Introduction to PvE damage calculation (Homestead)

caperon · February 2017

Impressive. Is this part of your Phd?

Can your simulation test this?

Frontbar: 2 illambris , 4 moondancer, 5 bsw (inferno bsw staff)
Backabr: 2 illambris, 4 BSW, 5 moondacer (inferno moondancer staff)

Great work.

caperon · February 2017

double post

Asayre · February 2017

@caperon, I can but it's not going to give you what I want. The current simulation will use synergies every 15 seconds without regard to your current bar. Since you only have 4 pieces of Moondancer on your main bar it will be quite unlikely that you will get the Moondancer buff.

Turelus · February 2017

Asayre for Dev.

These are some EVE Online levels of calculations right here, I mean graph pron! I think I am in love.

caperon · February 2017

Asayre wrote: »

@caperon, I can but it's not going to give you what I want. The current simulation will use synergies every 15 seconds without regard to your current bar. Since you only have 4 pieces of Moondancer on your main bar it will be quite unlikely that you will get the Moondancer buff.

I understand this is a more complex seting and the simulation is not designed for that particular setup, maybe could be simplified to proc synergy each 2 bar swaps, but thanks for the answer anyway, your post are allways very insightful.

Asayre · February 2017

@Turelus, you like that ternary graph? XD I finally found a use for it!

C4Bliss · February 2017

Really impressive! I always thought that for boss fights aether 3pc was better than moondancer...

In the pic you posted you used scathing with moondancer and 2inferno's. Wouldnt it be better to use aether with scathing for the crit bonus and a mix of lightning and inferno?

Gonna try and play around with it!

GilGalad · February 2017

C4Bliss wrote: »

Really impressive! I always thought that for boss fights aether 3pc was better than moondancer...

In the pic you posted you used scathing with moondancer and 2inferno's. Wouldnt it be better to use aether with scathing for the crit bonus and a mix of lightning and inferno?

Gonna try and play around with it!

Moondancer and Aether are pretty close to each other. The tests were made with a Sorc, meaning 8% extra magicka and no boost to crit dmg. I'm pretty sure that on a Templar with 10% extra crit dmg and no boost to magicka Aether will be slightly ahead of Moondancer.

Izaki · February 2017

@Asayre Thank ypu very much for all your answers its really appreciated and informative. So I have a few more for you!

1. I thought that doing heavy attacks removed the off balance effect..! So wouldn't heavy attack builds actually hinder this whole group set up based around Concussed and off balance?
2. If the "meta" does shift to the 75 Thaumaturge, is the fire staff still going to out perform a shock one? The damage on liquid lightning and blockade will be really boosted at this point, so maybe the front bar staves for sorcs will also change?
Thanks in advance!

SiliconShadow · February 2017

First of all I have to applaud you for the very thorough work that you have performed. Very thorough and very useful for something I have been working on.

I have some queries and thoughts:

1) Have you considered the change to critical damage in the new patch? It looks like the calculations you have are multiplicative, and it looks like now we are getting additive critical damage, drastically changing how TBS stacks up.

2) With the new patch the exploiter passive may be more beneficial than going more into elfborn. Requiring 75 into thaumaturge to get the 10% bonus to off balance mobs which may be better going forward in organised groups.

3) Have you thought about doing this the opposite way around in the application and using a tsp algorithm to calculate an optimal rotation for a weapon set? (I am working on one, but in c# currently this is why I ask)

4) Are you releasing what looks like the matlab application that you have written at all?

Masel · February 2017

IzakiBrotherSs wrote: »

@Asayre Thank ypu very much for all your answers its really appreciated and informative. So I have a few more for you!
1. I thought that doing heavy attacks removed the off balance effect..! So wouldn't heavy attack builds actually hinder this whole group set up based around Concussed and off balance?
2. If the "meta" does shift to the 75 Thaumaturge, is the fire staff still going to out perform a shock one? The damage on liquid lightning and blockade will be really boosted at this point, so maybe the front bar staves for sorcs will also change?
Thanks in advance!

