Introduction to PvE damage calculation (Horns of the Reach)
This topic by Asayre contains 469 posts by 68 members, and was last updated by EnormousRainbow, 4 days, 16 hours ago.

Hi Asayre , i’m wondering that what will happen when i use pet build? i mean if i use necro or bsw; one or two pets etc. i and my friends are following with interest and we wondered that.

@Nstunner, could you elaborate more on your question?
This were my previous estimates for a pet rotation, if it answers your question

Asayre said on March 27, 2017 :
@Leomed47, with 5 BSW, 2 Ilambris, 4 Moondancer with VMA inferno backbar I previously estimated a mean DPS of 42082 switching to a lightning staff on the front bar drops the mean DPS to 41993. So this is in accordance to your observation of comparable damage. With regard to your possible explanations I lean towards 3. For a single target, I usually estimate Direct Damage to be ~60% and AoE to be ~40%. Lightning staff LAs do not proc concussion so concussion uptimes for both setups are comparable namely 45% (Inferno) and 47% (Lightning). The difference being negligible given a standard deviation of 12%. I don’t feel there is a difference in LA weaving with a lightning and inferno staff. However, some people prefer medium weaving with an inferno staff and I don’t have a way to simulate that yet. Additionally, there is a antisweet spot when you weave heavy inferno attacks where you can get the animation of a heavy attack (2 fireballs) but it does no damage.
Medium weaving is not an option to go with this patch since it consumes off balance
But I’m more leaning towards what @Leomed47 saying, even with Inferno staffs my single target dmg from AOE abilities tend to be around 4950%. And since Sorc’s AOE abilities are considered dots they gets the boost from the 75 points in Thamuaturge. Here is a parse using Lighting/Inferno overall I think 53% from AOE abilities
Spoiler:
Can you compare the BSW double Inferno simulation as Dunmer with Necro Lightning/Inferno as Altmer? Considering both running Pet and Daedric Prey. I might be mistaken but I really noticed single target DPS jump when I switched over to Necro, Lightning staff main bar and Altmer.
Keep up the great work man!
 This reply was modified 7 months, 1 week ago by YoloWizard.

YoloWizard said on April 16, 2017 :
Asayre said on March 27, 2017 :
@Leomed47, with 5 BSW, 2 Ilambris, 4 Moondancer with VMA inferno backbar I previously estimated a mean DPS of 42082 switching to a lightning staff on the front bar drops the mean DPS to 41993. So this is in accordance to your observation of comparable damage. With regard to your possible explanations I lean towards 3. For a single target, I usually estimate Direct Damage to be ~60% and AoE to be ~40%. Lightning staff LAs do not proc concussion so concussion uptimes for both setups are comparable namely 45% (Inferno) and 47% (Lightning). The difference being negligible given a standard deviation of 12%. I don’t feel there is a difference in LA weaving with a lightning and inferno staff. However, some people prefer medium weaving with an inferno staff and I don’t have a way to simulate that yet. Additionally, there is a antisweet spot when you weave heavy inferno attacks where you can get the animation of a heavy attack (2 fireballs) but it does no damage.
Medium weaving is not an option to go with this patch since it consumes off balance
But I’m more leaning towards what @Leomed47 saying, even with Inferno staffs my single target dmg from AOE abilities tend to be around 4950%. And since Sorc’s AOE abilities are considered dots they gets the boost from the 75 points in Thamuaturge. Here is a parse using Lighting/Inferno overall I think 53% from AOE abilities
Can you compare the BSW double Inferno simulation as Dunmer with Necro Lightning/Inferno as Altmer? Considering both running Pet and Daedric Prey. I might be mistaken but I really noticed single target DPS jump when I switched over to Necro, Lightning staff main bar and Altmer.
Keep up the great work man!
That DPS doe

@Asayre , i mean i wondered what is Pet’s contribution to Dps? What is Dps with Pet and without Pet, with necro and with bsw etc.
Yes, your shared table was my seeked answer Can we say that the result is “the maximum known Dps that Sorcerer can make is 43.768″?
 This reply was modified 7 months, 1 week ago by NStunner.

