by 15% at level 1 and reduced by approximately 8% at level 20.


 * Damage increased by approximately 100% to compensate for the shotgunning mechanic change.
 * Base Cast Speed has been increased from a cast time of 240ms to 200ms.


 * Now has a cast time of 240 milliseconds instead of 160. Damage has been increased by 77% per cast and damage effectiveness for supports has been adjusted from 20% to 30%. The number of stacks required to progress through a stage has been reduced to four casts.


 * Incinerate now has an informational icon which displays what stage it is in when you continue to cast it.


 * Now progresses through the damage stages faster and does more damage at later stages. The mana cost has been reduced at higher skill levels.


 * Spells with Damage Effectiveness no longer have their own damage affected by Damage Effectiveness. Damage values on these skills have been updated to reflect this.


 * Mana cost progression has been reduced—higher levels cost less mana to use.


 * Increased the damage by 12.5%.


 * Incinerate has been added to the game.
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