Regeneration Durability Calculator

[Koopak]

This was a triumph.
I'm making a note here:
HUGE SUCCESS!

 

Regeneration Durability Calculator v1.0

HERE

 

   This has been a project of mine for the better part of this year, tweaking and tuning and building whenever I have the spare time and energy, and it is finally ready to share with all of you. Its not perfect, and its not as exhaustive and expansive as I'd like to make it in the future, but its ready for my Scrapper friends.

   So what is this? This is a spreadsheet that is able to calculate the durability of a regeneration build when provided the appropriate build information. I made it because while Mids is a masterful tool that I cant imagine living without, it lacks this kind of calculation, ultimately giving raw values. This wasn't good enough for my goals to master the Regeneration power set, I needed more, I needed to be able to see the impacts of my power picks and enhancements beyond how it felt, or abstracted testing such as the fantastic 801 series. Initially I intended to fork Mids and see if I couldn't develop a tool to do this regardless of powerset, and I may yet do that one day, work life permitting. However this was faster, and gave me results for my true goal.

 

   As I mentioned my goal is to master the Regeneration power set as a whole, and this is the first big step I feel to that beyond my years of experience with the Scrapper version and constant tweaking. As such you can expect updates in the future to include primary power set powers, as well as the addition of a sheet for Brute, Stalker, and Sentinel. Brute will be the fastest and thus the first, so keep an eye out for that.

 

   I tried to include notes that help explain the sheet's use and if anyone has suggestions or wants to offer help in improving its readability and function, or notices a mistake in my calculations, please let me know. For now to help add clarity the rest of this post, with the exception of the link itself will be an explanation of the sheet and how to make use of it.

 

Terminology

 

   Lets begin with clarifying some terminology. In my personal experience I've found a lack of consistent terminology when describing the durability of a character beyond the preexisting health, resistance, regeneration, and defense. I have seen things like survivability score, time till death, and a few other things, but nothing consistent. This frustrates me because the terms we need have mostly existed outside of CoX for some time. As such here I have adopted/created my own terminology for some of these values.

 

Effective Health: This refers to the amount of raw damage that must be thrown at a character to defeat them. This value factors in max health, resistance, and most importantly defense. This means this is an estimated value, as a high damage attack landing or missing can noticeably throw off the value in practice. However as an estimate it is more than capable of telling you what kinda abuse your character can sustain.

 

Effective Regeneration: This refers to the amount of raw damage per second that must be thrown at a character to begin doing permanent damage. This is ultimately the amount of damage per second you can sustain without dying. As such you can assume your Health will not meaningfully move so long as your incoming damage per second is below this threshold. This has been called a survival score or immortality score elsewhere I believe. Like with Effective Health this value fluctuates in practice due to luck, but over a long period of time will hold true.

 

Resisted Health: This is Effective Health but without defense factored in. As such this is the actual amount of raw damage that needs to be thrown at you and hit for your character to be defeated. This is not an estimate, and has no luck involved, however it is also inaccurate as a raw durability state because it does not take the possibility of a miss into account.

 

Resisted Regeneration: This is Effective Regeneration without defense factored in, it has all the caveats listed above in Resisted Health.

 

Use

 

   I tried to make the sheet as intuitive as I could but CoX is a complex game. As such to get the most accurate values possible you will need to keep some limits of both the sheet and Mids in mind. You will need to fill out each of the green fields which will require some extra work than just copy the totals tab of Mids. First you will want to disable all powers in Mids, including auto powers like Health, then copying the totals. This will provide you with the effects of all of your enhancement sets but there are exceptions. One example is Numina's Convalescence +Regeneration/+Recovery, which is actually a proc but is usually treated as a set bonus. Additionally to fulfill the "Additional HP/s" field you will need to consider the effects of procs like Panacea or Power Transfer. You can also factor in self heal primary powers like Life Drain if you wish but you will have to do the math yourself. Formula for procs is provided in the Notes. Lastly in order to properly enter the POST ED enhancement values. In Mids this is the value listed, but in game this will be the blue value when mousing over the power in the enhancement menu.



   I hope this will prove useful to everyone interested in optimizing my favorite power set in CoX and give us all a better view into how this set operates. The sheet also includes a small "Basic Calculator" for quick fire comparisons with any power set or AT or just for getting a quick estimate.

https://docs.google.com/spreadsheets/d/1FwIJzvmAOyni9hRWS7XKLeqD0fo6PiVnhhe6e5RTTqk/edit?usp=sharing

Edited May 3, 2022 by Koopak

[Koopak]

Update: V1.1

-Added support for all primary powerset powers for calculations.
-Note: -to-hit will be up to you to accurately convert into equivalent +defense. Reflecting this aspect of a set is well beyond reasonable scope for this project and more accurately would fit a true simulator like World of Warcraft's Simcraft.

Edited June 7, 2022 by Koopak

[Koopak]

Update: V1.2

-Added a Brute sheet and subsequent calculation. I'll likely migrate this post to the general builds forum once I finish stalker and Sentinel
-revised versioning to something a bit more logical

[Blackjoy]

I recently wrote a post talking about the shortcomings of /SR.  Someone in  that thread tried to insist /Regen was at or near the bottom of the curve, so rolled up a Savage/Regen and Double XP'd him up to 40+.   I was amazed at how easy /Regen was and how much it comparatively feels like the energizer bunny of secondaries, but also being reacquainted with its limitations.  Having already played /SR and /WP up to 50 and /Shield into the 30's, it got me thinking about how mitigation works and what explains the outcomes we experience.   A lot of this stuff was explored a decade ago and perhaps some more recently in Homecoming.  In truth, I've forgotten nearly all of it and have been having to relearn the mechanics.  

