Back to Back Attacks with Large Mana Pools

Discussion in 'General Archive' started by _Baragain_, Jul 7, 2015.

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  1. _Baragain_

    _Baragain_ Living Forum Legend

    Good afternoon my forum stalkers. Up to this point, I've kept my math restricted to the DK part of the forums with an analysis of 2H weapons and nice shields. While both of those have applications to the other classes, I primarily focused on DKs. Today however, a friend has asked me to look at back to back attacks with large mana pools, specifically "Lighting Strike."

    The question seemed simple enough on the surface... "How many lighting strikes can I do back to back?" The thing is that it is not so simple below the surface. It involves the size of the mana pool, the regen rate, the attack speed, the mana cost of the attack... and to make matters worse, you regen mana while you attack making this an iterative/recursive problem to solve.

    Please note that these calculations are based on continuous speed, not speed break points due to the fact that no one has calculated the speed break points for Lighting Strike

    Fist, for my fellow math lovers, my methodology. If math does not interest you, skip to below the spoiler box
    First, I began by defining my constants. These include the Base mana (100 mana), base regen (13 mana/sec), mana gained from items/gems, mana regen from items and sets, any % mana bonuses (ex Warlord, or Wolf Book), attack speed, and cost of the move in question.

    From here, I calculated the number of attacks you could fire off before depleting your mana pool, not accounting for regen. I used a FLOOR() function to round that down to the nearest whole attack.

    This and the attack speed were used to calculate the time it took to make those attacks. This too was rounded down with a FLOOR() function.

    That time allowed me to calculate how much mana regen'ed during those first set of attacks. This was then added to the mana that was remaining after the first set of attacks.

    This process is then repeated iteratively using the remaining mana, the remaining partial second from the first set and the calculations continued.

    Seen here is one full set of calculations based on the numbers said friend provided.
    I've also provided the formulas so that you can see the numbers that go with this process.
    [​IMG]

    You can see that through the use of floor functions, that you reach a point where they just come out to 0 and stop adding. Also, this functions like a half life equation so you rarely need more than 3 iterations to reach the end. Seen below is an extreme case where you have Grimag's torso (LVL 50), 2 Rings of Inner Fortitude (LVL 50), and 5 Solstice Stars. Remember, the slower the weapon and the more mana you have, the more time that this process has to iterate. Even under this extreme case, you are still converged to 0 for the last "Attacks with regen pool," in 3 iterations.

    [​IMG]

    Now that I have board you all to tears, lets start seeing what this means.

    Mods I hope you don't mind, but I'm going to break this into a couple of successive posts due to length to make it a little less unwieldy. If you feel you must, I guess you can merge them.

    --MERGED--

    Part two:
    Let see a couple of examples:

    So what does this mean for your SWs?

    Lets see three examples based on my friend's provided stats and Lighting Strike (LS).

    A little help reading these charts:
    Blue has to do with Mana.
    Green has to do with Mana regen.
    Yellow has to do with attack speed and time to execute a set of attacks.
    Red is attacks used.

    This is the stats that were given to me.
    [​IMG]

    As you can see, they can use four back to back lighting strikes before having to pause/switch attacks or telaport to replenish their mana pool. However, you may also notice that they have 48 mana after those 4 attacks are fired off due to the regen that happened in the approximately 3+ seconds that it took to use LS 4 times. Also notice that there is a remainder of 0.39 seconds after the first set of LSs. That means waiting 0.61 sec, and there would be another LS ready to go. On the other hand, if they were impatient (want to telaport immediately following their 4th attack), they could stand to lose a fair amount of Mana and it would not impact their final attacks. Seen below is their same build, only without the two solstice stars. These could then be replaced with something more useful like Jewel of rage or Onyx Skull, or Jewel of Immunity.
    [​IMG]

    You could think of this as almost like a "Mana Breakpoint." That is, mana gains that don't break those barriers allowing another use of the move in question may not help as much as some other item.

    Also interesting to note between the above two images, you are still looking at the same 0.61 seconds until the next regen amount is credited, but that would only get you to 49/50 needed for another LS, meaning you would need to wait another second, or 1.61 seconds, to get off a 5th lighting strike.

