PSA: Altmer "Spell Recharge" passive is providing less mitigation than intended

TheYKcid

Edit: discrepancy seems to be caused by a different bug, unrelated to Spell Recharge (detailed further down in the thread). Vulnerabilities (eg. Shock elemental status effect, Vampirism fire weakness, etc.) are being factored as additive bonuses, when they should instead be multiplicative ones.

Original post is archived below in the spoiler.

From my tests, it only provided a 4.1 to 4.3% mitigation value, as opposed to the 5% stated by the tooltip.

Before anyone interjects—I am aware that %-mitigation "stacks diminishingly" when calculated from a baseline of zero mitigation. However, my conducted tests compared damage taken before & after activating the passive as the only variable, in which case the incoming damage should have been reduced to a flat 0.95x as % sources are calculated multiplicatively. I also tested in a no-CP environment with no other % sources.

So please be aware the passive is not performing as advertised, and pressure ZOS to implement a timely fix.

More details in the bug report thread I submitted earlier: https://forums.elderscrollsonline.com/en/discussion/461466/altmer-spell-recharge-passive-is-calculating-wrongly-providing-less-mitigation-than-intended/p1

starkerealm

TheYKcid wrote: »

Before anyone interjects—I am aware that %-mitigation "stacks diminishingly" when calculated from a baseline of zero mitigation.

You tested this while naked?

You're sure this isn't a specific case anomaly, like how Akaviri Dragonguard and Powerstone result in a 27% discount, instead of 30%?

TheYKcid

starkerealm wrote: »

TheYKcid wrote: »

Before anyone interjects—I am aware that %-mitigation "stacks diminishingly" when calculated from a baseline of zero mitigation.

You tested this while naked?

You're sure this isn't a specific case anomaly, like how Akaviri Dragonguard and Powerstone result in a 27% discount, instead of 30%?

@starkerealm naked as far as the mechanic is question was concerned, yes.

The no-CP test had no other %-based mitigation sources involved, as I don't slot any in my build.

starkerealm

TheYKcid wrote: »

@starkerealm naked as far as the mechanic is question was concerned, yes.

@TheYKcid, so you're still wearing armor?

TheYKcid

@starkerealm yes, but to reiterate—nothing that had any implications for the test variable. Resistances and %-mitigation are completely separate terms within the damage equation. It's not analogous to Dragonguard/Powerstone since those two are both the same category (% ult cost redux).

In any case, I will run another test now whilst absolutely naked just to be sure, gimme a few mins.

Ajax_22

TheYKcid wrote: »

@starkerealm yes, but to reiterate—nothing that had any implications for the test variable. Resistances and %-mitigation are completely separate terms within the damage equation. It's not analogous to Dragonguard/Powerstone since those two are both the same category (% ult cost redux).

In any case, I will run another test now whilst absolutely naked just to be sure, gimme a few mins.

Numerical resistance is calculated within the same formula. No percent based mitigation in the game will give you the full value unless under special circumstances.

TheYKcid

Now that I think about it, is the Dragonguard + Powerstone interaction even an anomaly?

0.85*0.85 = 0.7225, rounded up to .73 which is exactly a 27% cost reduction.

This is assuming the rule for ult cost reduction is typically multiplicative, though IDK if that's the case for ult cost redux specifically.

starkerealm

TheYKcid wrote: »

@starkerealm yes, but to reiterate—nothing that had any implications for the test variable. Resistances and %-mitigation are completely separate terms within the damage equation.

Resistances are another source of % mitigation. It gets added in with the slurry of other stats. If you're running around 20% mitigation from that (figure roughly 14k phys/spell resist), you'll only see a 4% buff from the high elf passive. Also keep an eye out for Major Ward/Resolve, because that will further boost your resists, nibbling away at the HE passive.

TheYKcid wrote: »

It's not analogous to Dragonguard/Powerstone since those two are both the same category (% ult cost redux).

No, they're straight up derped. They should be additive. They are, but 3% falls off the back of a truck somewhere.

TheYKcid wrote: »

In any case, I will run another test now whilst absolutely naked just to be sure, gimme a few mins.

TheYKcid

Ajax_22 wrote: »

TheYKcid wrote: »

@starkerealm yes, but to reiterate—nothing that had any implications for the test variable. Resistances and %-mitigation are completely separate terms within the damage equation. It's not analogous to Dragonguard/Powerstone since those two are both the same category (% ult cost redux).