 

Quote

This is a spreadsheet that is able to calculate the durability of a regeneration build when provided the appropriate build information. 

I've been looking at this as well, but I'll tell you straight up, it's arguably not possible on a spreadsheet.   The more I identify all the moving pieces, the more I recognize how insurmountable it is to do this.   The best you can do is define a narrow context and try and develop a model that provides insight....which is kind of what you're attempting.   

 

Quote

In my personal experience I've found a lack of consistent terminology when describing the durability of a character beyond the preexisting health, resistance, regeneration, and defense. 

Yes.  One of the biggest steps in solving complex problems is finding a way to reframe into something that is solvable.   I've come to understand  secondaries as part of basic equation 

 

(Time to bring incoming dps (and peak) dps below the crossover point) - (Time until failure of your mitigation) > 0

 

OR

 

Kill Time - Survival Time > 0 

 

Let's call this the "I win" equation. Put simply, your secondary only has to give you enough time to reach, what I call, the crossover point.   This is the point where the steady-state and spike DPS is below the mitigation.

 

Quote

Numerically, if you could survive those damage spikes, regen actually is above average durability, with the potential to be the best when supported.

I pulled this quote of yours from a thread on /regen.  It believe this is also what contributes to the problems many have playing /regen.  Managing damage spikes, particularly the Alpha is a skill that has to be mastered..  It's also much different at 25 than it is at 50.

 

 

Edited June 15, 2022 by Blackjoy

[Koopak]

All true, I'll say that you aren't wrong about reflecting this being 'impossible' in a spreadsheet but that's mostly because to approach anything like a valuable equation you have to omit outlier or impossible to know data points. A key example is how this sheet does not attempt to calculate the impact of -to-hit attacks. This is because the sheet cannot know how many enemies were hit with it and how much of the incoming damage those enemies are responsible for.

However extrapolating certain things can give us close approximations. I have plans to possibly add -to-hit calculations with the assumption "you gotem all chief" and with the ability to choose the level of your enemies for the calculation with 54 being the default. Another thing is id like to get a good description of the average damage of each enemy group and the average presence of different enemy groups then use that to create Effective Regeneration values for those expectations. I'd also like to do this for debuff amount averages. This is all possible, just research heavy.

At the end of the day tools like this aren't for telling you the theoretical limit of a set in a specific piece of content, you'd need a full sim for that, they are merely to give you a better picture into what's going on under the hood.

[Blackjoy]

On 6/16/2022 at 12:43 PM, Koopak said:

they are merely to give you a better picture into what's going on under the hood.

Agreed.  I've been trying to do that from a theoretical approach rather than a computational one.  For example, I've noticed that there's a lot of misunderstanding about "the caps" and the benefit in hitting them.   I've also realized that there a lot of misconceptions about how beneficial some pool powers.  For example, Tough isn't nearly as good for +DEF based characters.  Or to put it another way, the benefit of +RES is inversely proportional to the amount of +DEF you have.  Where as the benefit of +Regen is independent, but suffers from artifacts of how the systems are implemented.

 

The challenge with modeling /Regen is that unlike most of the other sets, /Regen's survivability is dramatically impacted by the players skill and system mastery.   In short, the timing of when you use Recon, Dull Pain, IH, MoG, dominate the player experience.   So while the Survival Time when played optimally might far exceed other secondaries, when played by humans, it can be dramatically different.  

 

A perfect example occurred when my Sav/Regen hit 35 and went to Cimerora.  The first two mission at +1, I died like three times total.  The third and subsequent missions...no deaths.  Then I ramped it up to +2 and no deaths.  And this is without running any Insp or pool powers besides Hasten when I need to cycle DP or IH.   By the third mission, I had a much better feel for the DPS and DPS spikes that /Regen would experience.    And this is true for all encounters.  I tend to die in missions when I fail to spot the Boss in the group or I am running up a mob type I'm not experienced against with /Regen.   So two people can play the same build and have wildly different experiences with it because one is much more adept at predicting the incoming DPS/spikes.

 

 

 

 

[Erratic1]

25 minutes ago, Blackjoy said:

Agreed.  I've been trying to do that from a theoretical approach rather than a computational one.  For example, I've noticed that there's a lot of misunderstanding about "the caps" and the benefit in hitting them.   I've also realized that there a lot of misconceptions about how beneficial some pool powers.  For example, Tough isn't nearly as good for +DEF based characters.  Or to put it another way, the benefit of +RES is inversely proportional to the amount of +DEF you have.  Where as the benefit of +Regen is independent, but suffers from artifacts of how the systems are implemented.

 

Against equal level minions with no special abilities, perhaps. However the people tend to up the difficulty settings, mobs do have special abilities (like DDR and autohit), and +Res always reduces the amount of damage you take--its just a matter of how often you're going to take damage and how much when you do.

[Koopak]

+def will always out perform +res on average. This is because there are no ATs capable of 95% resistance, and because resistance only helps against -res, all other debuffs are unaffected. The only exception is against heavy single hits, where bad luck can end you at any time, this is why SR has some resist.

 

Your comment of inverse scaling is confusing me. If I understood it, then its wrong. All three defensive stats stack multiplicativly.

