Divines vs Infused: A Comprehensive Study

RomedyMC

Edit 5/23/14: Patch 1.1.2 has made changes to the tooltip values of Divines, reducing the bonus by .5%. (Confirmed, although whether this was a cosmetic change or a real value change is not verified.). Thanks to Ethoir for pointing this out.
Edit 5/22/14: Corrected the calculations. The entire post should now be accurate.
Edit 5/21/14: Change to the Mage stone increase to reflect in-game tests. Not yet applied to math within the cases, so cases are currently incorrect and an estimate at best.

TL;DR: It is my opinion that, when using health/magicka/stamina increase Mundus stones and with respect to total health/magicka/stamina, a player should use 2x Impenetrable and 2x Infused on their small pieces. The exception is, if a player is at the extreme upper end of total magicka (~2000) and not softcapped, then they should use 2x Impenetrable, 1x Infused, and 1x Divines for their small pieces.

Not a numbers person? Skip to the Conclusions to read the results of the math.

I know this has been discussed before in different threads, but wanted to bring it to a single location for the min/maxers out there. This will be a multi-post OP to try and keep things separated into baseline traits and special cases.

Cases to explore:
- The interaction of Mundus stone + Divines trait (Post 3)
- Subtractive nature of Divines = diminishing returns? (Post 3)
- The case of health glyphs: Is infused universally better?
- Other Mundus Stones

With regard to large pieces, my hypothesis is that Infused will universally provide more benefit than other traits. (Post 1)

With regard to small pieces, my hypothesis is that, at lower levels, Infused would give greater benefit than Divines but there exists a point at which the Infused increase is overtaken by the Divines increase. I will attempt to mathematically find this point. (Post 2)

The Mage stone does not give a universal increase to mana. A level 28 Templar received an increase of just over 7%, while a VR5 Dragonknight received slightly more than a 5% increase.

List of percentage increases for Infused and Divines traits:
Infused:
White = 8% Green = 11% Blue = 14% Purple = 17% Gold = 20%

Divines:
White = 3.5% Green = 4.5% Blue = 5.5% Purple = 6.5% Gold = 7.5%

(Source for trait percetnages)

First, we will need to separate our analysis into 2 categories: Chest, Legs, Helm, and Shield will be referred to as the "Large" category while Shoulders, Gloves, Belt, and Boots will be the "Small" category. Reason:
- Large items receive 100% glyph total
- Small items receive 40% of the glyph total

Large Pieces:Proof by induction: Given a starting point 1 and assuming a statement is true for an arbitrary x, then showing it is true for (x+1) means the statement will hold for any x in a given set.
- The starting point A level 1 cuirass with a white enchant. For simplicity, assume a player begins with 100 magicka and acquires the mundus stone The Mage. (A hypothetical to establish baseline, don't bash me for this being unrealistic.) The Mage's 5% increase would bolster magicka to 105. A Cuirass with Divines would increase magicka by 5 x .04 = .2. In order for Infused to give an equal return, a Lv1-10 glyph would need to add .2/1.08 = .19 magicka.

Conclusion: As long as the enchant provides 1 magicka it will be more efficacious than Divines.

- Arbitrary x+1: A Gold VR10 Cuirass with a gold enchant. Let's assume we have a mana pool of 2000 (Beyond softcap) and overcharge effects do not come into play. (For simplicity since the overcharge seems to be a linear percentage decrease and not an exponential decrease.) The Mage stone would increase our mana to 2100. Divines trait would increase by 100 x .08 = 8. Thus, our enchantment would need to increase magicka by 8/1.2 = 6.66 to be as effective.

Conclusion:Glyphs in the Vr3-5 range add 70 magicka, so when applied to a large gold piece the real value would be 84, an increase of 14 and well above our required 6.66 to be more effective than Divines.

The case of 1400 magicka
Mage stone increase: 1400 x .05 = 70
Increase from gold Divines trait: 70 x .075= 5.25
Minimum increase of enchant to be more effective: 5.25/1.2 = 4.375

The case of 1000 magicka
Mage stone increase:1000 x .05 = 50
Increase from gold Divines trait: 50 x .075 = 3.75
Minimum increase of enchant to be more effective: 3.75/1.2 = 3.125

Conclusion: Evidence suggests that, for large pieces, Divines should never be used as the gain from Divines is easily eclipsed by even low-level enchants. This finding supports the general consensus regarding Infused traits on large pieces.

RomedyMC

Edit 5/22/14: Updated the conclusion to be more readable and concise.
Edit 5/21/14: Updated the calculations to reflect new understanding of how the Mage stone influences magicka and how the Divines trait interacts with the Mage stone.