@YoloWizard, from what I’ve been testing, considering the few times I’ve seen @Nosferatuzod test and also taking into account what @Asayre has stated in a few posts throughout this thread, it looks like BSW gives the best single target dps when compared to Necro, this is while using Daedric Prey, however this comes from a *perfect* simulation in which all light attacks are hitting. T
he difference compared to Necro in single target is neglectable imo, 43768 average dps on skele vs 43458, Asayre mentioned that what makes BSW edge out is the fact that light attacks scale much more strongly off of spell damage than they do off max magicka, however, if you analyze his original posts in this thread, you’ll notice that missing some light attacks drastically diminishes their contribution to DPS, missing only a few light attacks will make Necro edge out over BSW in single target, not to mention that abilities Scale very strongly off max magicka and they will hit harder with Necro, which will end up raising not only single target DPS because of missed weaves (Let’s be honest, even Uber sorcs miss a weave now and then because of either a small lag spike or a brain fart :P) but also AOE damage since ground DoTs will be hitting harder.
As far as lightning vs Inferno front bar, I am also finding myself hitting for more with lightning on front bar as an Altmer with Necropotence, but wouldn’t be able to give a precise statement justifying this with maths as of now.
I have a proposed bar setup for you Yolo, if you don’t mind me C:, I switched Daedric Prey and Mage’s Wrath around from what you have in your build and I’ve been liking it a lot, So I can barswap animation cancel Blockade of Fire and cast both Pet and Daedric Prey from the lightning bar, this has three main advantages: 1) It increases the frags procs since there are more skill casts on the main bar. 2) It increases the time per rotation we spend on lightning bar, thus increasing all of our DoTs damage by that much! (6 skill casts vs 4 skill casts when having Prey on backbar). 3) Mage’s Wrath is considered a single target skill, so it’s nice to have it getting buffed by the inferno staff, plus if using BSW, light attack weaving on an inferno helps keeping those BSW procs during execute. Any thoughts on this would be appreciated, your work has inspired a lot of sorcs like me!
 This reply was modified 7 months, 1 week ago by Leomed47. Reason: Forgot to add third reason on the last paragraph

Leomed47 said on April 17, 2017 :
@YoloWizard, from what I’ve been testing, considering the few times I’ve seen @Nosferatuzod test and also taking into account what @Asayre has stated in a few posts throughout this thread, it looks like BSW gives the best single target dps when compared to Necro, this is while using Daedric Prey, however this comes from a *perfect* simulation in which all light attacks are hitting. T
he difference compared to Necro in single target is neglectable imo, 43768 average dps on skele vs 43458, Asayre mentioned that what makes BSW edge out is the fact that light attacks scale much more strongly off of spell damage than they do off max magicka, however, if you analyze his original posts in this thread, you’ll notice that missing some light attacks drastically diminishes their contribution to DPS, missing only a few light attacks will make Necro edge out over BSW in single target, not to mention that abilities Scale very strongly off max magicka and theywill hit harder with Necro, which will end up raising not only single target DPS because of missed weaves (Let’s be honest, even Uber sorcs miss a weave now and then because of either a small lag spike or a brain fart :P) but also AOE damage since ground DoTs will be hitting harder.
As far as lightning vs Inferno front bar, I am also finding myself hitting for more with lightning on front baras an Altmer with Necropotence, but wouldn’t be able to give a precise statement justifying this with maths as of now.
I have a proposed bar setup for you Yolo, if you don’t mind me C:, I switched Daedric Prey and Mage’s Wrath around from what you have in your build and I’ve been liking it a lot, So I can barswap animation cancel Blockade of Fire and cast both Pet and Daedric Prey from the lightning bar, this has three main advantages: 1) It increases the frags procs since there are more skill casts on the main bar. 2) It increases the time per rotation we spend on lightning bar, thus increasing all of our DoTs damage by that much! (6 skill casts vs 4 skill casts when having Prey on backbar). 3) Mage’s Wrath is considered a single target skill, so it’s nice to have it getting buffed by the inferno staff, plus if using BSW, light attack weaving on an inferno helps keeping those BSW procs during execute. Any thoughts on this would be appreciated, your work has inspired a lot of sorcs like me!
You are correct, the sole reason I’m running this bar setup is in some boss fight I won’t need shield specially if I’m guarded. So what I usually do is stack magicka on main bar by dropping Mages’ Wrath from front bar and shield from back bar and slot bound aegis. And by doing this I won’t break my rotation as it will stay the same.
 This reply was modified 7 months, 1 week ago by YoloWizard.