In any case, I will run another test now whilst absolutely naked just to be sure, gimme a few mins.

Numerical resistance is calculated within the same formula. No percent based mitigation in the game will give you the full value unless under special circumstances.

@Ajax_22 This is exactly what I alluded to in my second paragraph.

%-mit sources stack diminishingly with one another IF you take zero mitigation as your baseline.

In this comparison, on the other hand, it was purely a before/after comparison with and without the proc, in which the multiplicative nature of the equation results in an exact 5% reduction. Note that this is relative to the counterfactual (i.e without Spell Recharge), as opposed to relative to no mitigation.

Test it with minor protection if you're dubious. The damage you take after applying it will be exactly 8% less than the damage prior, all other things being equal.

TheYKcid

Resistances have no bearing on %-based mitigation when you're dealing with proportions, as opposed to absolute numbers.

starkerealm

TheYKcid wrote: »

Now that I think about it, is the Dragonguard + Powerstone interaction even an anomaly?

0.85*0.85 = 0.7225, rounded up to .73 which is exactly a 27% cost reduction.

This is assuming the rule for ult cost reduction is typically multiplicative, though IDK if that's the case for ult cost redux specifically.

Yeah, it is. If it was applying multiplicative, it'd be a 28% discount. I've sat their and crunched the numbers before. ALso, if that were the case, other ult discount effects would behave the same, they do not. Add in an Imperial for a 3% discount, and it goes exactly to 30%.

starkerealm

TheYKcid wrote: »

Resistances have no bearing on %-based mitigation when you're dealing with proportions, as opposed to absolute numbers.

Yeah, they do. Resistances generate a single % based mitigation value.

TheYKcid

starkerealm wrote: »

TheYKcid wrote: »

Resistances have no bearing on %-based mitigation when you're dealing with proportions, as opposed to absolute numbers.

Yeah, they do. Resistances generate a single % based mitigation value.

Which still has no effect on the final, proportionate change.

Eg. When taking a 100 damage attack:

50% resistances, 0% %-based mit = 50 damage taken
+ 20% %-based mit,
50*.8 = 40 damage taken (flat 20% damage reduction relative to counterfactual)

vs.

0% resistances, 0% %-based mit = 100 damage taken
+ 20% %-based mit,
100*.8 = 80 damage taken (flat 20% damage reduction relative to counterfactual)

While resistances affect the absolute value of damage taken in conjunction with %-mit, they have no effect on the proportionate change upon adding said %-mit, because all terms interact multiplicatively.

Slotting 5 %-based mitigation will ALWAYS reduce your final damage taken by 5% compared to not slotting it, assuming it's computed correctly.

TheYKcid

Aaaanyway.

Tested in no-CP. Zero gear, zero resistances. Zero %-based mitigation sources aside from Spell Recharge, when procced.

466 damage before, 446 after, 4.3% reduction.

It is not calculating correctly.

starkerealm

TheYKcid wrote: »

Slotting 5 %-based mitigation will ALWAYS reduce your final damage taken by 5% compared to not slotting it, assuming it's computed correctly.

I'll let Paul explain:

paulsimonps wrote: »

Now lets talk numbers. The way that mitigation is calculated is as following:

MITIGATION=100-(100*(1-((Resistance/660)/100))*(1-(Mitigation #1)/100)*(1-(Mitigation #2)/100)*(1-(Mitigation #3)/100))*etc etc)

DAMAGE TAKEN=Base Damage*(1-((Resistance/660)/100))*(1-(Mitigation #1)/100)*(1-(Mitigation #2)/100)*(1-(Mitigation #3)/100))*etc etc

So, if you have any flat resistances, those will be calculated, at a rate of 1% per 660, into your resist pool. This will reduce your damage taken, and will also reduce the gross effect of each % mitigation modifier in the stack.

TheYKcid

starkerealm wrote: »

TheYKcid wrote: »

Slotting 5 %-based mitigation will ALWAYS reduce your final damage taken by 5% compared to not slotting it, assuming it's computed correctly.

This will reduce your damage taken, and will also reduce the gross effect of each % mitigation modifier in the stack.