- The starting point A white level 1 belt with a white enchant. For simplicity, assume a player begins with 100 magicka and acquires the mundus stone The Mage. (A hypothetical to establish baseline, don't bash me for this being unrealistic.) The Mage's 5% increase would bolster magicka to 105. A belt with Divines would increase magicka by 5 x .04 = .2. In order for Infused to give an equal return, a Lv1-10 glyph would need to increase its base value by (.2/1.08) x 2.5 = .46 magicka.

Conclusion: Again, the glyph would only need to be increased by 1 to be more efficacious than Divines.

- Arbitrary x+1: Gold belt w/ Gold enchant and 2000 magicka
Again, ignoring softcaps and overcharged penalties,
- Mage stone increase: 2000 x .05 = 100
- Increase from gold Divines trait: 100 x .08 = 8
- Minimum increase of a glyph to be more effective: ( 8 / 1.2 ) x 2.5 = 16.67

The case of 1400 magicka
Mage stone increase: 1400 x .05 = 70
Increase from gold Divines trait: 70 x .08 = 5.6
Minimum increase of a glyph to be more effective: ( 5.6 / 1.2 ) x 2.5 = 11.67

The case of 1000 magicka
Mage stone increase:1000 x .05 = 50
Increase from gold Divines trait: 50 x .08 = 4
Minimum increase of a glyph to be more effective: ( 4 / 1.2 ) x 2.5 = 8.33

Conclusion: The revised numbers suggest that, for stones that behave like the Mage stone, using the Infused trait on small pieces is actually more efficacious than the Divines trait since the base values of many glyphs will provide a larger increase when paired with Infused than the increase from Divines.

It appears the choice of Infused or Divines is logically based off of your total magicka. It is easier for an infused trait on a small piece to overcome the increase from a Divines trait with respect to a small magicka pool. However, at the extreme upper end of magicka, the increase from Divines and Infused may be similar.

However, the subtractive nature of the Divines trait means that, at the extreme upper end of magicka (~2000), using Divines on a single piece will provide great benefit, but stacking Divines pieces will result in diminished returns.

RomedyMC

Edit 5/21/14: Cleaned up the post to make it more readable.

The Interaction of the Mage stone and Divines trait

Schnoffle pointed out that this interaction may not be as simple as I thought it to be. So I took my 28 Templar to find out. I crafted a green divines chest and a green divines shoulder.

Test #1
I started out by stripping my character of all gear and gaining a different mundus effect. (The Tower.) Without any enhancements my magicka pool was 790.

Verifying the increase of the Mage stone
If the mage stone adds 5% mana, I should jump to 829.5 by activating it, a difference of 39.5. Actual activation boosted my mana to 846, a difference of 56 and an actual change of 7%, suggesting mundus stone gains are not linear.

How Divines trait interacts with the mage stone
A green Divines trait adds 5% to the mundus effect. Predicted change of adding a Divines piece w/o enchantment will add 2.8 magicka. Adding a second piece should increase magicka by ( 56 + 2.8 ) x .05 = 2.91
- Real addition of a Divines piece moved magicka from 846 to 848. (expected 2.8 )
- Real addition of a second Divines piece moved magicka from 848 to 851 (expected 5.71 )
- Real addition of a third Divines piece moved magicka from 851 to 853 (expected 8.7955 )

This pattern follows neither the additive or multiplicative models. Additive would keep each piece separate, or adding 2.8 for each piece of Divines gear added. This would mean for three pieces, 2.8 + 2.8 + 2.8 = 8.4, which is more than the real 7 point gain. A multiplicative model would keep the gain of 2.8 for the first piece, but would then have ( 56 + 2.8 ) x .05 = 2.94 for the second trait and 3.087 for the third. So, there appears to be a slight exponential effect dragging the returns downward.

Test #2
I took my VR5 Dragonknight out to the mage stone to test magicka gain for a different class / level. Starting magicka was 1465. The previous 7% increase should result in a gain of 102.55 magicka. Actual magicka gain upon activation of the stone was to 1544, a change of 79 which is slightly more than 5%, lending further evidence that mundus stone gain is not linear.

Addition of Divines pieces
- 1 piece Divines brought magicka to 1547
- 2 piece Divines brought magicka to 1552

At this point, I noticed the same trend as above: the second and third pieces were not yielding a return as nicely as the first piece, which is in line with my previous test.