Please tell me you are going to update ur cp calculator to accou t for moreowind changes? Im so lost!

Hi! Magplar.
2xGroth,5bsw,4moondancer, staff lightning(moon) and inferno moondancer.
2Groth,5julian,5moondancer, dm(julian) and staff lightning (julian)or inferno?
2groth,5 bsw,5 moondancer,dm(moon) and lightning staff (moondancer) or inferno?
Best dps? And rotation?
Enchant staff?

Hi Asayre,
I was trying to calculate what the expected DPS increase from having a Moondancer/Infallible inferno as opposed to random sharpened on my magicka dragonknight, but it strikes me as very small, am I doing the math correctly?
If VMA frontbar:
Beserker uptime ~30% = 104 SD
VMA SD enchant 15s uptime/18s rotation = 158 SD
(MD backbar = ~3s uptime/18s rotation = 22 SD)
If VMA backbar:
Beserker uptime ~50% = 174 SD
VMA SD enchant 4s uptime/18s rotation = 42 SD
(MD frontbar = ~14s uptime/18s rotation = 100 SD)
So the MD frontbar setup gives about 50 spell damage increase over VMA frontbar, random sharp staff backbar, in a base pool of about 2.2k. With 42.5k magicka, and after major sorcery*, total resource pool goes from 70220 to 70850, which is about an 0.9% increase roughly 360 damage if already doing 40k. Not negligible, but not particularly large either?
 This reply was modified 7 months, 1 week ago by tribunal4555.

@YoloWizard, I got 43908 with the BSW and 43913 with the Necro setup. My BSW tends to over estimate because it has nearly incredulous uptime (64% in the simulation). The simulations were done with Major Breach. I didn’t put in all the buffs you have in your raid. I have been wanting to include off balance in the simulation but haven’t gotten around to it yet.
@Nstunner, I wouldn’t say it is the maximum known DPS. You can have offbalance and other buffs and you can crit a whole lot more. What the number represents is an estimate of the upper limit giving certain simulation conditions, sets, CP etc. and it’s just the average DPS of 100 simulations.
@Nosferatuzod don’t worry the CP changes seem easy to handle. It shouldn’t be any more difficult than it is now to calculate the optimal CP distribution
@Orair, have you considered visiting the Templar Theorycrafting subforum? It should adequately answer most of your questions.
@tribunal4555, I’m a bit confused by your question. It seems that you are asking what is the difference between using a Moondancer/Maelstrom setup compared to a Random/Maelstrom setup but then you show calculations for a Moondancer/Maelstrom setup compared to a Maelstrom/Moondancer setup. I think your calculation for the second question is reasonable.

