Help Me Understand Modifiers. Two Staffs, Why Is One Better?

Greetings,

Thanks for trying to help me out.

Basically, I am trying to understand why the new staff I found is worse than my old one, despite appearing to be a lot better.

The relevant different between them are below.

My "Old Staff" is the Dusk Pillar
https://cdn.discordapp.com/attachments/1318385407762763796/1318385409306267708/Old_Staff.png?ex=67622197&is=6760d017&hm=075dd4327231caa4724da5839bde19c8b96fcc67c471844fca15216d6d716cf9&
- 16% Damage as Extra Fire
- 19% Damage as Extra Cold
- 29% Cast Speed

The "New Staff" is Chimeric Song
https://cdn.discordapp.com/attachments/1318385407762763796/1318385408500957264/New_Staff.png?ex=67622197&is=6760d017&hm=a9ef9cb04b9e2fcddfea66ffaa4e4e34e44642a9b9c1b57e1dc597baa2f26ad1&
- 67% Increased Spell Damage
- 86% Increased Lightning Damage
- 61% Increased Crit Chance

The new staff is listed DPS on lightning spells at ~%11 lower than my old one. Which I just... Do not understand.

I know I am losing out on the 35% bonus damage from the Extra Fire/Cold, and the 29% Cast speed.

But on Arc for example, that is a difference of 0.88/sec cast and 0.69/sec cast.

I would have assumed the total of %153 extra damage on lightning spells would have MORE than made up for that. Especially with what amounts to roughly an extra 5% actual crit chance. (13.95% vs. 19.44%)

But maybe I don't understand how "Increased Spell Damage" and "Increased Lightning Damage" works?

The old staff has no damage modifiers to spell/lightning. And Arc's lightning damage does 415-2338.

The new staff has both damage modifiers, but and does 565-3117.

Which only adds up to roughly a total of 33% additional damage over the old staff when only looking at the lightning damage alone.

Which... feels... incorrect?

Please help.

I'm assuming the "% Damage as Extra" modifier is multiplicative, meaning it applies AFTER the "% increased Spell/Elemental Damage". So the numbers there ramp up quite a bit, which is why the numbers on those modifiers are usually very small, around 15-25%.

Also, the "% Cast Speed" modifier may not seem much but it's huge when you crunch the numbers (and that's what the DPS meter do). Think about it this way: 0.88/s and 0.69/s is 0.19/s, and since the DPS calculates per second, that's basically a 19% more modifier.

The crit is pretty irrelevant unless you have Critical Bonus on your tree or items, but I can't talk about that since I don't know your tree or other items.

TL;DR: Numbers can be tricky sometimes. DPS calculations using those numbers, even more so.

DISCLAIMER: These are thoughts based off of my PoE 1 experience and conjectures based on your explanation and images. I may be wrong on some stuff (and I would be ready to stand corrected if that's the case).