Hypothesis: The return from Divines pieces is subtractive.
- In our first trial, the first addition of a Divines piece yielded 56 x .04 = 2.8, with rounding down, as our expected and experienced return. The second increase, from 848 to 851, followed the pattern with rounding down, but the third addition yielded a result less than our expected return.

What happens if Divines works on Mundus increase minus any previous increase? Then our second addition would be ( 56 - 2.8 ) x .04 = 2.66. Our total gain is then 2.8 + 2.66 = 5.46, consistent with our rounding down experience so far. The third addition is then ( 56 - 2.8 - 2.66 ) x .05 = 2.527. Total change is thus 7.987, in line with our experienced results and rounding down.

Conclusion: The effect of the Divines trait appears to be subtractive, meaning that multiple pieces of Divines have reduced benefit. The formula seems to be something like (Mundus Effect - previous gains from Divines trait) x current Divines addition.

RomedyMC

Edit 5/23/14: The Thief is supposed to work as intended now, so a discussion can begin on how this stone behaves. I have added my initial thoughts and a plan for future research.

The Thief: Is Divines really better for stats that cannot be directly increased through enchantment?

Starting point: I first need to understand what influences the crit statistic.
- Passives?
- Total stamina?
- Weapon trait?

Starting point: My main character is a VR6 Dragonknight fully specced for tanking. Using "C" my physical and spell crit sit at 0% suggesting that, for DKs, no crit is gained from total magicka or stamina. I will investigate using the Thief stone with this DK and see the effects of Divines pieces upon the Thief and how the Theif affects my 0% crit.

Future: The Thief and my Lv28 Templar

Mansome

Can we get a TLDR version? Don't get me wrong this is good stuff, I am just not a numbers person.

Schnoffle

Maybe I don't understand divines as well, but it was my assumption that a divines increasing a mundus stone affect by 4% would only in theory increase the mundus stone bonus. ie in your example a 4% mundus stone boost would in theory increase your 5% mage stone boost by 4%*5% granting 5.2% total bonus from the mundus stone. It would not take the 105 magicka and then add 4% of that total (ie your calculation would give ~109 rather then 105.2 that I am getting. Maybe I am reading things wrong.

Maverick827

Someone took intro to discrete math and wants everyone to know about it.

RomedyMC

Maverick827 wrote: »

Someone took intro to discrete math and wants everyone to know about it.

Thanks for your judgement and uber-helpful addition to our thread!

Schnoffle wrote: »

Maybe I don't understand divines as well, but it was my assumption that a divines increasing a mundus stone affect by 4% would only in theory increase the mundus stone bonus. ie in your example a 4% mundus stone boost would in theory increase your 5% mage stone boost by 4%*5% granting 5.2% total bonus from the mundus stone. It would not take the 105 magicka and then add 4% of that total (ie your calculation would give ~109 rather then 105.2 that I am getting. Maybe I am reading things wrong.

Excellent and testable! I'll get back to you.

Edit 5/21/14: @Schnoffle - You were correct. I intended to work from only the mundus addition, but in fact worked from the entire magicka pool. Simple error! I'll be going back and editing the OP to correct for this oversight. Thank you so much for catching it!

RomedyMC

Mansome wrote: »

Can we get a TLDR version? Don't get me wrong this is good stuff, I am just not a numbers person.

See the conclusions for TL;DR as they are a good recap.

Natjur

I have divine trait on all my 'lesser' armor slots (belt, boots, solders & gloves) but I do it cause I like using the mundus that have stats that can not be increased any other way (The Shadow-critical strike damage, The Ritual-Increases healing effectiveness or The Steed-Increases run speed)

On the 'greater' armor slots, I still use Infused, but I would love the answer to the old
Infused vs Divine question (as they are the other traits that seem worth it)

Did you log out and back in after each 'test'. I found the mundus stones do not update currently when you change armor until you log out and back in. (same bug that the vampire stages has, the passives don't refresh correctly)

Halrloprillalar

Has anyone figured out the math for the Shadow stone?

phaneub17_ESO

The Atronach Stone (Magicka Recovery) seems to take into account the item material / level of the item being used in addition to Divines. I too use Divines on all the 4 smaller pieces while using Infused on the 3 or 4 larger items. I did at one point use 7 items with all 7% Divines, but there appears to be a cap to how far they will increase an effect. After the 5th piece the effect no longer gave any additional magicka recovery from Atronach Stone making it worthless beyond 4 items with Divines; however, that was at a lower level. At this point going 4 and 4 is a better off balance, I would like to know though just how far it goes.