@Asayre, I got a little impatient waiting for you to do the champion point update for Morrowind.. So I started editing a copy of your old excel file.
Very interesting design! I can tell it took you a long time to create it. Unfortunately ZoS is good at throwing curveballs…. I just tested each tree we have an interest in now, and it seems that ALL stars have jump points. (Elfborn, Ele Expert, Staff Expert, MasteratArms, and Thaumaturge.) Did not test stamina stars.
Spell Erosion is bugged (any points spent into it does not change any damage done from any damage source even completely naked) so I cant tell if it has the same type of jump points, but something of note here… The jump points are not like before. From 199 points, your jump point is anything ABOVE the value, so the first jump isn’t until 3 points for 25% stars, 4 points for 15% star, and 2 points for 35% star.
So for example, to get a difference of damage from 18% to 19% in a 25% star, your points would be 48 points and 52 points respectively. NOTE that point 51 is 19% tooltip display, but isnt actually applying it yet. The only point that actually works AT displayed value, is the 100th point. so at 81 to 99, you are 24% increase, and 100 gives you 25%.
I can share my updated spreadsheet if you would like me to, incase you haven’t gotten started. I’m going to continue working on it trying to update it. Its rather fun
If you already know all of this, then feel free to disregard my first post ever on Tamriel Foundry! I made an account just to post this lol.
EDIT: And in case you are wondering, I tested this wearing nothing but a maelstrom destro staff, casting whips, eruption or light attacks for each respective damage type, to watch for change in damage on each CP increase.
EDIT 2: Was curious about something else about the CP, it seems 14% in a 15% star actually gives 14% increase instead of the above mentioned requirement for a jump point. 23% on a 25% star is also the same, however 19% is NOT a jump point. Man this stuff is weird. Only 1 in 35% stars at 32%, and it is NOT a jump point either.
(To clarify, both 19% in a 25% star, and 32% in a 35% star, are 1 point away from being a jump point, but the actual nondecimal percentage is NOT a jump point. The only stars that ARE jump points at that nondecimal, are points at 100, and a 15% star’s 14% point, and a 25% star’s 23% point.)
 This reply was modified 7 months ago by WatchYourSixx.

WatchYourSixx said on April 25, 2017 :
@Asayre, I got a little impatient waiting for you to do the champion point update for Morrowind.. So I started editing a copy of your old excel file.
Very interesting design! I can tell it took you a long time to create it. Unfortunately ZoS is good at throwing curveballs…. I just tested each tree we have an interest in now, and it seems that ALL stars have jump points. (Elfborn, Ele Expert, Staff Expert, MasteratArms, and Thaumaturge.) Did not test stamina stars.
Spell Erosion is bugged (any points spent into it does not change any damage done from any damage source even completely naked) so I cant tell if it has the same type of jump points, but something of note here… The jump points are not like before. From 199 points, your jump point is anything ABOVE the value, so the first jump isn’t until 3 points for 25% stars, 4 points for 15% star, and 2 points for 35% star.
So for example, to get a difference of damage from 18% to 19% in a 25% star, your points would be 48 points and 52 points respectively. NOTE that point 51 is 19% tooltip display, but isnt actually applying it yet. The only point that actually works ATdisplayed value, is the 100th point. so at 81 to 99, you are 24% increase, and 100 gives you 25%.
I can share my updated spreadsheet if you would like me to, incase you haven’t gotten started. I’m going to continue working on it trying to update it. Its rather fun
If you already know all of this, then feel free to disregard my first post ever on Tamriel Foundry! I made an account just to post this lol.
EDIT: And in case you are wondering, I tested this wearing nothing but a maelstrom destro staff, casting whips, eruption or light attacks for each respective damage type, to watch for change in damage on each CP increase.
EDIT 2: Was curious about something else about the CP, it seems 14% in a 15% star actually gives 14% increase instead of the above mentioned requirement for a jump point. 23% on a 25% star is also the same, however 19% is NOT a jump point. Man this stuff is weird. Only 1 in 35% stars at 32%, and it is NOT a jump point either.
(To clarify, both 19% in a 25% star, and 32% in a 35% star, are1 point away from being a jump point, but the actual nondecimal percentage is NOT a jump point. The only stars that ARE jump points at that nondecimal, are points at 100, and a 15% star’s 14% point, and a 25% star’s 23% point.)
Really hoping for the updated website to go live soon:)