 

Effective Regeneration:

Regen / (1 - resist) / (1 - (0.5 + defense))

 

Effective Health:

MaxHP / (1 - resist) / (1 - (0.5 + defense))

 

Apply caps to above, plug in your values, and you have your definitive durability stats baring debuffs/buffs. This means that, for say a scrapper with a caped max hp of 2400 (real cap is 2409) defense cap brings that to 20 times, or 48000 and a resist cap of 75% will further multiply thag by 4 to 192000 effective health.

 

This is why people tend to suggest "layered defenses" however the equation above means that every 1% of resist or defense is better than the last. As an example 5% defense at 0% reduces damage taken to 90% of prior. Meanwhile 5% defense when already at 40% reduces damage taken by half. Youve gone from 10% of attacks hitting you to 5%.

 

So its almost always worth more to continue to build toward a cap than it is to invest in the other durability stat.

Edited June 19, 2022 by Koopak

[Blackjoy]

9 hours ago, Erratic1 said:

 

Against equal level minions with no special abilities, perhaps.

 Mob level is irrelevant, but obviously anything that decreases the value of +DEF makes other forms of mitigation more valuable.  

 

Remember, the point is to build models that provide insight on what happens. 

 

9 hours ago, Erratic1 said:

+Res always reduces the amount of damage you take--its just a matter of how often you're going to take damage and how much when you do.

Bolded for emphasis.   That's right.  It's a matter of how often you take damage.  So if you're only getting hit 5% of the time.   You're getting almost no benefit from Tough.   If you're getting hit 50% of the time, you're getting benefit from every other attack.  To put it another way, at the +DEF cap,  you're not getting hit enough that Tough is helping your survival on average   Now, Tough might be helpful against AV's or Incarnate mobs that are hitting you a higher clip, but it's waaaaaay more a factor if you're not relying on +DEF.  

 

 

[Koopak]

1 hour ago, Blackjoy said:

 That's right.  It's a matter of how often you take damage.  So if you're only getting hit 5% of the time.   You're getting almost no benefit from Tough.   If you're getting hit 50% of the time, you're getting benefit from every other attack.  To put it another way, at the +DEF cap,  you're not getting hit enough that Tough is helping your survival on average   Now, Tough might be helpful against AV's or Incarnate mobs that are hitting you a higher clip, but it's waaaaaay more a factor if you're not relying on +DEF.  

Okay I think this clarified your point that was confusing me, however I personally don't think this is a very useful fact, even if its true. City of Heroes applies a clamp that ensures that there is always at least a 5% chance for an attack to hit and a 5% chance for it to miss, regardless of stats. This is a call back to the tabletop games that influenced it and their use of the 20 sided die and rules regarding it.

For our purposes this means that one in twenty attacks will hit you, period, no matter what. When calculating durability this means you cannot discount, or ignore, or reduce the value of resistance simply because you have high defense. In a large pack, at agro cap you can safely assume that within 5 seconds you will take between 40 and 80 attacks, this means that at defense cap an average of 2-4 of them will hit. In high difficulty content these hits will be substantial, around 500-1000 damage, this means that you will take between 1k and 4k damage, which the high end of which is enough to flatten even hp capped tankers if you remove resistance.

At the end of the day you simply cant get enough defense for its impact on the value of resistance to matter.

[Blackjoy]

1 hour ago, Koopak said:

+def will always out perform +res on average. This is because there are no ATs capable of 95% resistance, and because resistance only helps against -res, all other debuffs are unaffected. The only exception is against heavy single hits, where bad luck can end you at any time, this is why SR has some resist.

So I feel like this conflates a bunch of concepts and evaluations.  What it seems you're focusing on is that for scrappers, 95% mitigation is going to be better than 75% mitigation. Sure.  But not everyone is at the cap.   What happens when both have the same level of mitigation?   And we need to define "out perform" because performance is contextual.   +DEF will not out perform +RES if the damage is PBAoE.   +DEF does not out perform +RES against AVs/GMs and in teams because +RES gives you more time to react to the incoming damage and benefit from all kinds of stop gap mitigation.    +DEF will not outperform +RES when +DEF can't hit the cap, or when the mobs have +to hit that puts them above the soft cap.  

 

1 hour ago, Koopak said:

this is why SR has some resist.

Yes.  The resists work great against paper cuts and they do provide a much bigger window to use stop-gap mitigation than without them. But the problem for /SR, is that when your +DEF is not working, those resists are usually not effective either.  Specifically when you're facing AVs or non-positional psionic/toxic damage.   The devs added the scaling resists to help /SR in the mid-game, when you're still fighting +0 to +2 and on large teams with lots of minions.  Those scaling resists slow down the incoming damage so you can actually see you're getting low on health.  But go run ITF solo at 4x8 with no +DEF on and see how well those resists work. 😄.   I have been using an IDF 4x8 door mission for a stress test and even with +DEF, they can kill my lvl 50 SR in like 10 seconds...and that's with all kind of set IO/proc +RES tacked on.  And I've seen the same with /SR scrappers who had Tough.  The problem is that they weren't +DEF capping those mobs and in the face of that much spike damage, scaling resist were adding only a few seconds of life.  

 

1 hour ago, Koopak said:

All three defensive stats stack multiplicativly.

I am not coming away with that in my models.  Or maybe I'm confused by what you mean.   Like defenses stack additively.   +DEF and +RES work multiplicatively.  So as Erratic points out, you're only benefiting from +RES when you get hit.   If your +DEF is 99%, you're only getting a 1% benefit from your +RES.    Here's a simple illustration:

 

Let's look at Scrapper RES and Scrapper DEF each with 100 hitpoints.   RES has 50% +RES and DEF has 50% +DEF.   If we say the incoming damage per second is 20.   Then on average, they have the same mitigation and same life span.  

