Alternative Quality: Spell Echo Gem + Pledge of Hands Interaction

yo guys, i am playing a build with pledge of hands as a weapon with the "hidden" symbiotic mechanic of the greater spell echo + spell echo as a gem in the 6 link additionally.
and i was wondering if the normal spell echo or the divergent spell echo gem, gives more dps in combination with the internal 35% more dmg multipler we get of the greater spell echo for each repeat. so i tried so basic maths only calculating with 1000 base damage as an example. do i have any errors in my initial idea?
spell echo gives 10% less dmg on all repeats, divergent spell echo gives 30% less dmg on all repeats but 60% more on the last repeat!

divergent spell echo:
1000x0,7+1000x1,05+1000x1,4+1000x2,35 = 5500
first repeat 2cd 3rd 4th

normal spell echo
1000x0,9+1000x1,25+1000x1,6+1000x1,95 = 5700

so that would mean normal spell echo is better? or does not it?
or do i need to include crit etc or any other "more" multipler. to get the real dmg on the last repeat of the divergent spell echo.
obviously the first 3 repeats of the divergent deal less dmg than with the normal gem, but the last repeat of the divergent version should be able to outvalue the missing dmg of the first 3 repeats!? or am i wrong about that?
so theoretically in my mind we should be able to abuse the bigger multiplier on the last repeat since it should scale multiplicative with all the rest of the further andupcoming dmg calculation? or?


Edit: or do i have a fundamental calc Error?
Can i even combine the less dmg from the Spell echo Gem with the more per repeat of the greater Spell Echo and the 60% more of the divergent to the Last repeat, or are they all their own Multiplicator?

All you really need to do is look at the overall multiplier; you can drop any pseudo dps value.

Spell Echo
= .9(1 + 1.35 + 1.7 + 2.05) / 4
= 1.3725
= 37.25% more damage

Spell Echo (quality 3)
= .7(1 + 1.35 + 1.7 + 2.05 * 1.6) / 4
= 1.28275
= 28.28% more damage

Awakened Spell Echo
= .85(1 + 1.35 + 1.7 + 2.05 * 1.19) / 4
= 1.379
= 37.90% more damage

Without taking anything else into account, a max ASE is better than the original, but the original is clearly better than the alternate quality 3.

Thank you very much sir!
It can be so simple 🙂

Why put a spell echo gem in POH? Seems counter-intuitive since it already has Greater Spell Echo lvl 30. Wouldn't you benefit from a different staff?

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Gulch wrote:

Why put a spell echo gem in POH? Seems counter-intuitive since it already has Greater Spell Echo lvl 30. Wouldn't you benefit from a different staff?

Greater Spell Echo
- Does not provide any cast speed incentive
- Deals 35% more damage per repeat, and gets a 3rd repeat from SE

Spell Echo is normally the #1 dps support gem, and it gets even more powerful when combined with the staff.

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Aldonés wrote:

"

Gulch wrote:

Why put a spell echo gem in POH? Seems counter-intuitive since it already has Greater Spell Echo lvl 30. Wouldn't you benefit from a different staff?

Greater Spell Echo
- Does not provide any cast speed incentive
- Deals 35% more damage per repeat, and gets a 3rd repeat from SE

Spell Echo is normally the #1 dps support gem, and it gets even more powerful when combined with the staff.

Right, but if they're going to pop in the spell echo gem, wouldn't they be better off using a rare staff that has stuff like crit and crit multi and +2 to gems?
I'm asking because a buddy of mine is using the POH for ball lightning, and if spell echo gem is better than one of his other supports I'll have him toss it in there.

"

Gulch wrote:

Right, but if they're going to pop in the spell echo gem, wouldn't they be better off using a rare staff that has stuff like crit and crit multi and +2 to gems?
I'm asking because a buddy of mine is using the POH for ball lightning, and if spell echo gem is better than one of his other supports I'll have him toss it in there.

The two are different support gems that only have "repeat" in common, but since the repeats stack this isn't an issue. PoH is a staff designed for a skill using Arcmage. GSE comes with a 50% more multiplier, making the damage boost from Arcmage even more potent, but since it has +2 repeats and SE +1 repeat, you only have to actually pay for mana every 4 casts. GSE also does 35% more damage per repeat, so having that 3rd repeat makes the spell do 105% more damage on the final hit (thus why the OP questioned if alternate 3 would be viable).

I would say this, if using PoH and you only have 2 sockets, then Spell Echo in 100% of cases should be your support gem.

Basically if I were to look at PoH and compare dps of Spell Echo or Awakened Elemental Focus (ignoring that SE has a higher mana multiplier, the cast speed is a massive QoL difference, and AEF prevents you from inflicting elemental ailments)

PoH + SE
= .9(1 + 1.35 + 1.7 + 2.05) * 1.7 / 4
= 2.333
= 233.3% more damage

PoH + AEF
= (1 + 1.35 + 1.7) * 1.54 / 3
= 2.079
= 207.9% more damage

Note that L20 SE normally provides 53% more dps whereas L5 AEF provides 54% more dps. Again the only time repeats are bad is if you are playing an Unleash build since the extra Unleash casts will not repeat.