    Lets look at one more.
    Here we see what happens if we only take off one Solstice Star.
    [​IMG]
    You still see 4 LS back to back. However, if you wait that 0.61 second now, you will still get that 5th LS (56/50 mana), like in case 1, but you've managed to remove one Solstice Star to be replaced with a different gem that better helps the build.


    See, isn't math fun!:D

    --MERGED--

    Part 3:
    Fun with charts.

    Unfortunately, because there are no know speed breakpoints for LS, I've just picked a couple of landmark speeds to give you an example of what is possible. This doesn't tell you how close you are to being able to use another LS following your last consecutive one, but it gives you a rough idea.

    Worth noting is that some of theses numbers are not possible due to the items required to reach the point not working together. For example, to reach max regen, you'd have to use the "Bone Pauldrons," but that wouldn't work with the Warlord set to get the 30% Mana making the 300/19.5 number impossible to reach for a 0.83 speed build. Many others like this exist, so I leave it up to you to use this chart as best as you can to help you look are truly possible builds.

    Up first is my chart for 0.83 Attack Speed.

    [​IMG]
    I can not think of any build that could result in 300/17 as using two Rings of Inner Fortitude would also push you up to about 1.00 attack speed, but if you could make a build like that (Maybe with Grimag's torso at LVL 51+ in the future), something interesting could happen. Because of the slow speed of the weapon, you'd be able to attack using LS infinity with a telaport every 10 seconds.



    I'll add more after I have some food in me, but for now, all I can say is:
    "More Coming Soon."
     
    Last edited by moderator: Jul 7, 2015
    Xaite, sebastian_fl and silverseas like this.
  2. Morinphen

    Morinphen Forum Overlooker

    A bunch of things I wanna ask.

    Firstly, at what point does it become reckless/not worth it to equip mana expanding items? I wonder what the max. mana a SW can theoretically have is... and what would the optimal + mana as to avoid neglecting other stats. Let's see what uniques fit here (some of which you've mentioned yourself), just for the purpose of having a list:
    Now, of course not all of them can be used at once and some outclass others, so there are a few combo options. There's also the Solstice Star, as you have mentioned as well. I mean, there can be an even more extreme case than a lv50 robe + 2 lv50 rings + 5 gems, no? To put it simpler and possibly clearer, what's the max. vs. most usable setup when talking about + mana items/sets?

    As for the other question, how do factors like Teleport, Magic Missile & Mana Potions add into this? Since you said "back to back", I'm guessing it's without replenishing mana with other skills (well, Teleport would work, but Magic Missile takes too long), but the potions could theoretically mean "infinite" strikes (provided one has a really large amount)?
     
    Last edited: Jul 7, 2015
  3. silverseas

    silverseas Count Count

    Thank you Baragain for taking the time to post this. There really isn't much in the literature about mana, so this is very helpful.

    That would depend largely upon the setup of said SW's other gear, to be honest. I mean, I could equip a Ring of Inner Fortitude, and I could equip Roshan's Wisdom. Combine that with Grimmag's Starry Robe, a few Solstice Stars and the Warlord Set and I might be spamming close to 7 lightning strikes in a row. But because of the setup of my gear, I'd be losing 3/4 of my crit, something like 35% CD and something like 50 damage. So I don't think it's worth it--you hit more often, but the hits become too weak.

    I tend to think of it terms of ess usage. What setup allows me to output the maximum damage without consuming too much ess? To a certain extent, a larger mana pool means more lightning strikes -> less time/ess spent spamming magic missiles -> more efficient damage. Until you reach the point where large mana pool -> too much loss of damage/crit/CD -> why'd you even bother.

    Because of that, I am of the opinion that any of the weapons/offhands that offer mana stats are really just for show. They aren't usable as other leg/unique weapons/offhands can far surpass them. Except maybe the Lost Crystal Ball. I haven't used an orb in so long I don't even know what's good anymore. :p
     
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  4. Morinphen

    Morinphen Forum Overlooker

    You hit the nail on the head. Thanks for the answer. Also, yeah, that orb is pretty good... though one could find legendary ones far better (higher stats, but no added mana).
     