Heavy attacks remove off balance, yes. BUT blockade of storms sets enemies immediately off balance again because they are still concussed. So it doesn't really affect the uptime on concussion or off-balance

Izaki · February 2017

Masel92 wrote: »

IzakiBrotherSs wrote: »

@Asayre Thank ypu very much for all your answers its really appreciated and informative. So I have a few more for you!
1. I thought that doing heavy attacks removed the off balance effect..! So wouldn't heavy attack builds actually hinder this whole group set up based around Concussed and off balance?
2. If the "meta" does shift to the 75 Thaumaturge, is the fire staff still going to out perform a shock one? The damage on liquid lightning and blockade will be really boosted at this point, so maybe the front bar staves for sorcs will also change?
Thanks in advance!

Heavy attacks remove off balance, yes. BUT blockade of storms sets enemies immediately off balance again because they are still concussed. So it doesn't really affect the uptime on concussion or off-balance

Oh okay that's cool! Perfect! Thanks!

BigBragg · February 2017

@Asayre Check this out:

https://twitter.com/SlashLurk/status/828030840408068096

Masel · February 2017

Asayre wrote: »

IzakiBrotherSs wrote: »

What is your take on the Lightning vs Inferno staff on the main bar?

For single target, I think Inferno staff is better for a main bar. If you are using Burning Spellweave then the light attacks are helping in maintaining a good uptime. But even if you are not using Burning Spellweave, an Inferno staff is preferable on your main bar because the majority of your damage is single target. In terms of simulation comparison, DPS for 2 Ilambris, 5 Julianos, 3 Moondancer with two Inferno staves is 42167 but 41903 if using a lightning staff on the main bar.

IzakiBrotherSs wrote: »

As well as the Exploiter passive, is it worth spending 75 CP into Thaumaturge and rely on setting enemies off balance for the 10% damage increase?

It depends a bit on how far away you are from putting 75 CP into Thaumathurge. If I assume 40% of my damage is from DoT and I'm just getting Major Breach, then my CP optimiser says to put 100 in Elemental Expert, 46 in Spell Erosion, 42 in Elfborn and 12 in Thaumathurge. The optimisation function output is 1.793. If you open the developer console on my CP optimisation webpage you can see the optimisation function output. If I force it to put 75 points into Thaumathurge it then suggest 100 in Elemental Expert, 5 in Spell Erosion, 22 in Elfborn with an optimisation function output of 1.745. So you'll be losing about 3% damage. This suggest that you need your target to be off-balance for at least a third of the time, possibly higher since Exploiter is presumably additive with other forms of damage done.

I think @Masel92 provides interesting comments. Putting 75 points to get Exploiter is probably best done in raids where you have heavy attack builds going on. @Masel92 do you happen to use Combat Metrics? And if so, does it show the debuff uptime of Off-balance?

IzakiBrotherSs wrote: »

I noticed that your setup (6) was using Aether and a random staff, yet there is no considerable DPS loss in comparison to setup (4). Also your minor vulnerability uptime is significantly higher, this leads me to guess that you were using Boundless Storm over Curse?.

Woops I made a mistake there. (6) should have been with an Aether staff. When compared to (4) it is just comparing the difference between using 3/4 pieces of Infallible instead of Moondancer and I find that the difference is too small to be detected by my simulation which agrees well with the weighted ability metric calculations. A straight ability metric calculation for 2 Ilambris, 5 Burning Spellweave, 3 Moondancer is 86580 and for 2 Ilambris, 5 Burning Spellweave, 3 Infallible it is 85870. That means that 3 Moondancer should do about 0.8% more damage than 3 Infallible but neglects to take into account that the damage difference is in favour of Infallible for light and heavy attacks thus the damage difference is smaller than 0.8%. I also made a mistake of putting my notes on Minor Vulnerability for (5) into that of (6). (5) has higher Minor Vulnerability because Blockade of Storms is being used. I've updated my figure. Sorry for the confusion and thanks for spotting it. That simulation was more personal because I have a Sharpened Maelstrom Lightning staff and was interested in what I could expect.

Combatmetrics does indeed show the concussion debuff and the off-balance uptime!

Asayre · February 2017

IzakiBrotherSs wrote: »

@Asayre Thank ypu very much for all your answers its really appreciated and informative. So I have a few more for you!
1. I thought that doing heavy attacks removed the off balance effect..! So wouldn't heavy attack builds actually hinder this whole group set up based around Concussed and off balance?
2. If the "meta" does shift to the 75 Thaumaturge, is the fire staff still going to out perform a shock one? The damage on liquid lightning and blockade will be really boosted at this point, so maybe the front bar staves for sorcs will also change?
Thanks in advance!