• DEF gets hit (on average) ever other attack, takes 20 points on those hits, so after 2 seconds, averages out to 20 hp/s.  On average, DEF dies after 5 seconds, but it could be longer or shorter (Gaussian distribution around 5 seconds)
• RES gets hit every attack takes half, so after two seconds, takes 20 hps.    After 5 seconds, RES dies, and this is far more predictable than for the +DEF build (because in reality there is still a RNG working the hits).

 

Now, let's add 30% +RES to both. 

• RES is at 80% +RES.  So the 20 dps gets reduced to 4 points.   After two seconds, RES has taken 8 points, an average of 4 per round.  100/4 = 25 seconds it takes RES to get defeated.  A 30% +RES has increased RES' lifespan by a multiple of 5
• DEF gets tricky.   It still is getting hit every other attack (on average), but it's not getting the benefit of +RES when it does not get hit.   So the first second it gets hit for the full 20 minus 30% +RES = 14 points.   The next attack misses.  So after 2 seconds, DEF has taken 14 points, an average of 7 per round.  100/7= 14 seconds.   Huge different despite adding the same +RES to both, when both have the same total mitigation of 50%.  The same +RES boost to DEF only increase the life span by a multiple of slight less than 3.

 

So this simple model shows that while +DEF still benefits from adding +RES, the more +DEF you have, the less benefit you get from that +RES comparatively.  You're much better off adding +DEF to +DEF, if the incoming damage is always affected by +DEF.   You add +RES to give you that "layered" benefit.

 

In engineering terms, adding other forms of mitigation effectively gives you composite mitigation, which is more robust.   The more types of mitigation you have, the better you'll perform on average.   However, that is entirely dependent on the context.  If +DEF worked all the time, then you're don't need other forms of mitigation.  So the game has to throw things out there that +DEF doesn't work against so that other sets can shine.

 

Adding +REGEN  at least by my early models, says the benefit is the same, but +DEF only exist when DEF is below health, so +RES gets more actual benefit.    The reason why +RES benefits more is the same reason as above.  If a +DEF scrapper doesn't get hit....then it's not accruing any benefit from other mitigation.   Let's look at our example from earlier:

• Let's add 5 hp/s +regen to both DEF and RES scrappers instead of adding the 30% +RES
• RES
  • gets hit for 20 pts each hit, mitigates that to 10, and after 1 second, regens 5. RES is taking 5 pts a second.  100/5 = 20 second life span
• The benefit for DEF is tricky.  
  • If DEF gets hit the first attack, it takes 20 in round 1 but gets missed in round 2.  It benefits from +regen both rounds and ends -10 hps after 2 seconds an that averages out to the same 5 /s. 100/5   20 second life span.  Looks to be the same right?

 

But what happens if DEF scrapper's incoming damage follows a different patter, but the same average?

• DEF scrapper gets missed twice in row but then gets hit twice in a row for 20 each hit.   Same average 10 dps over that 4 second span.  But the first two rounds, there's no +regen benefit because there is no damage.  
  • Then next two rounds, DEF regens 10 points total and is left with 30 points of damage after 4 seconds.  That's an average of  7.5 dps.  100/7.5 = 13.3 second life span.   The RES scrapper is lasting 50% longer with the same +regen benefit.

 

It's important to note that as soon as a DEF goes a single round where it doesn't need the +regen, it's performance falls behind the RES.  What's more, is that this is an asymmetrical outcome, or put another way, an upper bound.  DEF will never out perfom than RES and is more likely to under perform. 

 

1 hour ago, Koopak said:

def will always out perform +res on average. This is because there are no ATs capable of 95% resistance

So given my examples above, we have some possible insight as to why the +DEF cap might be higher.  If we find that the same amount of total mitigation of +RES actually outperforms +DEF when combined with other forms of mitigation, then we'd have to give +DEF a higher cap.   Or put another way, +DEF at the 75% cap would not perform as well as +RES does at that same cap due to a variety of factors.

 

1 hour ago, Koopak said:

and because resistance only helps against -res, all other debuffs are unaffected

And given that fact, they devs still put the +DEF cap at 95% vs 75%.   It's possible the +DEF cap is a result of broader game mechanics, where as the RES cap is more specifically ties to AT performance.  I don't know.    But for me, it's informative to understand how these basic forms of mitigation work mechanically when combined and from where I sit, capping +DEF means you're getting less benefit from other forms of mitigation.   Perhaps the only way to balance that is to raise the cap for +DEF.    

 

But, if other sets with lots of other forms of mitigation can all reach the soft cap, then a set that only relies on +DEF, is going to underperform at the high end.

 

Granted, these are simplistic models used to examine basics.  I still haven't looked at how +Heal /+Absorb, +Hit Points fit in these models.  And no where close to understanding +recharge and how debuffs factor into secondary mitigation.   But I do welcome any constructive criticism as to the models I've presented and where you think they might be counter-factual. 

 

Edited June 19, 2022 by Blackjoy

[Koopak]

This is a bit frustrating because your math and examples are correct, as is your understanding of the mechanics at play, but your conclusions are false due to scale. To put it simply you are focusing on the micro, small segments of activity, and attempting to incorporate all edge case scenarios. This results in a very top heavy model that, given correct information will result in the same conclusions, but only after you provide it the correct data, that being the real hp values, real regen values, real attack rates, and real damage values at play.

