Attack Chain

[Boon]

Is there anyone that can tell me how to calculate an attack chain, like is there a mathmatical formula that takes all the variables or what, I am wanting to learn how to do it myself so I don't have to ask and optimal attack chain for x or y.

 

[Werner]

Current Mids can be configured to show Arcanatime as the Cast time. It's not technically the Cast time, but as far as attack chain calculations, that's the number you want to use. I don't know if this is the default setting. In any case, it makes the calculations easier.

[Murcielago]

1 hour ago, 5099y_74c05 said:

@BoonI would repost under the Scrapper section if you are not getting a response here. With all the number cruncher min-maxers on the forums I am actually surprised this hasn't been answered for you. I can give you a general answer, in truth it can get very complicated depending on the powersets, IO Sets and procs involved. I believe the optimal chains have been calculated so you can check the math there (found the thread):

 

You can also check the old forums Player Help, Scrapper and Brute sections:

https://web.archive.org/web/20120904103849/http://boards.cityofheroes.com/forumdisplay.php?f=550

 

To answer your question lets get a few terms out of the way first:

• Cast Time (CT) - The time spent activating a power
• BaseRechargeTime - The unmodified time required to pass before the power can be available to be recast again. The timer typically doesn't restart until the full cast time has been completed. For toggles the timer starts after de-activation.
• Damage per Activation (DPAct) - The damage of the attack per activation.
• Damage per Animation (DPAni) - DPAct/Cast Time. As it is named in Mid's/Pine's tool. This is what most people mean when the use DPA.
  •   Note article uses Damage per Activation but means Damage per Animation: https://paragonwiki.com/wiki/DPA
• Modified "Recharge Time" (Mod RT)- The recharge of the power after buffs and enhancements
  • RechargeTime = BaseRechargeTime / ( 100% + Buffs - Debuffs )
  • The recharge mechanics are discussed here; worth the read: https://paragonwiki.com/wiki/Recharge
• DPS article for reference: https://paragonwiki.com/wiki/DPS

Generally speaking and with exception, you want to build a endless chain using your highest DPAni attacks possible. This will typically mean you want the uptime (Modified Recharge Time) of the longer charging power to fall within the sum of the "Cast Times" of the other powers in the chain. Here is an example of this.

 

You have determined powers A, B , and C are your highest DPAni attacks. Attack [A] has the longest Modified "Recharge Time" of 5s. In this situation you want the sum of  B +C  Cast Times to be 5s or longer. So Mod RT A < (CT B + CT C).  For a seamless attack chain you want the same to be true for the other attack as well such that Mod RT B < (CT A + CT C) and Mod RT C < (CT A +  CT B) is true.  **Note it is possible to have an attack chain with gaps, in these situations you will have to calculate your DPS instead (Check the article for the math). I don't know of a specific situation where this is optimal in-game I am just noting it is possible. In situations with gaps in your attack chain, you can begin to consider bringing in an AoE attack to fill out the chain, I think in cases such as Titan Weapons and Spines, some of the highest DPS chains include AoE attacks (I could be wrong)

 

So how does it get more complicated? Well some sets have -RES attacks or a -DEF attacks that can slot -RES procs. While these powers are typically a DPS loss (lower DPAni) the overall -RES Debuff can improve the DPS of your whole chain; at least by 10% but often+30% or more in some cases. The Brute ATO proc is another to consider; for specifics optimal slotting was discussed in a thread here on these forums. Regarding other damage effect procs, I don't know how valuable they are to Brutes since you have a high DPAni on most attacks. As a general rule of thumb I probably would only look at damage procs once you hit ED numbers on damage. You should evaluate this on a case by case basis. Unless its the FF proc, you can make an argument for slots to be used elsewhere instead of procs in most cases  Search these forums for  PROC, PROCS, or PPM to understand how procs are working. Bopper, among others players, is the player doing a lot of the PPM related posting; there is also an very informative proc thread on the Defender forum section.

 

So how do you figure out your highest DPS chain?:

 

• Evaluate your powers to identify your highest DPAni attacks (if no procs are involved you can safely use Mids/Pines)
• Determine if it is feasible to get the recharge necessary to achieve the chain, basically determine if you can have a gapless attack chain.
• If its is not gapless, calculate DPS instead. **This should be a rare situation and most likely is not optimal

 

If you are trying to build a model with greater fidelity you will want to account for Accuracy, To Hit Buffs, Arcanatime and Endurance per second (EPS) as well. This will give you a closer value to actual in-game DPS. What I provided is information needed to determine the optimal potential of a set; there are certainly exceptions that require special additional considerations not outlined in my post.