1. You're right for some reason I always think that heavy attacks on concussed gives off balance but it's not that way.
2. It doesn't quite reach 50% yet so not really for single target. It'll definitely be useful for trash.

SiliconShadow wrote: »

1) Have you considered the change to critical damage in the new patch? It looks like the calculations you have are multiplicative, and it looks like now we are getting additive critical damage, drastically changing how TBS stacks up.

The critical damage formula I have implemented is

SiliconShadow wrote: »

2) With the new patch the exploiter passive may be more beneficial than going more into elfborn. Requiring 75 into thaumaturge to get the 10% bonus to off balance mobs which may be better going forward in organised groups.

I answered a similar question so just copy pasting the answer

IzakiBrotherSs wrote: »
As well as the Exploiter passive, is it worth spending 75 CP into Thaumaturge and rely on setting enemies off balance for the 10% damage increase?
It depends a bit on how far away you are from putting 75 CP into Thaumathurge. If I assume 40% of my damage is from DoT and I'm just getting Major Breach, then my CP optimiser says to put 100 in Elemental Expert, 46 in Spell Erosion, 42 in Elfborn and 12 in Thaumathurge. The optimisation function output is 1.793. If you open the developer console on my CP optimisation webpage you can see the optimisation function output. If I force it to put 75 points into Thaumathurge it then suggest 100 in Elemental Expert, 5 in Spell Erosion, 22 in Elfborn with an optimisation function output of 1.745. So you'll be losing about 3% damage. This suggest that you need your target to be off-balance for at least a third of the time, possibly higher since Exploiter is presumably additive with other forms of damage done.

SiliconShadow wrote: »

3) Have you thought about doing this the opposite way around in the application and using a tsp algorithm to calculate an optimal rotation for a weapon set? (I am working on one, but in c# currently this is why I ask)

No, I haven't but I like the idea. I'm not familiar with C#, I tried it out a bit when I was learning Unity but didn't do much else. If you don't mind could you explain the core process?

SiliconShadow wrote: »

4) Are you releasing what looks like the matlab application that you have written at all?

If you want you can send me a PM for a Windows executable or the Matlab source code. I understand that not many people will have Matlab but it is like the only programming language that I can write anything decent in.

@BigBragg
Thanks! I didn't know that =D

SiliconShadow · February 2017

I don't have access to PM you here, so I have sent on Tamriel Foundry.

Asayre wrote: »

IzakiBrotherSs wrote: »

SiliconShadow wrote: »

3) Have you thought about doing this the opposite way around in the application and using a tsp algorithm to calculate an optimal rotation for a weapon set? (I am working on one, but in c# currently this is why I ask)

No, I haven't but I like the idea. I'm not familiar with C#, I tried it out a bit when I was learning Unity but didn't do much else. If you don't mind could you explain the core process?

This is a time based algorithm, where we cover as much distance as possible using a limited amount of points over a set period of time. For distance we use the damage dealt presuming number of targets in different scenarios.

Each skill has:
Cast time
Animation time
Initial damage
Damage over time (Which includes a more complicated component of which point to clip or not to clip, or to leave down)

We also have
Bar swap
Light attack
Heavy attack

Given a finite number of inputs of skills, which can be taken from the skill dump, and a finite number of armours (which would require work to change from a sheet in a format of descriptions to actual values) we can create a timeline of how skills are to be cast in order.

To determine the order we can use one of a number of methods but the two I would go for with this are organic or brute force. Brute force would be immensely hard to calculate unless we use restrictions such as giving a role to a skill (DOT / Spammable / Reactive) we can then create the algorithm to create every combination of skill bars possible, then every combination of DOT > Reactive > Spammable possible. In our case a TSP algorithm fits the problem quite closely in respects to brute force or organic. (Brute force here: https://programmingpraxis.com/2010/03/12/traveling-salesman-brute-force/)

The brute force algorithm describes cities and calculating the distance between cities for the shorted route possible between them all. Our problem is the inverse to this where we want to travel the most amount of distance (Damage caused) in the shortest amount of time possible using the skills as our destinations. The algorithm here can either done recursively or iteratively using the same method. We can pre-calculate skill time lines giving them points of time which can overlap on different tracks of damage. This data then is compiled and each possible combination is recorded, and the best result is given. This brute force algorithm may be fine for our scenario however even with a 50 or so destinations, the number of permutations would be immense albeit giving the perfect answer every time, however the alternative would be organic.