It would be nice if they would show Base effect + Bonus from Standing Stone and Divines improvement as separate numbers, especially a few unique ones like Ritual Stone which only affects healing.

killedbyping

Why in the world would you use worthless stamina\health\magicka Mundus stones, which give really insulting ammount of bonus instead of regen\damage\crit stones ?

phaneub17_ESO

killedbyping wrote: »

Why in the world would you use worthless stamina\health\magicka Mundus stones, which give really insulting ammount of bonus instead of regen\damage\crit stones ?

This gives a more concrete number of increase from Divines to calculate the effect when there's a larger pool of increase to measure.

RomedyMC

killedbyping wrote: »

Why in the world would you use worthless stamina\health\magicka Mundus stones, which give really insulting ammount of bonus instead of regen\damage\crit stones ?

I thought the easiest stones to figure out would be the increase to health/magicka/stamina stones since the calculations are straightforward and can be understood by pretty much anyone.

In addition, there is good evidence that the Thief (crit) stone is currently broken and adds nothing. A little tinkering with my rings has put my VR5 DK over the softcap for all regen stats, making that stone basically useless.

Believe it or not, I do not have a DPS spec on my tanky DK (Primary 1h/shield, Secondary resto staff) so I am disinclined to use the weapon damage stone since that addition will not help me keep multiple mobs on me / CC'd like an increase to mana pool would be.

Keep in mind my goal is to understand how the stones function and how to gear a character with respect to armor traits. That means the scenarios are not always "real" or feasible.

RomedyMC

Natjur wrote: »

Did you log out and back in after each 'test'. I found the mundus stones do not update currently when you change armor until you log out and back in. (same bug that the vampire stages has, the passives don't refresh correctly)

I did not, although I was able to see increases when changing gear that were in-line with the expected values. Further, I transitioned between the Tower and the Mage a couple times to ensure the changes were consistent between magicka and stamina and found that they were.

My experience is that the mundus passives are working as intended and do not require a relog. I will happily test it this afternoon but feel certain of the outcome.

Xnemesis

So why not go with infused on your pieces that gain 100% of your glyph and divines on the others. This is ideal for the min maxer. Also seems stacking your attributes into health until overcharged is the way to go and then use glyphs to reach either max stam or magika. I only recommend the attribute stacking after vet 10 and only redo your attributes after you redo all of your skillpoints so that you can take into account your passives. When you have all your skill points allocated and your hotbar laid out go ahead and start putting in attribute points till you hit cap in health or until you are at what you feel is a proper amount of health.

Also keep in mind I do not believe their is a softcap on weapon or spell crit

RomedyMC

Xnemesis wrote: »

So why not go with infused on your pieces that gain 100% of your glyph and divines on the others. This is ideal for the min maxer.

What I have found suggests this is actually not the ideal case for the min/maxer. In fact, when paired with Mundus stones that raise health, magicka, and stamina, it appears you should never have Divines at high levels.

RomedyMC

I have edited the second and third posts to reflect information gained on 5/20 regarding the increase provided by the Mage stone and the subtractive nature of multiple Divines pieces.

Xnemesis

RomedyMC wrote: »

Xnemesis wrote: »

So why not go with infused on your pieces that gain 100% of your glyph and divines on the others. This is ideal for the min maxer.

What I have found suggests this is actually not the ideal case for the min/maxer. In fact, when paired with Mundus stones that raise health, magicka, and stamina, it appears you should never have Divines at high levels.

Ahh good to know I will have to do some more tinkering then.

Xnemesis

Xnemesis wrote: »

RomedyMC wrote: »

Xnemesis wrote: »

So why not go with infused on your pieces that gain 100% of your glyph and divines on the others. This is ideal for the min maxer.

What I have found suggests this is actually not the ideal case for the min/maxer. In fact, when paired with Mundus stones that raise health, magicka, and stamina, it appears you should never have Divines at high levels.

Ahh good to know I will have to do some more tinkering then.

Well on second thought maybe divines is still ok on my lesser pieces because I am using only the increase to crit damage. Has the crit damage and crit chance stones been tested and is this a loss in dps/heals compared to an infused build that increases magika or stam?

RomedyMC

Xnemesis wrote: »

Well on second thought maybe divines is still ok on my lesser pieces because I am using only the increase to crit damage. Has the crit damage and crit chance stones been tested and is this a loss in dps/heals compared to an infused build that increases magika or stam?

I have not yet looked at those stones. I am just beginning to understand how the increase to health/magicka/stamina stones work and those softcap values are readily available.

It would be logical to assume the subtractive nature of Divines would apply to other stones as well, but I have no evidence to back it.