Extrapolation is key here to remove this, and I start with resolving the first problem I see most people make when talking about calculating durability, assumed damage values. In your example for instance you assumed 20 damage done evert second by a single attack. This normally is fine on the surface, but as you outlined, it makes defense weird to calculate with regeneration due to not regenerating while at full health. This is ultimately a useless piece of information in my opinion however as if you are at max health then the only thing that will matter is your Effective Health for the next attack.

So in order to eliminate variables we do not have, I have rearranged the problem, instead of calculating the 'survival time' of a given amount of health, regen, resistance, and defense, I have instead calculated the total amount of damage necessary to tend one's health down, and how much beyond that must be done to bring that health down to zero, all averaged. This eliminates the need for assumed damage, and attack rates by scaling our calculations to a larger scope. This scope id a bit to large to be 100% accurate, there are after all attacks that can just one shot you (with the exception of one shot protection), but for 90% of situations it is accurate.

 

Addressing your assertion that resistance is reduced in value by defense, I feel you are conflating two details in your example of a 50% def and 50% resist characters. As I stated +30% resistance is more valuable to the +resist character, this has NOTHING  to do with defense however, this is simply the result of exponential growth from linear scaling. I feel that mentally linking the two stats in the way you outline is detrimental to an understanding of the system even if it is, on the the surface accurate that more defense is better as you gain more defense, the same is true for resistance, and its merely a matter of where the caps lie and the costs of obtaining those stats.

They DO scale multiplicatively however and your example does not disprove that, it merely proves what I outlined above, that Resistance and Defense grow exponentially in value the more you have. To reproduce your math in a better model:
 

Effective Health:

MaxHP / (1 - resist) / (1 - (0.5 + defense))
 

DEF only (this is zero +def as the base to hit is 50%)
100 / (1 - 0) / (1 - (0.5 + 0))

200 EHP

RES only (removing base to hit to match your example)
100 / (1 - 0.5) / (1 - (0.5 + -0.5))

200 EHP

 

DEF + 30 RES

100 / (1 - 0.3) / (1 - (0.5 + 0))

285.71 EHP

RES + 30 RES

100 / (1 - 0.8) / (1 - (0.5 + -0.5))

500 EHP

This seems to support your point, but the real issue here is the exponential value, lets look at the reverse, +30% defense added to both.

 

DEF + 30 DEF

100 / (1 - 0) / (1 - (0.5 + 0.3))

500 EHP

RES + 30 DEF

100 / (1 - 0.5) / (1 - (0.5 + -0.2))

285.71 EHP

These EHP values are the amount of damage, on average, that needs to be thrown at you. This extrapolates away attack rates and magnitudes. As we can see the results are the same, this has nothing to do with defense and everything to do with scaling. Again you are right in that an attack that doesn't hit doesn't benefit from the other stats, but its also a 100% mitigation, thus we can treat defense as eliminating attacks. The other benefit to this model over yours is that it handily handles regeneration, easily, again not longer needing to worry over edge cases.

Lets look at that with real numbers on a real scrapper with max hp cap, 200% regeneration, and 25% +defense (plus 50% base) and 50% +resist, these being chosen because on average +defense comes in values roughly 1/2 that of +resistance, for every 1.5% defense you can get you can usually get 3% resistance for similar investment.

 

Scrapper hp cap is 2409, 200% regeneration is 20hp/s.

 

Effective Regeneration:

Regen / (1 - resist) / (1 - (0.5 + defense))

 

Effective Health:

MaxHP / (1 - resist) / (1 - (0.5 + defense))

 

DEF only EHP
2409 / (1 - 0) / (1 - (0.5 + 0.25))

9,636 EHP

 

DEF only EHP/s
20 / (1 - 0) / (1 - (0.5 + 0.25))

80 EHP/s

RES only EHP
2409 / (1 - 0.5) / (1 - (0.5 + 0))

9,636 EHP

RES only EHP/s
20 / (1 - 0.5) / (1 - (0.5 + 0))

80 EHP/s

 

So what does this mean? Well it means that if you are taking 80 dps or less, you will never die. If you are taking 100 dps a second it will take EHP / (EHPs - DPS) seconds to die. Thus...
9,636 / (80 - 100) = 481.8 seconds or 8.03 minutes on average.

Now lets try +10% Resist and +5% Defense respectively, and if you want a time to die, we will assume 200dps

 

DEF + 10 RES - EHP

2409 / (1 - 0.1) / (1 - (0.5 + 0.25))

10,706.66 EHP

 

DEF + 10 RES - EHP/s

20 / (1 - 0.1) / (1 - (0.5 + 0.25))

88.88 EHP/s

 

10,706.66 / (88.88 - 200) = 96.35 seconds

RES + 10 RES

2409 / (1 - 0.6) / (1 - (0.5 + 0))

12,045 EHP

RES + 10 RES

20 / (1 - 0.6) / (1 - (0.5 + 0))

100 EHP/s

 

12,045 / (100 - 200) = 120.45 seconds

 

DEF + 5 DEF

2409 / (1 - 0) / (1 - (0.5 + 0.3))

12,045‬ EHP

 

DEF + 5 DEF

20 / (1 - 0) / (1 - (0.5 + 0.3))

100 EHP/s

 

12,045 / (100 - 200) = 120.45 seconds

RES + 5 DEF

2409 / (1 - 0.5) / (1 - (0.5 + 0.05))

10,706.66 EHP

RES + 5 DEF

20 / (1 - 0.5) / (1 - (0.5 + 0.05))

88.88 EHP/s 

 

10,706.66 / (88.88 - 200) = 96.35 seconds

 

Again we see defense compounding with defense better and resistance compounding with resistance better.