Ants. How ants find food is they forage on paths randomly with equal probability, during the path they travel they leave pheromones. Once an ant has reached it's destination then it evaluates the quality of the food and returns home leave a pheromone trail marking how good the source was. This can be applied to optimising skill rotations. We don't necessarily have to calculate every permutation. We can put a number of ants on each starting point, and let them pick skills determining the skill order to be the best outcome of damage and cast time giving a value to that route, the value would be the dps dealt over the amount of time of the ants travels. We can repeat this process by combining path sections with the highest pheromone values as biases for which path the ant takes to optimise the route. The number of passes determines how close we get to the perfect value, but this then becomes very close within a few % of the optimal brute force solution, however we have calculated far fewer paths over the same processing time.

GilGalad · February 2017

SiliconShadow wrote: »

I don't have access to PM you here, so I have sent on Tamriel Foundry.

Asayre wrote: »

IzakiBrotherSs wrote: »

SiliconShadow wrote: »

3) Have you thought about doing this the opposite way around in the application and using a tsp algorithm to calculate an optimal rotation for a weapon set? (I am working on one, but in c# currently this is why I ask)

No, I haven't but I like the idea. I'm not familiar with C#, I tried it out a bit when I was learning Unity but didn't do much else. If you don't mind could you explain the core process?

This is a time based algorithm, where we cover as much distance as possible using a limited amount of points over a set period of time. For distance we use the damage dealt presuming number of targets in different scenarios.

Each skill has:
Cast time
Animation time
Initial damage
Damage over time (Which includes a more complicated component of which point to clip or not to clip, or to leave down)

We also have
Bar swap
Light attack
Heavy attack

Given a finite number of inputs of skills, which can be taken from the skill dump, and a finite number of armours (which would require work to change from a sheet in a format of descriptions to actual values) we can create a timeline of how skills are to be cast in order.

To determine the order we can use one of a number of methods but the two I would go for with this are organic or brute force. Brute force would be immensely hard to calculate unless we use restrictions such as giving a role to a skill (DOT / Spammable / Reactive) we can then create the algorithm to create every combination of skill bars possible, then every combination of DOT > Reactive > Spammable possible. In our case a TSP algorithm fits the problem quite closely in respects to brute force or organic. (Brute force here: https://programmingpraxis.com/2010/03/12/traveling-salesman-brute-force/)

The brute force algorithm describes cities and calculating the distance between cities for the shorted route possible between them all. Our problem is the inverse to this where we want to travel the most amount of distance (Damage caused) in the shortest amount of time possible using the skills as our destinations. The algorithm here can either done recursively or iteratively using the same method. We can pre-calculate skill time lines giving them points of time which can overlap on different tracks of damage. This data then is compiled and each possible combination is recorded, and the best result is given. This brute force algorithm may be fine for our scenario however even with a 50 or so destinations, the number of permutations would be immense albeit giving the perfect answer every time, however the alternative would be organic.

Ants. How ants find food is they forage on paths randomly with equal probability, during the path they travel they leave pheromones. Once an ant has reached it's destination then it evaluates the quality of the food and returns home leave a pheromone trail marking how good the source was. This can be applied to optimising skill rotations. We don't necessarily have to calculate every permutation. We can put a number of ants on each starting point, and let them pick skills determining the skill order to be the best outcome of damage and cast time giving a value to that route, the value would be the dps dealt over the amount of time of the ants travels. We can repeat this process by combining path sections with the highest pheromone values as biases for which path the ant takes to optimise the route. The number of passes determines how close we get to the perfect value, but this then becomes very close within a few % of the optimal brute force solution, however we have calculated far fewer paths over the same processing time.