 

Other notable articles or posts:

• Arcanatime by Arcanaville: http://web.archive.org/web/20120904191140/http://boards.cityofheroes.com/showthread.php?p=810428

Attack Mechanics: https://paragonwiki.com/wiki/Attack_Mechanics

Hopefully this helps you. Feel free to point out where the information provided is not accurate. Good luck!

I have nothing to add other than to say this is a well formatted post. 

[Werner]

And I almost feel like I should apologize for not answering the question. I saw it and thought about answering, but knew a good answer would take more time than I had to give. Fortunately 5099y_74c05 took the time and gave probably a better answer than I'd have given. 🙂

[Bopper]

There is nothing I can say that Soggy Tacos did just cover in absolute excellent detail. As for finding an optimal attack chain, that's some serious calculus... you have to think about so many things. Base damage, cast/arcana time, recharge time, proc damage, buffs, debuffs, etc. On top of that, you have to think about practicality. For instance, how long can you do your attack chain before you need to do something else (buff, taunt, heal, whatever)? How much does that interruption disrupt your chain? So much to consider.

 

Honestly, try to focus on making a good attack chain as a starting point, then try to grow from there, piece by piece.

 

If you would like help as a starting point, tell us your build/AT, and some of us can try to theory craft some ideas for you. But seeing as how you're aiming more for a "teach me how to fish", perhaps the best advice is simply to practice. Something that helped me was to build an excel sheet that could do the calculations for me. I put in all the information of each power I could pick (base damage, recharge, etc), then I type a chain (for Sonic Attack, I might type into 4 cells: Shriek, Shout, Shriek, Scream). My spreadsheet pulls the info of those powers into a formula that calculates the required recharge for each attack to keep it gapless (if it requires more that 400%, it calculates the gap time). I then plug in values for damage boost, resistance debuffs, proc damage, etc to try to calculate the effective DPS. 

 

Truth is, that's too much work. But that is what I did to get myself to start thinking about how to optimize attack chains. It helped me realize how to identify my bread a butter attack, then go from there, adding things into the attack chain that keeps my DPS up while still trying to get back to my bread and butter attack as soon as possible.

[Sir Myshkin]

There used to be a program floating around back in the old days called "NoChain," but I can't for the life of me find the zip library for it anymore or where it was originally linked from. That program would pull the highest DPA attack and try and cycle down the list down to the most optimal chain right out of the gate. Pretty neat tool. If anyone still has a packaged version of that, we should get that back out into the wild again.

 

[Werner]

14 minutes ago, 5099y_74c05 said:

Did you post under "John**something**" on the old forums?

John Printemps, if I recall?

[Sir Myshkin]

11 hours ago, 5099y_74c05 said:

I think that is it!

Yup. And I dug around in the archives a bit trying to see if it was on the surface somewhere, but searching through those archives is quite a task when the actual forum search function doesn't really work. Going page by page is an incredible chore, but IIRC it gets mentioned somewhere in the Pylon thread for Scrappers, but that thing is like 300 pages long and covers a lot. All I can say is I don't remember seeing a link to it in the last ~20 or so pages when I went there looking for something else a couple months ago.

[Werner]

How about I give an example, a basic flow of thought of me trying to figure out a good attack chain. I've never looked at Street Justice before, so let me work with that.

 

Pull up Mids. Options -> Configuration -> Effects & Maths -> Use ArcanaTime for Animation Times (if it isn't set). Brute. Street Justice. Window -> Power Graphs -> Damage / Anim. Now I'm looking at a graph of all the attacks, and their basic damage per ArcanaTime, which is a very good initial pass at the relative amount of DPS they'll contribute. That's where I'd probably start every time.

 

Crushing Uppercut is the clear winner, followed by Shin Breaker. After that there's a bunch with similar DPS. Heavy Blow is best of the rest, but I bet the best chain will come down to using Crushing Uppercut and Shin Breaker as close to the recharge maximums I can get as possible. However, there may be special considerations for why I might want to include specific other attacks. So maybe it's time for me to look at the attacks themselves. 

