The Lightning Capacitor

The Lightning Capacitor is an epic trinket for DPS casters. As its Equip: ability implies, it is crit-based and thus might be priorized to Mages, Elemental Shamans, Balance Druids and Destruction Warlocks. For some classes and specs it is said to be the most powerful trinket in the game.

Source
This item drops from Terestian Illhoof in Karazhan with an estimated drop rate of 7% - 13% (Armory: Low (15% -24%)).

Mechanic
The way, this trinket works is quite complicated and on most sites fairly misunderstood. First of all, the bolt emitted by this trinket is not affected by +spell damage anymore (since Patch 2.1), it can however crit/be resisted and is affected by the characters Nature spell crit and hit chance, and any nature damage vulnerability debuffs (such as Stormstrike). The crits of the bolt do not produce a charge, but any spell-like critical hit inflicted by your character will produce a charge, e. g. Molten Armor, Lightning Shield, etc. and of course single target direct damaging spells and AoE spells.

The tooltip is somewhat misleading regarding the 2.5 second internal cooldown. Electrical charges CAN be gained on every critical strike except for the first 2.5 seconds after a bolt goes off. This means it's possible to get 3 crits at once (for example, from an AoE spell hitting multiple targets) and fire off a single bolt. However, any further crits will not produce charges until after 2.5 seconds. This effectively limits the bolts to one per 2.5 seconds. A more correct tooltip might read: "Electrical Charge cannot be gained for 2.5 seconds after a Lightning Bolt is fired."

The effect of this trinket is badly expressed as spell power, but rather as a flat crit-damage bonus and can easily be calculated as dps-gain, as the calculations below will demonstrate.

Because it is direct nature damage it can be partially resisted, but this is not considered in the following calculations, as most PvE encounters are either completely nature immune or do not have noticeable resistances at all. These calculations refer to single target direct damage casting. The italic lines are examples with 30% nature crit, 94% hit chance and Scorch spamming (34% scorch crit, same hit, 1.5s casting time). It has to be noted, that Arcane Missiles have to be considered as 1s casting time, as every missile can crit and thus produce a charge, 5 missiles in 5 sec is 1 missile / sec.

Terms used:

-hit(n): hit chance against the current target with nature spells as factor (e. g. 0.83 as 83%)

-hit(m): hit chance against the current target with your main spell school as factor

-crit(n): crit chance with nature spells as factor

-crit(m): crit chance with your main spell school as factor

-crit(b): The critical damage bonus as factor, e. g. 0.5 for normal crits, 1.1 for ignite crits as a fire mage.

-cast(t): time to cast your spell in seconds

The average bolt damage would be:

( ( 694 + 806 ) / 2 * ( 1 + crit(n) * crit(b) ) ) * hit(n) = Bolt(d)

( ( 694 + 806 ) / 2 * ( 1 + 0.3 * 0.5 ) ) * 0.94 = 810.75

1/3 to Bolt(d) is a flat addition to your crit damage. 270.25

The average time it takes to produce 3 crits with your main spell school and consequently producing a bolt is:

( 1 / ( crit(m) * hit(m) ) ) * 3 * cast(t) = Bolt(t)

( 1 / ( 0.34 * 0.94 ) ) * 3 * 1.5 = 14.08

Note: Due to the internal cooldown the minimal time between two bolts is limited to 2.5 seconds. The subsequent effect, that a crit right after an emitted bolt is not counted for a charge is definitely decreasing the damage output, but is quite difficult to calculate.

The dps-gain is now easily calculated by:

Bolt(d) / Bolt(t) = Bolt(dps)

810.75 / 14.08 = 57.58

You can now calculate yourself, how much bare spell power you would need with your main spell(rotation) to gain an equivalent dps boost. For Scorch it would be 153 with the given hit/crit chance, as the following calculation states (assuming 800 spell power and fully stacked Fire Vulnerability):

( ( 305 + 361 ) / 2 + 800 * 1.5 / 3.5 ) * ( 1 + 0.34 * 1.1 ) * 0.94 * 1.15 / 1.5 = Scorch(dps) = 669.231039428571

It has to be noted, that there are several talents and multiplicators missing in this calculation; they are left out for simplicity and because these calculations are exemplarious, they differ largely for every class and spec.

Now the same with Scorch(dps)', which is the result above plus the dps gained from The Lightning Capacitor and resolved to the unknown amount of spell power (x):

Scorch(dps)'= 669.231 + 57.58

( ( 305 + 361 ) / 2 + x * 1.5 / 3.5 ) * ( 1 + 0.34 * 1.1 ) * 0.94 * 1.15 / 1.5 = 726.81

( 333 + x * 0.4286 ) * ( 1 + 0.34 * 1.1 ) * 0.94 * 1.15 / 1.5 = 726.81

( 333 + x * 0.4286 ) * 1.374 * 0.94 * 1.15 / 1.5 = 726.81

( 333 + x * 0.4286 ) * 0.990196 = 726.81

329.735268 + x * 0.4243980056 = 726.81

x = (726.81 - 329.735268) / 0.4243980056

x = 935.6188

The respective calculation with crit(m) as variable and constant spell power:

( ( 305 + 361 ) / 2 + 800 * 1.5 / 3.5 ) * ( 1 + x * 1.1 ) * 0.94 * 1.15 / 1.5 = 726.81

( 333 + 800 * 0.4286 ) * ( 1 + x * 1.1 ) * 0.94 * 1.15 / 1.5 = 726.81

( 333 + 342.88 + 366.3 * x + 377.168 * x ) * 0.94 * 1.15 / 1.5 = 726.81

( 675.88 + x * 743.468 ) * 0.7206¯ = 726.81

492.26593¯ + x * 535.7926053¯ = 726.81

x = 0.43776

So you would need 935.6 spell power or 43.776% spell crit to achieve the same +57.58 dps boost, thus The Lightning Capacitor is theoretically adding 153 spell power or 11.36% spell crit (251.056 Spell Crit Rating). This spell power or spell crit is unaffected by the base spell power in the calculation, but it is scaling with base spell crit and nature critical strike chance, of course, the more crit, the more dps-gain and therefore more required spell power or spell crit to compensate it. The dps-boost is largely affected by cast(t), the caststime of your main nuke spell, shorter casts will result in more frequent procs. The Lightning Capacitor is thus one of the rare trinkets that scale directly with the subsequent equipment of its wielder and the effective circumstances.
 * note: A math error using formulas above was corrected. The analysis below is wrong but was left as the author originally wrote. Formulas are also suspect, but were not altered.

Dps Calculator for trinket
It is difficult to evaluate this trinket. Generally there are better options for most builds at the point you first enter Kara. Later when your spell crit has increased, this trinket really shines. Input your stats into the following spreadsheet to see how much benefit this trinket gives you: [[Media:Lightning Capacitor dps calculator.ods]] (Spreadsheet contains no macros. If it does, it's been infected.)

Additional notes
You do not need to face the mob, which is supposed to be hit by the bolt.

The caused damage by the Lightning Bolt is unaffected by the characters spell power, which can be explained by the fact, thet the Lightning Bolt might appear like an instant cast spell, but it does not trigger the Global Cooldown and hence it's damaging coefficient is 0 / 3.5 = 0. Firing a Lightning Bolt also does not interrupt channeled casts like Arcane Missiles.

The Lightning Bolt does not have a max-range, as long as you can crit the mob, the Bolt can reach it. The Bolt is also unaffected by LoS-mechanics. Think of the following situation: You have 2 charges and you cast a fireball on a mob, while the fireball is in mid-air, the mob runs behind a wall or some LoS blocking obstacle. The fireball crits, giving the 3rd charge and thus releases the bolt; even though the mob is not hittable by your spells, the bolt will fly right through the obstacle and hit the mob. The same applies to silencing effects, stuns and other incapacitating effects, basically there is nothing that could prevent The Lightning Capacitor from firing it's Bolt when reaching 3 charges, by any available means, except the case that the mob died from the 3rd crit, then the charges are lost and no Bolt is fired.

The Lightning Bolt always hits the mob which received the last crit that stacked the 3rd charge and released the Bolt, even though you may not have targeted it, except it died from the crit, as mentioned above.

The Electrical Charges are displayed as a stackable, typeless buff on you. This buff has an infinite duration and even persists if you unequip The Lightning Capacitor or logout. It does not persist through death, however, and like other buffs, it disappears upon entering an Arena match.

It can proc from any ability that is considered a spell, which includes Flametongue Weapon, Frostbrand Weapon, Lightning Overload-casts, Firestone attack and Molten Armor. Wand crits are not considered spell crits and hence do not produce charges.

This item was changed in Patch 2.3. It now has a 2.5 second cooldown after each lightning bolt. The tooltip is quite misleading. It is actually meant to be "cannot be discharged more than once every 2.5 seconds". This seriously damages the worth of the item for casters who were using this with a heavy AoE spell rotation. Specifically Arcane Mages. But as this changes effect depends largely on critluck and the current situation, it is hardly possible to calculate the actual loss of DPS for single-target damage casting. In most cases, it just takes one or two more casts to produce the necessary 3 charges (because one or two crits might have been in vain because of the CD).

The damage of the Lightning Bolt is affected by debuffs (e.g. Stormstrike, Misery) and talents (e.g. Arcane Instability, Molten Fury) which improve all, or at least nature spells. However, talents which specifically mention their affected spells do not improve it. Furthermore, even the Shaman's talents which improve Lightning Bolt do not affect it, as these only affect the Shaman's spell; these include Concussion, Elemental Mastery and Elemental Fury. Especially in raid environments, where many buffs and debuffs are in effect, the dps boost provided is slightly higher (~80 dps), especially with spell crit increasing auras, totems or buffs.

As the rank of your nuke spell is irrelevant, it is possible to spam rank 1 spells while being oom and still sustain quite a bit of dps. While normally it is probably better to stay out of the 5 second rule, in combination with specific abilities (e.g. Judgement of Wisdom, Insightful Earthstorm Diamond, Clearcasting), spamming a rank 1 spell (for example, Scorch) might increase your damage by more.

The proc of this trinkets appears in your combat log as "Your Lightning Bolt hits/crits %t for %d.", just like the Lightning Bolts fired by Shamans.