I think you can heavily reduce the size of the problem especially the permutations if you make use of additional information:

The total dmg per cast time
The total dmg per duration (e.g. dot or buff duration)

In oder to understand how these two criterias help to get the perfect rotation we need to calculate the perfect rotation:
We consider a rotation consisting of one spamable and DOTs. In case we have two different spamables (normal spamable and execute) we can just split up the fight into two phases and optimize them individually. Every buff like minor slayer can be treated like a DOT while its dmg is given by the dmg increase it provides during its duration. Weaving has to be included in the way that the weave dmg is added to the skills dmg, so we consider lower weave dps for abilities with higher cast times correctely.
Therefore our minimum DPS is given by

minDPS = S/Cs
S: Spamable dmg
Cs: Spamable casttime

The maximum DPS is given by:

maxDPS = 1/T*[Ns*S+SUM_i(Di*Ni)]
Di: DOT number i, i = 1, 2, ..., M, with M the total number of DOTs
Ci: Cast time of DOT i
Ti: Duration of DOT i
Ns: Number of spamable casts
Ni: Number of DOT casts for DOT i
T: Total fight duration

Using Ni=T/Ti and T = Ns*Cs+SUM_i(Ni*Ci) <-> Ns= T/Cs(1-SUM_i(Ci/Ti) we get for our final DPS:

maxDPS = [1-SUM_i(Ci/Ti)]/Cs * S + SUM_i(Di/Ti)      (1)

The highest DPS increase a DOT can provide is given by its dmg per duration (Di/Ti). So ideally you have DOTs with a long duration and a high DPS, but that is often not the case. A high cast time on DOT or Spamable lowers the total DPS.
Trivially we find that only DOTs with a higher dmg per cast time than the spamable damage per cast time add DPS:

DPS = S/Cs + 1/T1(D1/C1-S/Cs),  only a gain by D1 if D1/C1 > S/Cs

Limiting the general formula (1) to one DOT gives us a criteria to decide which DOT should be prioritized:

DPS = [1-Ci/Ti]/Cs * S + Di/Ti

So inserting the values for all DOTs Di will give a DPS ranking that can be translated into a cast priority. In a standard rotation the priority is only relavant in the beginning of the fight and when two dots expire at the same time and you have to decide which you refresh first. It can also be used to determine at which health % a templar should start using execute over sweeps and how long it is benefiting to keep every individual DOT up compared with the execute.

Since you have a cast priority now you can let your program optimize a rotation by reducing the number of bar swaps to a minimum. Ideally you would take into account the different weapon types.

I hope that helps!

SiliconShadow · February 2017

GilGalad wrote: »

I think you can heavily reduce the size of the problem especially the permutations if you make use of additional information:

When I first used this process for creating rotations in another MMO (I'm sure it's not allowed to name other games so I won't) I did use a similar method to the one you describe, however I quickly dropped it.

It came down to, you have to use a timeline with multiple tracks.

The largest reason not to do this is because there are many effects which are reactive, and random that effects the skill damage. Due to the coefficients of the skills, and effects of some skills (Venomous claw which increases in damage over time, or Radiant Oppression etc) You can't simple state x skill is better than y.

What you need to do is x skill is the most powerful in this scenario, and used in this way, with a combination of these other skills.

Even the order in which you cast skills effects DPS when they don't effect each other due to animation times.

Clipping is also a factor of dots in a rotation as you sometimes want to clip and other times don't want to clip ever (Venomous claw never clip, blockade of fire clip for example).

Asayre · February 2017

@SiliconShadow
Thanks for the explanation. So if I understand correctly, if we wanted to simulate let's say just Force Pulse we have a Force Pulse Node that loops back on itself and we would use that path. The path length is proportional to damage and you would want to keep using paths until you reach the target health. And if you had two skills say one is a DoT and one is a spammable then some nodes would be deactivated for a duration equal to the length of the DoT? I imagine that the path lengths have to be updated every time you get a buff as well?

@GilGalad
I considered that approach initially but I didn't pursue it much further because I couldn't think of a way to capture the behaviour of certain procs, namely Crystal Fragments, and the damage change during bar swaps. I thought of using the average magicka and spell damage and then predict the average damage of a DoT but I don't know that felt a bit iffy. Would you mind explaining a bit more on how to handle these cases?

Edit: I think @SiliconShadow addresses this better than me in his comment. If we could overcome this somehow it would probably be super computationally efficient.