 

Forgive me if this is a bit rambling, i'm struggling to keep all my thoughts in order currently due to work

Edited June 19, 2022 by Koopak

[Erratic1]

1 hour ago, Blackjoy said:

 Mob level is irrelevant, but obviously anything that decreases the value of +DEF makes other forms of mitigation more valuable.  

 

Remember, the point is to build models that provide insight on what happens. 

 

Bolded for emphasis.   That's right.  It's a matter of how often you take damage.  So if you're only getting hit 5% of the time.   You're getting almost no benefit from Tough.   If you're getting hit 50% of the time, you're getting benefit from every other attack.  To put it another way, at the +DEF cap,  you're not getting hit enough that Tough is helping your survival on average   Now, Tough might be helpful against AV's or Incarnate mobs that are hitting you a higher clip, but it's waaaaaay more a factor if you're not relying on +DEF.  

 

 

 

Key word bolded and underlined and only in context of the resistance mechanic (as Tough also provides slotting opportunities for set bonuses should you going that route). Regeneration is not known for its Defense Debuff Resistance. While there are some things which debuff resistance, they are by comparison more rare than things which debuff defense and resistance is its own defense against being debuffed--which is why you do not hear about cascading resistance failure but do hear about cascading defense failure.

 

 When someone says to me, "You'll only be hit 5% of the time" my question is, "How many attacks are going to be incoming at a time and for how much damage?" The first statement is meaningless without the second question being answered. One attack coming in every two seconds for 100 damage is one thing, seventeen attacks coming over the same time period for the same damage is another. It should also be noted that "5% of the time" is an average...maybe a dozen attacks come your way and none hit but then again maybe a dozen attacks come your way and (subject to streak breaker) all of them hit. Resistance, as I noted, always applies to any hit which lands.

 

Quote

Let's look at Scrapper RES and Scrapper DEF each with 100 hitpoints.   RES has 50% +RES and DEF has 50% +DEF.   If we say the incoming damage per second is 20.   Then on average, they have the same mitigation and same life span.  

• DEF gets hit (on average) ever other attack, takes 20 points on those hits, so after 2 seconds, averages out to 20 hps.  On average, DEF dies after 5 seconds, but it could be longer or shorter (Gaussian distribution around 5 seconds)
• RES gets hit every attack takes half, so after two seconds, takes 20 hps.    After 5 seconds, RES dies, and this is far more predictable than for the +DEF build (because in reality there is still a RNG working the hits).

Now, let's add 30% +RES to both. 

• RES is at 80% +RES.  So the 20 dps gets reduced to 4 points.   After two seconds, RES has taken 8 points, and average of 4 per round.  100/4 = 25 seconds it takes RES to get defeated.  A 30% +RES has increased RES' lifespan by a multiple of 5
• DEF gets tricky.   It still is getting hit every other attack (on average), but it's not getting the benefit of +RES when it does not get hit.   So the first second it gets hit for the full 20 minus 30% +RES = 14 points.   The next attack misses.  So after 2 seconds, DEF has taken 14 points, an average of 7 per round.  100/7= 14 seconds.   Huge different despite adding the same +RES to both.  The same +RES boost to DEF only increase the life span by a multiple of slight less than 3.

 

First off, your math is wrong. If you have 100 damage and face incoming 20 dps you would without any defense or resistance last 5 seconds as that is 100 damage / (20 damage/sec) = 5 seconds. You've calculated the RES character only surviving 5s when in fact they would survive 10s. Likewise the DEF character who avoids half the incoming attacks will last twice as long and that is 10s.

 

Secondly, you are not comparing apples to apples here. You're talking about benefits to a regen character but you're comparing added resistance to a character with resistances to added resistance to a character with no resistances but instead defenses. That does not speak at all to the merits of defense or resistance to a regeneration based character.

 

[Erratic1]

3 hours ago, Koopak said:

+def will always out perform +res on average. This is because there are no ATs capable of 95% resistance, and because resistance only helps against -res, all other debuffs are unaffected. The only exception is against heavy single hits, where bad luck can end you at any time, this is why SR has some resist.

 

The starting point is half of all attacks missing--50 attacks out of 100 get through regardless of your protection. At max defense 5 attacks out of 100 get though meaning 90% of the attacks you would have faced with no defense have been eliminated. At max resistance 90% of damage is eliminated but the starting point is half of attacks miss. At max resistance 50 attacks still hit you but for only 10% of the damage, which is the equivalent of 5 attacks.

 

90% resistance is the same as 45% defense as goes applied damage.

 

Yes, defense means other things which might arrive with damage do not apply. On the other hand resistance is its own protection to being debuffed and while you cannot apply more than 90% to incoming damage the full amount counts against being debuffed--so if you build to 100% resist value you will NEVER see your resistance decreased whereas DDR for most defense sets never gets to 100% and there are things in the game which autohit and ignore defense all together.

[Koopak]

31 minutes ago, Erratic1 said:

90% resistance is the same as 45% defense as goes applied damage.

 

Sorry yes this is correct, i cant tell i should probably wait before replying to this discussion further im making some trivial mistakes i should be able to remember and did when making the calculator above.

 

One note is that -def does still effect a character at 100% pre cap resistance since the base to hit is 50% and you can be debuffed to a capped 95% chance to be hit

[Blackjoy]

Apologies, I haven't had time to digest this all, but wanted to respond to some of these points sooner.