 

Ah, hmmm, a combo system, huh? All right, Crushing Uppercut is a combo finisher, combo level 1 or 2 increases disorient, 3 turns it into a hold. It also does knock up. OK, but that's active mitigation, not DPS. Still, I'd probably rather a hold than disorient. I hate my enemies wandering around. So now my goal is probably Crushing Uppercut at recharge limits with combo level 3. Recharge is 25 seconds. Eeesh. This build wants recharge, recharge, and more recharge, and you're still looking at a long attack chain. So let's say we're running a very high recharge build, with Agility Core, perma Hasten, and Ageless. Let's estimate for now that we can get up to 350% recharge in Crushing Uppercut, taking it to 7.14 seconds of time we have to fill with lesser attacks. In that time we want to get to a combo level 3 and spam as much damage as we can, but waste not much more time than 7.14 seconds on the lesser attacks. 

 

Cast   Rech    
2.376  7.14  Crushing Uppercut, knockup, finisher

 

How about Shin Breaker? Recharge 8 seconds, 1.584 seconds ArcanaTime, adds 1 combo, has -7.5% defense so can slot an Achilles Heel for -7.5% resistance as well. Very nice. At our super high recharge, we'd expect it to come back in 2.29 seconds. So the hope is to use it twice. (1.584 + 2.29) * 2 = 7.748, so that's good timing for Crushing Uppercut. Well, Crushing Uppercut is one of those 2.29s. So we just want to fill one more. Except that wouldn't allow enough for Crushing Uppercut to recharge. Anyway, now we have a fairly awkward time we want to fill. And I'm being premature because I really should see what the other attacks have to offer before even halfway committing to anything.

 

Cast   Rech    
2.376  7.14  Crushing Uppercut, knockup, finisher
1.584  2.29  Shin Breaker, +1, -7.5% def, -40% speed, AH proc

 

We're forced into Initial Strike or Heavy Blow, so those are of particular interest to me as I don't like taking more attacks than I have to. Initial Strike is a basic light fast attack with a disorient. It won't fill our gap without help. Heavy Blow is also a basic light fast attack, but with knockdown. I prefer knockdown, both in terms of damage mitigation, and perhaps slotting Force Feedback since recharge looks so critical to our performance here. It's kind of looking like Shin Breaker -> Heavy Blow -> Initial Strike -> Shin Breaker -> Heavy Blow -> Initial Strike -> Crushing Uppercut at this point, but we haven't even looked at the other powers yet, and that chain "wastes" combo points. Sweeping Cross is a cone and a finisher. Meh. Rib Cracker is a 7.5% resistance debuff for 13.6 seconds, OK, now we're talking. 1.584 seconds, 6 second recharge, or about 1.71 seconds in our proposed high recharge build, also a combo builder. We'd really like to spam that one too. 

 

Cast   Rech    
2.376  7.14  Crushing Uppercut, knockup, finisher, disorient or hold
1.584  2.29  Shin Breaker, +1, -7.5% def, -40% speed, AH proc
1.584  1.71  Rib Cracker, +1, -7.5% res, -11.25% dmg

 

Spinning Strike is an AoE. Probably not. OK, so we basically want to spam those three attacks. Can we make a chain of just them? I'm not seeing it. There's just not enough recharge. 

 

And now I've become more curious about what procs I can put in Crushing Uppercut. With its long recharge, I think that gives us good proc chances. Well, if we're using Crushing Uppercut in its finisher role for the hold, Lockdown has a chance for 2 hold, so then probably it's a 4 or 5 hold? I don't know if that's helpful. What does it take to lock down bosses? I'd have to research. Hello, paragonwiki. OK, it takes 3 to lock down a boss. So what's the power itself got? Mids isn't telling me. Probably 2 or 3. If 2, a hold proc would be nice to lock down bosses. If 3, we're already there. Anyway, problem for another day - we're talking about DPS, not active mitigation. It'll take a Force Feedback proc. Might be a good place for a purple proc as well. 

 

OK, so I think what I need is one more attack. I think I need to go Shin Breaker -> Rib Cracker -> ????? -> Shin Breaker -> Rib Cracker -> Crushing Uppercut. And I want to minimize the time spent on that extra attack while getting some sort of useful benefit. Well, the minimal time attack is Initial Strike at 1.056 seconds. And that's plenty of time added to allow Shin Breaker and Rib Cracker to recharge. How about Crushing Uppercut? 1.584 + 1.584 + 1.056 + 1.584 + 1.584 = 7.392, and Crushing Uppercut is recharging in as low as 7.14 seconds. Perfect, but Heavy Blow at 1.32 seconds is a perfectly good option, with slightly better DPS itself, and a longer recharge to help make procs in it work if any, and it does knockdown so can take a Force Feedback proc where Initial Strike won't, and I prefer knockdown to disorient. So it looks like we have our winner.