Yes, relative to zero, but not relative to the counterfactual. A lot of people get confused between the two. Both methods of calculating resistances are equally valid. I'm well aware of how resistances are factored (if you view my sig you'll see I even made an entire calculator about it).

Either way, the case has already been settled, as I retested with zero resistances and got the same result.

starkerealm

TheYKcid wrote: »

Aaaanyway.

Tested in no-CP. Zero gear, zero resistances. Zero %-based mitigation sources aside from Spell Recharge, when procced.

466 damage before, 446 after, 4.3% reduction.

It is not calculating correctly.

4.3% reduction means you have 14% mitigation before it applies, meaning the resists showing up on your character sheet are ~9,240. So 7 pieces of light armor, maybe?

That's where you're losing mitigation.

TheYKcid

Please re-read my post. I re-tested with zero external mitigation.

Also, you are still continuing to calculate with respect to zero mitigation, not the counterfactual. Not that it matters at this point.

starkerealm

TheYKcid wrote: »

Both methods of calculating resistances are equally valid.

Objectively, no. If you have two different methodologies that result in different data, only one of them can be correct. I mean, we're talking about stuff that is, literally, being passed through a calculation by a computer. One formula is correct. The computer doesn't pick off the menu depending on its whims.

starkerealm

TheYKcid wrote: »

Please re-read my post. I re-tested with zero external mitigation.

Also, you are still continuing to calculate with respect to zero mitigation, not the counterfactual. Not that it matters at this point.

It's a controlled environment, you can eliminate unwanted variables. You can test with no mitigation of any kind.

TheYKcid

Sigh.

You are not wrong, but you're also missing the point entirely

TheYKcid wrote: »

Eg. When taking a 100 damage attack:

50% resistances, 0% %-based mit = 50 damage taken
+ 20% %-based mit,
50*.8 = 40 damage taken (flat 20% damage reduction relative to counterfactual)

vs.

0% resistances, 0% %-based mit = 100 damage taken
+ 20% %-based mit,
100*.8 = 80 damage taken (flat 20% damage reduction relative to counterfactual)

The amount of damage taken in case 1 was 40 in absolute terms, and 80 in case two (a loss of 50%). This is the dimishment caused by resistances that you refer to, and objectively you are correct.

However, if you compare within each case, slotting the 20% mitigation always resulted in a 20% proportionate reduction relative to the counterfactual within the same case (50 > 40, 100 > 80).

So both are correct and occur simultaneously—you're just trying to interpreting data presented for one case through the perspective of the other.

In any case—and repeating for the third time—I REPEATED THE TEST WITH ZERO MITIGATION AND ZERO RESISTANCES—so the principle of diminishing stacking doesn't even apply anymore.

TheYKcid

starkerealm wrote: »

It's a controlled environment, you can eliminate unwanted variables. You can test with no mitigation of any kind.

Um yes that's precisely what I did.

Reorx_Holybeard

I've found in testing that there are some effects (name Vulnerability debuffs) that stack mitigation additively but unless you're dealing with that or some other unknown issue then mitigation should indeed be multiplicative.

What attack/NPC and where are you testing this? Did some quick tests on PTS templates in Eastmarch with Bears and found inconsistent results based on the attack used so you may be seeing a similar effect.

Naked

1. Swipe: 1901-1909 before, 1783-1876 after (2 - 5.4% ? )
2. Crushing Swipe: 3601 before, 3421 after (5%)
3. Savage Blows 1: 2345 before, 2228 after (5%)
4. Savage Blows 2: 2157 before, 2157 after (?)

With 17252 Physical/Spell Resist (74%)

1. Swipe: 1388-1407 before, 1337 after (4% ? )
2. Crushing Swipe: 2665 before, 2532 after (5%)
3. Savage Blows 1: 1736 before, 1649 after (5%)
4. Savage Blows 2: 1596 before, 1596 after (?)

I've seen this in other tests with other mob abilities not being affected by certain mitigation buffs (like Major Protection) for no obvious reasons. Try with a few different NPCs and attacks and see if you get the same results.

TheYKcid

@Reorx_Holybeard

All vulnerabilities are additive with each other—and this summated modifier is then applied multiplicatively to incoming damage. This is intended and always worked that way, so that's another story.

