Increase Spell Damage (Before XX Crit) by XX% to XX% question

Hi folks. Might someone shed some light exactly how various AA's or Spells or songs or clicks or focus, work on increasing spell damage?

Please undersand I am coming from a DOT/Necro setup, but this would apply to all casters.

We all have (well most) ADPS or self, that gives us increase to spell damage.
If I were to BE VERY simple and use an example of ONE DD/DOT that does 10,000 damage. And we assume/presume there are NO other modifiers, no type 3, no luck, no crit no focus, NOTHING so if were to cast that SAME spell for 10k OVER and over and it always gives me 10K damage... how would the various aa/clicks/songs work for that?

I am trying to wrap my head around BEFORE CRIT and AFTER CRIT.
I know this might be simple for some folks, but it baffles me.
Is BEFORE crit better or is AFTER crit better? Does it matter for DOTS vs DD? How does BASE damage work?
Is there a hard cap for how MUCH before or after?
I shall give an example: Necro HAND OF DEATH AA. At max level says "Before DoT Crit) by 50% to 140%". Ok.. so let's say the worse possible scenario --- 50%.. so that means if I were to cast the above 10K spell it would be 15K? But if it crits, twincasts, lucky, focus etc... it blows up? How would this work for the AFTER CRIT? In other words, do I want BEFORE CRIT or AFTER CRIT?

"Before crit" and "after crit" are not a great way to separate SPAs nowadays, but for the sake of explanation:

Back when things were less complicated, before crit meant that something was multiplied by your critical damage modifier. Note that there is no difference between these on a non-critical hit. Using the example of a 10k base spell with no other modifiers and a 50% focus, both a before or after crit focus would produce a 15k hit. However, let's say you have a 400% critical damage modifier (+100% base, for a 5x total multiplier). Without any modifiers, your 10k base spell would do 50k on a crit (10k * 500%). With a 50% after crit modifier, you would do 55k damage (10k * 500% + 10k * 50%). With a 50% before crit modifier, you would do 75k damage (10k * 150% * 500%).

The problem nowadays is lots of SPAs have different interactions with each other. For DoTs, for example, Hand of Death (SPA 124) is applied "before crit" (i.e., it is multiplicative with your critical damage modifier), but it is also multiplicative with SPA 413, 302, and 461. There are other "before crit" SPAs (e.g., 296) that are not multiplicative with the aforementioned effects. DDs and DoTs also treat a number of SPAs differently; for nukes SPA 124 is after crit and only multiplicative with 413 and 461.

If you are looking to maximize your personal burns, the most convenient way is to link Spire -> Twincast -> Frenzy Dead -> Hand of Death together with a single hotkey press. If you are lazy, you can add Mercurial Torment to this, though it should generally be cast beforehand since it has a longer duration and makes your spellcasting faster. Note that since Hand of Death has a short cast time (the others are instant cast), it must be the right-most of these buttons on your hotbar, else the instant cast AAs won't fire until you press the hotkey a second time.

Do this on top of Illusions of Grandeur (from enchanters) + Glyph for maximum fun.

Technically getting a Blood nuke proc is better than Hand of Death while it has charges (which would encourage casting Hand manually), but linking those will help you a lot (you can then bang the 'burn' hotkey again to trigger just spire or spire+hand when Twincast is down).

Thank you so much for all the info!

As part of the burn "Frenzy Dead" what is that? The only thing I could find is that it's an aegis/haste for pet. Is that part of the burn listed above?

For necros, "Frenzy Dead" is the name of the hotkey that gets created when you click "Hotkey" on the Companion's Fury AA on the Archetype tab. It adds a nice chunk of DPS while it is up. At max level, it puts the following buff on your pet:

[53367/31550] Frenzy of the Dead XII
Classes: NEC/254
Skill: Melee
Target: Pet
Range: 200'
Resist: Beneficial, Blockable: Yes
Focusable: Yes
Casting: 0.25s
Duration: 60s+ (10 ticks), Dispelable: Yes
1: Cast: Lingering Nightmares VI (v374)
2: Increase AC by 46 to 61, Based on Class
4: Increase Melee Haste by 22% (v119)
7: Increase STR by 40
8: Increase Pet Chance to Flurry on Double Attack by 5%
9: Increase ATK by 700
10: Increase Chance to Hit by 35%
11: Increase Hit Damage by 200% (v185)
Triggers Lingering Nightmares VI.
Increases armor class 700 points, overhaste by 22%, strength by 40 points, attack power by 700 points, chance to perform a flurry of attacks on a successful double attack by 5%, accuracy by 35%, and base melee damage by 200%.
Since it has a cast time, you may need to fire it manually or just hit your hotkey twice to get it to go off after Hand of Death. In my setup I have it on a second hotkey to cast it manually. It is a 10 min recast, so not quite on the same general timers as Spire (7:30), Hand (8:30) or Heretics Twincast (15).

Thank you Silu!