 

One thing I should have brought up earlier, and maybe I did, is that I think there are two parts to his topic:  1) How do the secondaries perform empirically, 2) How do people perceive those outcomes?  I do not think there is perfect alignment between how a set can perform and how a set performs in the hands of a player.  I'll come back to this periodically, but just wanted to slip that in to explain some of how I approach this discussion.

 

9 hours ago, Koopak said:

This is a bit frustrating because your math and examples are correct, as is your understanding of the mechanics at play, but your conclusions are false due to scale. To put it simply you are focusing on the micro, small segments of activity, and attempting to incorporate all edge case scenarios.

 

I'm not sure what you mean by "false due to scale."   However, I will say that I am not attempting to incorporate any edge cases.  My goal is to understand and map out the basics., the fundamentals, and then try and understand where it breaks down and does something completely different.  So if I'm making conclusions, it's not about the actual sets, but just about the baseline mechanisms.  The actual secondaries are far more complex and I do no think these models are sufficient.

 

9 hours ago, Koopak said:

This results in a very top heavy model that, given correct information will result in the same conclusions, but only after you provide it the correct data, that being the real hp values, real regen values, real attack rates, and real damage values at play.

I don't think simplistic models I've discussed so far gives correct results because I don't think it comes close to accurately modeling the systems.  I think it does shed light on why Tough isn't nearly as valuable to +DEF scrappers as they think it is, something I've witnesses first hand.   I believe it also provides insight on why adding the same power pools to the different sets doesn't give the same results.  As I'm sure you would agree, if the 5% from something like Weave puts you at the +DEF cap, it's a lot more valuable to you than to someone who is not at the cap.   The underlying point is that power pools may provide asymmetrical benefits to some sets and thus make them look better than they actually are.  As you point out, the +DEF cap for scrappers is higher, so depending on what the game throws at you, +DEF sets may seem to peform look better they actually are because that last bit of off-AT +DEF is actually adding as much survival time as the rest of the set combined.  But this is a bit of digression.

 

9 hours ago, Koopak said:

I see most people make when talking about calculating durability, assumed damage values

Sure.  "assumed damage values" are used to study a specific aspect of the mitigation.   As I believe you and I agree, there are too many variable to do this computationally, the truth has to come from statistics.  But as I said before, my approach it so break it off in chunks and try to understand the pieces and see how/if that provides insight on the larger problem.  

 

9 hours ago, Koopak said:

This normally is fine on the surface, but as you outlined, it makes defense weird to calculate with regeneration due to not regenerating while at full health. This is ultimately a useless piece of information in my opinion however as if you are at max health then the only thing that will matter is your Effective Health for the next attack.

Naturally I disagree.  Part of that is the different mitigation model we are using.  You're coming at it from the Effective Health approach and I'm looking at it from the Survival Time approach.  Knowing that IH is best when I'm below health means I can probably buy more seconds by popping it after the fight starts and I've started taken damage.  It means I will hold off on using Recon or DP to bring me to full health...and save those for counter-acting spikes or save them for when IH stops.  

 

9 hours ago, Koopak said:

I have rearranged the problem, instead of calculating the 'survival time' of a given amount of health, regen, resistance, and defense, I have instead calculated the total amount of damage necessary to tend one's health down, and how much beyond that must be done to bring that health down to zero, all averaged.

 

I totally get why this seems a fruitful approach.  You're 100% right that the "I win" equation is dependent on information I don't have and is hard to get.   But, at least for me, it represent the most accurate model of what I am trying to understand, especially in how it speaks to the players concepts of "performance."    I've also not had much success identifying a robust transformation for the different mechanics.   I haven't looked closely at your models, so it may take me some time to wrap my head around them. 

9 hours ago, Koopak said:

Addressing your assertion that resistance is reduced in value by defense

So I may have phrased it like that, but that's no the intent.  The point I'm trying to make, which I believe you agree with, is that stacking different forms of mitigation isn't the same as stacking the same form of mitigation.  And when a set like /SR says it maxes out at 60% +RES, that's not the same as getting 60% +RES on a +RES based secondary.  

 

9 hours ago, Koopak said:

As I stated +30% resistance is more valuable to the +resist character, this has NOTHING  to do with defense however, this is simply the result of exponential growth from linear scaling

You're disagreeing with me for a reason that agrees with me.   +DEF and +RES don't combine to scale linearly is exactly the point.  Both can start out with 50% mitigation, but adding more +RES or +DEF will only stack linearly with itself.   However...+RES and +REGEN do stack linearly where +DEF and +REGEN have an upper bound and will under perform.   So it has everything to do with the mechanics of +DEF:  Mitigations that are dependent upon the character getting hit/taking  are totally curtailed by +DEF when +DEF applies.   Everyone benefits from more mitigation, but some stack linearly and some don't.

 

I'll look over the rest later, but enjoying the exchange.

Edited June 20, 2022 by Blackjoy

[Koopak]

Okay lets see if i cant keep my thoughts together today.

 

21 hours ago, Blackjoy said:

1) How do the secondaries perform empirically, 2) How do people perceive those outcomes?  I do not think there is perfect alignment between how a set can perform and how a set performs in the hands of a player.

That is just a fact that players wont perform a set to its optimal potential unless it is one of the sets that is just a series of toggles with no room for skill expression.
 

 

21 hours ago, Blackjoy said:

I'm not sure what you mean by "false due to scale."   However, I will say that I am not attempting to incorporate any edge cases.