Interesting point about different NPCs being affected differently, though. It might explain why my results fluctuate by a few decimals even under the same conditions (but different NPCs). I'll test further.

starkerealm

TheYKcid wrote: »

In any case—and repeating for the third time—I REPEATED THE TEST WITH ZERO MITIGATION AND ZERO RESISTANCES—so the principle of diminishing stacking doesn't even apply anymore.

At which point, the next step becomes, testing it under known variables in other situations. Also, I'd strongly recommend testing this on a PTS template, rather than a live character, as existing characters can, sometimes, pick up difficult to detect buffs that shouldn't be there.

TheYKcid

@Reorx_Holybeard

You were right! Different NPCs interact with %-mit differently!

I used minor protection as a control. In some cases, both performed correctly at 5 & 8% respectively. But against NPCs for which Spell Recharge was under-calculating, Minor Prot also under-calculated by an identical proportion!

Nice find. Looks like this is a bug with specific NPCs, not Spell Recharge.

Going to have to test this against players too. Lots of people have been complaining that damage seems way higher after the update 21 patch, and I wonder if this is related.

starkerealm

@Reorx_Holybeard, I wonder if this is damage type related. Some enemies are specifically flagged to bypass resistance, and of course bleed DoTs can't be mitigated at all, which could lead to odd results.

Minno

starkerealm wrote: »

@Reorx_Holybeard, I wonder if this is damage type related. Some enemies are specifically flagged to bypass resistance, and of course bleed DoTs can't be mitigated at all, which could lead to odd results.

percentage based reduces bleeds but the question is still a valid one to ask.

TheYKcid

So I just tested and %-based mitigation is functioning fine vs. players (5% & 8% on Spell Recharge and Minor Prot respectively, tested naked).

Seems like it's an issue with specific NPCs then.

Minno

TheYKcid wrote: »

@Reorx_Holybeard

You were right! Different NPCs interact with %-mit differently!

I used minor protection as a control. In some cases, both performed correctly at 5 & 8% respectively. But against NPCs for which Spell Recharge was under-calculating, Minor Prot also under-calculated by an identical proportion!

Nice find. Looks like this is a bug with specific NPCs, not Spell Recharge.

Going to have to test this against players too. Lots of people have been complaining that damage seems way higher after the update 21 patch, and I wonder if this is related.

Alot of players were reporting heavy dmg, but not accounting for crits with the shadow/kitty changes. Ive found that the dmg people were taking, specifically from nightblades, were from 103% CHD modifer builds against a 3000 crit resistance value. Everyone said they were taking 10-15k incaps, and that is exactly the range of dmg incap is doing on paper with a 1.58 modifier after being reduced by 3k with 16k-18k resistance after 10k penetration.

TheYKcid

Minno wrote: »

TheYKcid wrote: »

@Reorx_Holybeard

You were right! Different NPCs interact with %-mit differently!

I used minor protection as a control. In some cases, both performed correctly at 5 & 8% respectively. But against NPCs for which Spell Recharge was under-calculating, Minor Prot also under-calculated by an identical proportion!

Nice find. Looks like this is a bug with specific NPCs, not Spell Recharge.

Going to have to test this against players too. Lots of people have been complaining that damage seems way higher after the update 21 patch, and I wonder if this is related.

Alot of players were reporting heavy dmg, but not accounting for crits with the shadow/kitty changes. Ive found that the dmg people were taking, specifically from nightblades, were from 103% CHD modifer builds against a 3000 crit resistance value. Everyone said they were taking 10-15k incaps, and that is exactly the range of dmg incap is doing on paper with a 1.58 modifier after being reduced by 3k with 16k-18k resistance after 10k penetration.

Yeah it might be that along with Khajiit, frankly. And possibly a few ticks of the newly god-tier siege that they may not have noticed.

Anyway, with regard to:

Minno wrote: »

starkerealm wrote: »

@Reorx_Holybeard, I wonder if this is damage type related. Some enemies are specifically flagged to bypass resistance, and of course bleed DoTs can't be mitigated at all, which could lead to odd results.

percentage based reduces bleeds but the question is still a valid one to ask.

...it still wouldn't affect the before/after delta of Spell Recharge or Minor Prot. The absolute numbers would be different, but the percentage change would be identical—and this was the metric Reorx and I were testing.

So the issue must stem from elsewhere, but it certainly seems to be NPC-specific.