@WatchYourSixx, thanks for joining Tamriel Foundry just to post here! Also thanks for sharing your findings. I was already aware but it is always good to hear about it. I’ve reported the broken nature of Spell Erosion on the first day of the PTS. It appear that roughly speaking the tooltip shown in game is rounded down to the nearest integer for in game calculations leading to all the jump points. However as you have found this rule is not quite correct. I presume that it is related to how Elfborn is treated on Live, in that there is some underlying equation that gets rounded to 2 decimal places for in game calculations but the tooltip is derived another way.
Anyway, I am interested in your spreadsheet solely to see how you approach the optimisation process. If you could describe what you intend to do that would be worth more than any spreadsheet.
In the spreadsheet, I use equations which relate the number of points to the tooltip value and then apply a gradient descent approach to find the maximum of the optimisation function which is
Optimisation of Elfborn jump points is then performed by redoing the calculation but fixing Elfborn at a jump point lower and higher than that obtained with the initial optimisation procedure. Thus for the current CP cap this requires ~600 function calculations.
This method has some problems with the changes on the PTS. My best fits so far are obtain with the following polynomials
y = 0.0015 * Point^2 + 0.3 * Point (for 15% stars)
y = 0.0025 * Point^2 + 0.5 * Point (for 25% stars)
y = 0.0035 * Point^2 + 0.7 * Point (for 35% stars)it is straightforward to use gradient descent or the normal equations to get the function maximum. However, I am not too sure on how to deal with all the jump points. If I were to do what I am doing now and do the optimisation for a jump point lower and higher than the initial optimisation then I would expect to do 2^10 * 210 + 210 function calculations which is far too large! Even if we restrict it to the 6 stars pertinent to magicka builds that would be ~2^6 more function evaluations than what is currently needed.
My second thought was because there are so many jump points we might be able to just evaluate the entire function for all possible combination of jump points. So for magicka builds we are interested in Elemental Expert, Elfborn, Spell Erosion, MasteratArms, Staff Expert and Thaumathurge. The number of function calculations is then 15*25*100*25*35*25 ~820 million which is ridiculous higher than the previous approach.
The next idea was to use gradient descent on the jump points instead and normalise the value to the number of points spent. So for instance if you needed 10 points to reach the next jump point in Elemental Expert and it would increase the function by 1% but you could alternatively increase the function by 0.3% by putting 2 points in Staff Expert then the latter would be picked because the normalised increase is 0.15 going with Staff Expert as opposed to 0.1 with Elemental Expert. This approach should require less than 210 function evaluations which is very promising. But I am a bit worried I won’t hit the global maximum and might get stuck in some sort of local maximum.
I note that the jump points are kind of significant because suppose we had a solution that did not take into account jump points, denoted by a. And denote <b>b</b> as the solution that takes all jump points lower than a and let c be the solution that takes all jump points higher than a then the difference between c and b is maximally 6%. In terms of damage observe this will lead to a damage difference of ~14% due to the additive nature of CP and damage done (new change not mentioned in patch notes). So it is a worthwhile problem to solve.
Anyway, that’s just a bit of my rambling thoughts on how to solve it. I would like to know how you did it in the spreadsheet.
@Nosferatuzod, is there anything else you would like added/removed/changed from the website?
 This reply was modified 7 months ago by Asayre.

Sorry if this is out of place, but what addons do you use? I’m just getting back into ESO yet again (lol) and don’t have any addons and can’t remember which ones were awesome besides the discontinued Tactical Combat.

Ghnami said on April 26, 2017 :
Sorry if this is out of place, but what addons do you use? I’m just getting back into ESO yet again (lol) and don’t have any addons and can’t remember which ones were awesome besides the discontinued Tactical Combat.
Assuming you are reading this thread because of your interest in theorycrafting, computational simulation, minmaxing and/or other calculations, I would suggest Combat Metrics, it has almost everything you need.
There is a number of options for buff tracking, I personally use Srendarr, but other users will have other preferences.

I’m curious, what’s your % error with those 3 equations? I struggled to come up with them on my own, so I downloaded a plotting software called curve expert. Using that I was able to find a 3rd degree polynomial for all the equations except for the penetration Star, which I had to use a 5 degree polynomial. With those my error on calculated is very very small.
Also, doesn’t the equation need to be changed to account for the new direct damage cp Star master at arms? Was thinking of taking out the initial part, the elemental damage, bc that’s just used to make the remaining ratio percentage as just base damage. I’d replace that with direct damage calculation that would have it, and the Ele expert calc, and then add direct damage to the staff expert equation calculation due to it affecting that star as well like Ele affects all damage increase stars.
I will link my spreadsheet after work.
 This reply was modified 7 months ago by WatchYourSixx.