21 hours ago, Blackjoy said:

I don't think simplistic models I've discussed so far gives correct results because I don't think it comes close to accurately modeling the systems.  I think it does shed light on why Tough isn't nearly as valuable to +DEF scrappers as they think it is, something I've witnesses first hand.

21 hours ago, Blackjoy said:

Naturally I disagree.  Part of that is the different mitigation model we are using.  You're coming at it from the Effective Health approach and I'm looking at it from the Survival Time approach.  Knowing that IH is best when I'm below health means I can probably buy more seconds by popping it after the fight starts and I've started taken damage.  It means I will hold off on using Recon or DP to bring me to full health...and save those for counter-acting spikes or save them for when IH stops.

21 hours ago, Blackjoy said:

However...+RES and +REGEN do stack linearly where +DEF and +REGEN have an upper bound and will under perform.

 

When I said it is 'false due to scale' and 'edge cases' I was intending to refer to your note on how Regeneration does nothing while at max health. This complication simply doesn't yield useful, actionable information. This is because if you are under an amount of fire sufficient to need the use of your survival tools, you will not be at max health for more than a game tick or two. As such your regen is disabled for a very small amount of time, often less than the regeneration tick rate. Further trying to model this element requires simulation, not just computation.

All of this combines with relatively high damage spikes compared to Effective Health in the game such that often using a power like Instant Healing on reaction rather than proactively will simply get you killed as the time it takes for you as the player to process you need to use the power, and then physically start the activation, and then for that power to complete casting, and in the case of +regen powers, for it to tick enough times to save you.

 

21 hours ago, Blackjoy said:

My goal is to understand and map out the basics., the fundamentals, and then try and understand where it breaks down and does something completely different.

21 hours ago, Blackjoy said:

But, at least for me, it represent the most accurate model of what I am trying to understand, especially in how it speaks to the players concepts of "performance."

 

The problem with this is the model you have chosen, while it yields a seemingly intuitive result, a 'Survival Time' it's actually misleading. This is because a Survival Time is actually a largely useless piece of information without an accurate damage model, and, preferably, a target survival time. Sure you can focus simply on getting this value as high as possible, but that doesn't yield valuable insights in my opinion as every stacking source of defense, resistance, and regeneration modifies the Effective Regeneration and Health contributed by every other source. Further this shift is not easily visible, since the result is considered in seconds. I feel quite certain this 'Survival Time' model is the source of a significant amount of misunderstandings on the actual durability of Regeneration specifically.

If your goal is to understand the fundamentals, then I assure you they are exactly as simple as the model I outlined, it is only when factoring in player performance and edge case attack types that it changes.
 

21 hours ago, Blackjoy said:

I think it does shed light on why Tough isn't nearly as valuable to +DEF scrappers as they think it is, something I've witnesses first hand.

 

I cant speak to the degree to which one person or another may have argued with you but I will say this. Most Defense sets reach defense caps to either all damage types or to the three positions very easily, and almost never have +MaxHp.  As such Tough becomes a critical source of Resistance to reduce the risk of a bad luck streak resulting in their death or as simply the only path forward in durability after hitting the defense cap. I would definitely agree that for many defense based armor sets, Tough is a key power to making the build able to handle tough customers like AVs or to solo +4 Incarnate content, especially if the player is not comfortable with Rune of Protection.

 

 

Alright I think that about covers my main points. I want to apologies if I came off a bit antagonistic. Keeping my thoughts together lately has been hard, which is a lot of why I have Brute added to the spreadsheet but not Stalker despite Stalker being about as easy to implement.

[SomeGuy]

this thread is pretty lol

[Gobbledygook]

Is it possible to add the Incarnate powers that effect Regen, Def, and Resist. In the case of the Destiny powers, just showing the base that is added. I.E. Rebirth Radial Epiphany gives a constant 200% buff for as long as it is active.

[ScarySai]

Isn't rebirth's regen still bugged?

[Gobbledygook]

No clue, haven't played in about 6 months.

Working on that Rad/SS Tank you inspired.

Is it bugged in game, or Mids.

[ScarySai]

Couldn't tell you, it's only something I've heard about and haven't experienced, since I don't really use rebirth ever. Something about it is broken and makes it not useful/a detriment.

[Bill Z Bubba]

12 hours ago, ScarySai said:

Couldn't tell you, it's only something I've heard about and haven't experienced, since I don't really use rebirth ever. Something about it is broken and makes it not useful/a detriment.

 

Don't know if this helps but I logged on my shield/nrg tank that bounces between Ageless Core and Rebirth Radial.

Regen without rebirth is 37.15 hp/sec.

Click rebirth, goes up to 240 hp/sec then cycles down through 113.22 hp/sec, 87.86 hp/sec, and 62.50 hp/sec where it stays until it drops.

Seems to be workin just fine.

[ScarySai]

I remember what it is now, regen resist actually resists Rebirth Radial's regen buff.

 

So if you're playing a set like regen or rad, or someone near you pops ageless, not great.

[Koopak]

On 7/1/2022 at 10:22 PM, Gobbledygook said:

Is it possible to add the Incarnate powers that effect Regen, Def, and Resist. In the case of the Destiny powers, just showing the base that is added. I.E. Rebirth Radial Epiphany gives a constant 200% buff for as long as it is active.

Hey sorry I haven't been on the forums for a bit, IRL got messy. That is on my goals list for this project, I just haven't prioritized it because things like Alpha get super messy and may need structural changes. If I recall I don't even have the regeneration cap implemented at this time, which Rebirth Radial in conjunction with Instant Healing will actually let you hit, just as an example.

It's on the to do list though.