@caperon
Actually, I can sort of answer your question. What I did was to set up the stats as you described
Frontbar: 2 illambris , 4 moondancer, 5 bsw (inferno bsw staff)
Backabr: 2 illambris, 4 BSW, 5 moondacer (inferno moondancer staff)

But then I gave the Frontbar the 5p bonus of Moondancer as well. So this allows every synergy the chance to activate Moondancer. The mean DPS was 43616 with a SD of 1560. SD of setups using Moondancer tend to be high due to the nature of the five piece bonus.

altemriel · February 2017

wow!!

SiliconShadow · February 2017

Asayre wrote: »

@SiliconShadow
Thanks for the explanation. So if I understand correctly, if we wanted to simulate let's say just Force Pulse we have a Force Pulse Node that loops back on itself and we would use that path. The path length is proportional to damage and you would want to keep using paths until you reach the target health. And if you had two skills say one is a DoT and one is a spammable then some nodes would be deactivated for a duration equal to the length of the DoT? I imagine that the path lengths have to be updated every time you get a buff as well?

Create timeline matrix (1ms blocks x skills + buffs + potion)
Create an ant for every skill
Ant activates a skill/buff/potion records the DPS on the timeline
Ant's switch skill keeping buffs for the time allowed these stay person, skill is picked by it's potency
- If there is a DOT left to pick that isn't active pick a DOT
- If all DOTs are active pick a spammable - firstly determined at random then by pheromone strength when all have a value

Rinse and repeat
Buffs / potions will automatically get picked, and determined if they provide a boost to the skills dps, combinations of skills will naturally also be selected on higher dps, as the dps value is stored against the skill when it was up. This process is repeated and repeated until a rotation emerges with the highest constant DPS possible.

I would like to use machine learning for this process - don't own the toolset though! Maybe I could use CUDA with GGPU and C#.

Joy_Division · February 2017

Thank you @Asayre for all the work you are not getting paid for!

You are super awesome for sharing all this stuff.

Personofsecrets · February 2017

Thank you for this information @Asayre . I wish there were more of you!

Do you have any information about the vampire passive that causes damage mitigation and how it stacks with other forms of damage mitigation?

Neoauspex · February 2017

@Asayre if you didn't get invited to playtest... $#!&

DHale · February 2017

This is really good work thank from all of us.

montiferus · February 2017

Simply amazing. Thank you so much for your contributions to the community. Zos needs to hire you!

Would love your take on magplar as well.

Currently I'm running 2pc grothdar 5pc tbs and 5pc mothers sorrow. Would like to see how it stacks up. I have BSW but have been hesitant to use over uptime concerns. That said it seems like even with a Templar it could be BIS.

geonsocal · February 2017

geez @asayre...no wonder I get my butt kicked so much in cyrodiil...being able to know all this kinda stuff shouldn't even be legal

ugh, I guess the 'ol "eye" and "feel" test pales next to graphs and spreadsheets...

really good work sir...hopefully I'll only run into you if we're on the same side

Asayre · February 2017

@Personofsecrets I think @paulsimonps has more extensive knowledge of this than me. I'm positive his thread will cover your question
https://forums.elderscrollsonline.com/en/discussion/279426/damage-mitigation-explanation-and-list-of-options-updated-for-a-third-time/p1

@montiferus I'm a bit undecided on what class to simulate next. Templars are a bit of annoyance because I have to make sure magicka cost calculations are exactly right or else their Radiant Oppression goes a bit wonky. Magicka dragonknights or nightblades are probably the easiest because I have most of their skills done already but I'm also thinking of stamina nightblades.

@geonsocal Game experience counts for a lot too. That is how most people theorycraft and in general they get it right. My attempt is sort of going the other way around and starting from theory to derive what to do. This is a more time consuming approach but allows for more quantification rather than just this set is quite good but it's not too clear how much better it is.

montiferus · February 2017

Asayre wrote: »

@montiferus I'm a bit undecided on what class to simulate next. Templars are a bit of annoyance because I have to make sure magicka cost calculations are exactly right or else their Radiant Oppression goes a bit wonky. Magicka dragonknights or nightblades are probably the easiest because I have most of their skills done already but I'm also thinking of stamina nightblades.

Thanks looking forward to all of it!

On a side note I tried using your CP calculator but it did not seem to be working. Do you have an up to date link you could post?

Asayre · February 2017

@montiferus, Were you using http://asayre.mygamesonline.org/CPOptimisation/CPOptimisation.html#? It should work. Sometimes the host breaks down since it is a free host. What problems did you run into?