What we would also want to consider is the effect of total magicka on spell crit / total stamina on physical crit. I have absolutely no idea how those interact, although that would be my starting point for looking into what you ask.

NerfEverything

Thanks for doing the math on this. I think most of us have been disappointed with the benefit of divines on our small pieces. Based on what the tooltips tell us, divines on small pieces and infused on large pieces makes the most sense. Although in practice, we have seen this is not the case.

We already know a bunch of the mundus stones are completely broken. I can't help but wonder if there is an underlying issue with all mundus stones, because the subtractive effect of stacking divines is certainly not intended, since it renders that trait almost completely useless, but it hasn't even been recognized as a bug by the devs.

RomedyMC

NerfEverything wrote: »

We already know a bunch of the mundus stones are completely broken. I can't help but wonder if there is an underlying issue with all mundus stones, because the subtractive effect of stacking divines is certainly not intended, since it renders that trait almost completely useless, but it hasn't even been recognized as a bug by the devs.

With everything else on their plate it is entirely possible that this has not been on their radar. I cannot fault them for focusing on botting, bugs, and Craglorn. Perhaps the stones will find a seat along with guild store search updates as Tier 2 projects.

I would point out that the subtractive effect of stacking Divines may certainly be intended, but I am unable to form a cogent statement as to why in the world that would be the case. Diversity of traiting, and reasons and so forth....

NerfEverything

RomedyMC wrote: »

NerfEverything wrote: »

I would point out that the subtractive effect of stacking Divines may certainly be intended, but I am unable to form a cogent statement as to why in the world that would be the case. Diversity of traiting, and reasons and so forth....

It is quite possible that at some point in the design process they decided that having a full or half set of divines gear would be too OP since you can change your mundus so easily. Unfortunately, it seems like the whole trait system was never really polished, since infused is the best choice 99% of the time.

Xnemesis

Wish someone would develop a spreadsheet that calculates all the stats from stones, passives, passives from abilities slotted, traits, and gear. It will take time but I am sure its in the works for those serious number crunchers. Also aren't all the variables and way things are calculated in the coding somewhere? Or is all that coding kept Server side?

Dorgon

A very nice read.

RomedyMC

Edited the first two posts to be mathematically accurate. The conclusions are updated, and I added a TL;DR to the top of the first post with my opinion.

Ethoir

The tooltips for a number of traits were changed, presumably either a nerf to their effectiveness or more likely because the tooltips for the affected traits were displaying incorrect values.

These are the values before and after the 1.1.2 patch for Divines. Values are up to blue quality (I don't have enough mats to go to purple let alone Yellow/Gold. So I'm guessing their values above blue quality).

Divines Before: W 4 - G 5 - B 6 - P 7 - Y 8
Divines After: W 3.5 - G 4.5 - B 5.5 - P 6.5 - Y 7.5

A loss of 0.5% at each quality level has been observed. Infused looks unchanged. Well-fitted got affected by the updates to the tooltips as well, but that's a completely different topic and someone else can start a thread about that.

RomedyMC

Ethoir wrote: »

The tooltips for a number of traits were changed, presumably either a nerf to their effectiveness or more likely because the tooltips for the affected traits were displaying incorrect values.

These are the values before and after the 1.1.2 patch for Divines. Values are up to blue quality (I don't have enough mats to go to purple let alone Yellow/Gold. So I'm guessing their values above blue quality).

Divines Before: W 4 - G 5 - B 6 - P 7 - Y 8
Divines After: W 3.5 - G 4.5 - B 5.5 - P 6.5 - Y 7.5

A loss of 0.5% at each quality level has been observed. Infused looks unchanged. Well-fitted got affected by the updates to the tooltips as well, but that's a completely different topic and someone else can start a thread about that.

Thank you for this info. I'll verify and update when I get home this evening. That is not good news for Divines unless the math has changed in some way as a decrease to Divines just means we'll be seeing more Infused pieces. It's probably worth revisiting the stacking equation now as well.

Ethoir

RomedyMC wrote: »

Thank you for this info. I'll verify and update when I get home this evening. That is not good news for Divines unless the math has changed in some way as a decrease to Divines just means we'll be seeing more Infused pieces. It's probably worth revisiting the stacking equation now as well.

Do keep in mind that while I think its a nerf, the patch notes say this:

•Addressed minor text issues in trait tooltips on clothing stations.

So chances are the tooltips we saw gave us wrong information about what the trait did prior to the patch. Will keep an eye on this to see if they nerfed it or if the tooltips were indeed incorrect before.