 

Shin Breaker -> Rib Cracker -> Heavy Blow -> Shin Breaker -> Rib Cracker -> Crushing Uppercut

 

Cast   Rech    
2.376  7.14  Crushing Uppercut, knockup, finisher, disorient or hold, FF proc, maybe damage or hold proc
1.584  2.29  Shin Breaker, +1, -7.5% def, -40% speed, AH proc
1.584  1.71  Rib Cracker, +1, -7.5% res, -11.25% dmg
1.320  fast   Heavy Blow, +1, knockdown, FF proc

 

I don't want to count on Force Feedback to run gapless, so let's see where we stand on required recharge. 

 

Shin Breaker = 8 / (1.584 + 1.32) = 276% recharge
Rib Cracker = 6 / (1.584 + 1.32) = 207% recharge
Heavy Blow = totally no problem
Crushing Uppercut = 25 / (1.584 * 4 + 1.32) = 327% recharge

 

So we have our work cut out for us on recharge, but that is a number we can hit. Figure 100% base + 100% enhancement + 20% Agility + 10% Ageless + 70% Hasten + 42.5% from 5 Luck of the Gamblers and you're there. You're past there.

 

Is it the best chain? I don't know. So let's see what other people came up with. Mind you, that might be the place to start, but I like to do my own thinking, and the whole point was to show the thinking, not just give the answer. So I'm looking at the spreadsheet that has chains at 275% and 200% recharge. We're rocking a required 327% recharge for our chain, but let's see what we see. OK, the 275% chain they picked was my chain with an extra Heavy Blow to reduce the recharge required for Crushing Uppercut. That's a good sign, and that's a good idea for if we're recharge debuffed - just throw an extra Heavy Blow in there. How about the Pylon damage thread in the Scrapper Forum? Anyone using Street Justice? There's a Stalker, but Assassin's Strike throws everything off. Ah, a Scrapper, that's better. Built by Nihilii. That's good too.

 

Shin Breaker -> Rib Cracker -> Moonbeam -> Shin Breaker -> Rib Cracker -> Crushing Uppercut

 

Moonbeam? Otherwise the same chain, but with Moonbeam instead of Heavy Blow? Huh. Well, we don't have access to Moonbeam on our Brute, but it points out that we should look at our Epic pools just in case there's something that would fill the role even better than Heavy Blow. But I'll call it good enough for now. If it were my character, I'd probably do the due diligence of checking out every possible attack going where Heavy Blow is now, but I'm also betting that we're right we want to be.

Edited August 11, 2019 by Werner

[Werner]

A few more thoughts:

• An optimal attack chain doesn't always mean the highest DPS.
• It's good for the chain to have a simple rhythm your fingers can follow without thought.
• It's good to use fewer attacks where practical.
• It's good for the chain to provide some active mitigation.

On my old Katana/Dark Scrapper, I took simple rhythm and fewer attacks further than most people would, skipping the two big hitters and going with Divine Avalanche -> Gambler's Cut -> Sting of the Wasp -> Gambler's Cut. It lowered my DPS, but saved a power pick and five slots, stacked my melee/lethal defense a little better, was trivially simple to get right under pressure, and the knock up/down of the big hitters wasn't going to help much against AVs, my then prey of choice.

 

I can imagine skipping Crushing Uppercut on a Street Justice Brute, and having a chain this simple:

 

Shin Breaker -> Rib Cracker -> Heavy Blow

 

As with my Katana/Dark, I doubt many people would do this, but it saves a power pick and slots, and it makes for a trivially-simple chain and no mistakes under pressure. I also prefer knockdown to knockup. I don't like having to reposition to stay on an enemy I just knocked up. I think faster attacks build Fury faster. You'll get more resistance debuffs out of it. I can't imagine it's enough to equal the DPS of using Crushing Uppercut, but it'll at least help ease the sting of losing it. I would personally give very serious consideration to that simpler chain, probably coming up with top end builds with and without it, and comparing both DPS and survivability before committing.

Edited August 13, 2019 by Werner

[arcanaville]

I'll toss this out there as a related idea I was processing right up to shutdown.  I had made the big defense spreadsheet where I tried to score defensive sets based on their survivability, using reasonable assumptions.  It wasn't perfect and real world combat was highly situational, but it was an interesting and useful metric nonetheless.  Could I do the same thing with attack sets?

