double Collateral Damage jewel question [solved by adghar]

Collateral Damage can be interpreted 2 ways:

1) 50% to deal double damage+50% to deal double damage = 100% chance to deal double damage; DPS multiplier = 2.0, spike (max) multi = 200%

Damage probability square:
2.0 2.0
2.0 2.0
8.0/4=2.0

2) 50% to deal double damage AND 50% to deal double damage = 50% chance to deal double damage, rolled twice; DPS multiplier = 200%, spike (max) multi = 400%

Damage probability square:
1.0 2.0
2.0 4.0
9.0/4=2.25

Not only is this a significant DPS difference, but the spike difference would be a huge factor for status effects (okay, not poison, but freeze/shock/burn/bleed), as well as peak reflected damage.

From my understanding, it should work as #2, as that is how I remember hearing Weight of the Empire worked back when I made a build that used it. Also, the maths pedant in me wants to read it that way. However, every build and Reddit post that I've seen says it's #1. Anyone have a definitive answer?

Something seems funky with how you've computed DPS multiplier. Not sure what kind of system of axioms causes 100% chance to deal double damage to result in a 1.5 DPS multiplier, certainly doesn't pass this caveman's sanity check --->. Similarly, second case should probably be 2.25 DPS multiplier with simple expected value method (Bayesianism?).

Anyways as to your actual question,

https://www.pathofexile.com/forum/view-thread/1480913/

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NickK_GGG wrote:

This does exactly what it says. If the threshold is met, 10% of the time, you will double the damage of your heavy strike. That, by the way, works with critical strikes. Building a critical heavy-striker? Be prepared for massive spikes in damage! Two of these doubles the chance (as opposed to doubling the double-damage. Sorry guys!)

Not sure how your testing ever resulted in 400% spike multiplier with Weight of the Empire (maybe it was a limited sample size and you forgot to account for natural variance of damage ranges? Daggers in particular, I believe, tend to go something like min dmg to 3x or 4x min dmg), but these mechanics tend to work similarly. I believe Mark_GGG is also on record somewhere that chance to x stats will always stack additively unless otherwise noted (can't think of any exceptions off the top of my head, actually).

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adghar wrote:

Something seems funky with how you've computed DPS multiplier. Not sure what kind of system of axioms causes 100% chance to deal double damage to result in a 1.5 DPS multiplier, certainly doesn't pass this caveman's sanity check --->. Similarly, second case should probably be 2.25 DPS multiplier with simple expected value method (Bayesianism?).

Yes, absolutely. I wrote it just before bed, and I think that I mixed up TOTAL Shrapnel Shot damage (including the arrow) with cone-only damage (which is what I intended). Regardless, it was wrong, and is now fixed. The total DPS difference is much smaller, but the spike difference remains the same.

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adghar wrote:

Anyways as to your actual question,

https://www.pathofexile.com/forum/view-thread/1480913/

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NickK_GGG wrote:

This does exactly what it says. If the threshold is met, 10% of the time, you will double the damage of your heavy strike. That, by the way, works with critical strikes. Building a critical heavy-striker? Be prepared for massive spikes in damage! Two of these doubles the chance (as opposed to doubling the double-damage. Sorry guys!)

That makes it clear, thanks for dragging up the reference! I had only searched for Collateral Damage, which wasn't released at that time, so it hadn't popped up.

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adghar wrote:

Not sure how your testing ever resulted in 400% spike multiplier with Weight of the Empire (maybe it was a limited sample size and you forgot to account for natural variance of damage ranges? Daggers in particular, I believe, tend to go something like min dmg to 3x or 4x min dmg), but these mechanics tend to work similarly. I believe Mark_GGG is also on record somewhere that chance to x stats will always stack additively unless otherwise noted (can't think of any exceptions off the top of my head, actually).

I meant that I thought that I remembered hearing from someone that the chance for doubled damage (20% for Weight of the Empire) was rolled twice, not added. Which would, theoretically, have allowed a double-double (or 4.0 or 400%) damage modifier (albeit only in 20%*20% or 4% of cases). However, the link that you provided to Nick's quote clears it up that it's added, so it would give a 40% chance of doubling the damage, not two independent rolls for doubling.