Asayre said on April 26, 2017 :
@WatchYourSixx, thanks for joining Tamriel Foundry just to post here! Also thanks for sharing your findings. I was already aware but it is always good to hear about it. I’ve reported the broken nature of Spell Erosion on the first day of the PTS. It appear that roughly speaking the tooltip shown in game is rounded down to the nearest integer for in game calculations leading to all the jump points. However as you have found this rule is not quite correct. I presume that it is related to how Elfborn is treated on Live, in that there is some underlying equation that gets rounded to 2 decimal places for in game calculations but the tooltip is derived another way.
Anyway, I am interested in your spreadsheet solely to see how you approach the optimisation process. If you could describe what you intend to do that would be worth more than any spreadsheet.
In the spreadsheet, I use equations which relate the number of points to the tooltip value and then apply agradient descent approach to find themaximum of the optimisation function which is
Optimisation of Elfborn jump points is then performed by redoing the calculation but fixing Elfborn at a jump point lower and higher than that obtained with the initial optimisation procedure.Thus for the current CP cap this requires ~600 function calculations.
This method has some problems with the changes on the PTS. My best fits so far are obtain with the following polynomials
y = 0.0015 * Point^2 + 0.3 * Point (for 15% stars)
y = 0.0025 * Point^2 + 0.5 * Point (for 25% stars)
y = 0.0035 * Point^2 + 0.7 * Point (for 35% stars)it is straightforward to use gradient descent or the normal equations to get the function maximum. However, I am not too sure on how to deal with all the jump points. If I were to do what I am doing now and do the optimisation for a jump point lower and higher than the initial optimisation then I would expect to do2^10* 210 + 210 function calculations which is far too large! Even if we restrict it to the 6 stars pertinent to magicka builds that would be ~2^6 more function evaluations than what is currently needed.
My second thought was because there are so many jump points we might be able to just evaluate the entire function for all possible combination of jump points. So for magicka builds we are interested in Elemental Expert, Elfborn, Spell Erosion, MasteratArms, Staff Expert and Thaumathurge. The number of function calculations is then 15*25*100*25*35*25 ~820 million which is ridiculous higher than the previous approach.
The next idea was to use gradient descent on the jump points instead and normalise the value to the number of points spent. So for instance if you needed 10 points to reach the next jump point in Elemental Expert and it would increase the function by 1% but you could alternatively increase the function by 0.3% by putting 2 points in Staff Expert then the latter would be picked because the normalised increase is 0.15 going with Staff Expert as opposed to 0.1 with Elemental Expert. This approach should require less than 210 function evaluations which is very promising. But I am a bit worried I won’t hit the global maximum and might get stuck in some sort of local maximum.
I note that the jump points are kind of significant because suppose we had a solution that did not take into account jump points, denoted by a. And denote <b>b</b> as the solution that takes all jump points lower than a and let c be the solution that takes all jump points higher than a then the difference between c and b is maximally 6%. In terms of damage observe this will lead to a damage difference of ~14% due to the additive nature of CP and damage done (new change not mentioned in patch notes). So it is a worthwhile problem to solve.
Anyway, that’s just a bit of my rambling thoughts on how to solve it. I would like to know how you did it in the spreadsheet.
@Nosferatuzod, is there anything else you would like added/removed/changed from the website?
Well only in respect to Master At Arms. It currently buffs jabs/sweeps ans Balista but not Rend…how would we go about optimizing with that in mind?

@Nosferatuzod, sounds like it’s counting ballista as a direct damage ability and rend as a dot ability. Does thaum buff both skills or just rend? Same for jabs?
iirc jabs is direct damage, bc I know it procs sets like selenes.

WatchYourSixx said on April 26, 2017 :
@Nosferatuzod, sounds like it’s counting ballista as a direct damage ability and rend as a dot ability. Does thaum buff both skills or just rend? Same for jabs?
iirc jabs is direct damage, bc I know it procs sets like selenes.
Havent tested thaum on balista yet but thaum buffs jabs. I think the reasoning is that rend stays on target and i tjink can be purged, versus balista and jabs being damage over time but non purgeable.
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