 

The problem boiled down to the fact that to a first order approximation we can assume all defense powers are always on.  Even things like heals can be estimated by averaging their heal out over time, as if they were a constant regen power that was always on.  We could *roughly* estimate the strength of the set in a time-invariant way.  But attack powers aren't like that, because of attack chains.  It isn't possible to simply assume all attack powers are contributing an average amount of DPS all the time.  Once your chain is full, no other powers "matter."

 

Long story short: I came up with a metric that tried to roughly guestimate how much damage an attack set could generate by using a rough heuristic.  We start by taking all the attack powers and sorting them in descending order by DPA - using "Arcanatime" for the DPA.  Basically, we assume that our highest DPA attack is being fired as often as possible, and then we assume that we will try to "fit in" our nest highest, and then our next highest, and so on.  If we have AoEs, we assume a certain average number of targets, like three, and calculate as if that AoE was a single target attack with three times the damage.

 

Every attack has a DPS - a damage per second - over its total cycle time (recharge + cast time).  If you use the attack as often as possible, that's how much damage it will do over time.  If we start with the best DPA attack and work downward, we will add more and more DPS, but if we add everything we will be adding up attacks that take up more than 100% of the time - they won't "fit" into a real chain.  So we calculate the attack's "uptime" which is Arcanatime / CycleTime.  In other words, this is what percentage of the time you're "attacking" when you cycle that attack over and over.  If you use an attack with one second arcanatime and ten seconds cycle time, you're "attacking" 10% of the time.  The rest of the time you can use other attacks.

 

So keep adding up attacks until the cumulative total uptime is 100%.  If you reach 95% and the next attack would take up another 10%, prorate - add half that attack's DPS to your running total.  That's metaphorically like using the attack only some of the time.

 

You now have a list of attacks which are your best DPA attacks (with one "fractional" attack) that you could theoretically cycle constantly, and when you do you will do the total DPS of that set of attacks.  This doesn't match reality perfectly, because in practice those attacks won't necessarily form a perfect attack chain.  But it gives a kind of rough estimate for the theoretical maximum damage output of the set under theoretically optimal conditions.

 

PS: finding the optimal attack chain is probably a knapsack problem, which means there's no likely way to find it outside of a full search of all possible attack chains.  That's why estimates like the above could be useful.

[Werner]

2 hours ago, 5099y_74c05 said:

Interesting. I vaguely remember a contentious "Immortality" thread on one of the melee forums. I think it was you or Lumina(sp??) that put together a framework used to evaluate the melee defensive sets.

I don't remember an immortality thread, and you weren't talking to me, and this surely isn't what you're referring to, but I do remember one of my survivability spreadsheets getting reworked by someone, I no longer remember who, and posted online somewhere, I no longer remember where. But the basic idea is relatively straightforward. Assign percentages to all of combinations of damage types and vectors. Calculate the % of each combination that gets through your resistance and defenses. Weight those percentages for a weighted average. Add up all your means of recovering hit points and convert to an average hit points per second. Divide by the % of damage that gets through. You now have a survivability number that roughly reflects the DPS that you can survive indefinitely. And it's easy to plug in a 50% or 64% base chance to hit to see regular vs. incarnate performance. It doesn't take a number of important factors into account (status protection, for example), and it's difficult to avoid apples to oranges comparisons. But I do use it for fine tuning a build once I think I have a fairly good foundation. I don't follow it blindly, though, even when exploring small changes. But I find it more useful than having nothing but an intuition about how changes will affect my survivability. 

 

I never tried to score defensive sets in a vacuum, though, only specific builds. I wouldn't think the numbers for a defensive set would have much meaning on their own. I'm going to be adding pool powers, incarnate powers, and a ton of set bonuses to that base. The final result won't much resemble where we started, even if that starting foundation determines which direction and how far I can go.

 

But I guess I'm straying off topic now.

Edited August 14, 2019 by Werner

[Boon]

I want to thank everyone for their responses, I will admit my post on the general forums asking this same question and the response was rather disheartening. I am so thankful to everyone that took the time out of their day in order to share their knowledge and answer my question.

 

[Pyro Technix]

In case anyone else is looking for the "NoChain" and other DPS sheets mentioned by Sir Myshkin (John Printemps), They are provided as links (by him) in the thread he mentioned here. They're more elegant than the spreadsheet I quickly threw together for myself. I haven't been up to date on CoH the last couple months so I'm not sure if there is another tool aside from Mid's Reborn DPS Calculator that incorporates correct PPM. It shouldn't be too difficult to link the sheet with macskull's excellent proc calculator which is mentioned here. Hope this helps if someone else was lurking the sleeping thread