  5. _Baragain_

    _Baragain_ Living Forum Legend

    I considered what is the optimum, but as silverseas said, there comes a point where it is just for show. The biggest thing is balance, like with everything else in this game. Too much of one, but not enough of another and you don't have a good build. I agree with silverseas that mana on any item that could give you significant damage or crit is a bit of a waste. That is what makes Grimag's/Warlord's/Solstice Stars the best combo for high mana and the Roshan's set is nice for a little regen boost. You might be able to make use of the Rings Of Inner Fortitude (the attack speed is nice too), the Wolf Book and the Grimag Ball are both nice enough off hand items to use for a small mana boost, but I'd say that the rest of the mana/mana regen items are much less useful either due to low stats or the fact that they prevent you from using better combos if you are looking at mana.

    This guide is more useful for tweaking a build for little changes. That set of three examples that I showed was a perfect example where less is more. 206 looks better, but it is functionally the same as 200 with the regen value set at 14, but it frees up another gem slot.

    On the topic of "Optimum," there is also speed to consider. It doesn't show yet because I haven't gotten to the higher speeds yet, but at higher speed, Regen rate becomes less important because of you have less time in between attacks to regen mana. Past about 2.00, you only get one mana regen cycle per two attacks, so it is almost insignificant compared to about 1 regen cycle per attack at speeds close to 1.00. At higher speeds, the size of the mana pool is more important than the regen.

    Finally, to answer your question about "Max" mana, this is what I came up with.

    Base Mana: 100
    Grimag's Torso at 50: 55 Mana
    2x RoIF at LVL 50:2x31 mana, 62 Mana total
    Starlight (LVL has no effect): 40 Mana
    5x Solstice Stars (Possible from Nightmare map drops):25
    Total Mana before %s:282
    Wolf Book: 15%
    Warlord set: 30%
    Total Mana after %s: 408 (Rounded down because the RoIF were both rounded up)

    I chose the Wolf Book because 15% of 282=42.3 compared to the ball at LVL 50 having 31*0.3=39.3.

    So there you have it... max possible mana at this time is 408, but the rest of your stats would be garbage. Your speed would be a minimum of 1.2 (because of the 2xRoIF paired with Starlight's 1.00). If you used only damage/crit gems and no speed gems and use Roshan's for a total of 17 regen/sec, you'd be able to do 10 lighting strikes back to back . That would take 8.3333333 seconds and would leave you with a mana pool of 44 which is more than enough for MC/TP. Then on your second set of lighting strikes, you'd have to wait about 1.66667 seconds for your next telaport, but in that time, you'd regen enough for at least one more lighting strike. Then after that third telaport, you'd be looking at another 8.33333 seconds of LS followed by 1.66667 of what ever, and hopefully you'd wait another .83333333 seconds to have another mind control ready and you'd start the whole process over. All told, you'd be looking at about 30-32 LSs every 30 seconds. This should also answer your question about "infinitely" spamming LS. 30 LS, 3 TP, 1 MC, and maybe 1 MM or CL every 30 seconds and then starting over seems pretty "infinite" to me.
    [​IMG]

     
    Last edited: Jul 8, 2015
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  6. Morinphen

    Morinphen Forum Overlooker

    On point, as always. Thanks! You sure are one dedicated fella (and way better at Maths than I'd ever be in 10 lifetimes :D).
     
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  7. sebastian_fl

    sebastian_fl Count Count

    What a nice reading, thank you. So rare nowadays.

    Another nice topic on mana vs dmg is aggro. Sometime, when I know I will play mortis with an 'not a rockstar tank' I replace one of the dmg rings by ring of inner fortitude, and also one of the speed gems by dmg gem.

    It lowers dmg by 60 or so, and it is significant when you play with 3K lighting strike staff on blue, but you can strike 3 times vs 2. Easier for tanks to hold aggro, similar overall dmg.

    Before I got that ring, I was replacing dmg by crit not to hit mortis too hard.
     
    Last edited: Jul 8, 2015
  8. _Baragain_

    _Baragain_ Living Forum Legend

    I'm glad you like the content. In fact, if you have a math related analysis that you think could be interesting for me to look into, let me know. I like having a challenge and these types of math questions keep my brain flexible.
     
  9. silverseas

    silverseas Count Count

    I can always oblige... :D
     
  10. Novadude

    Novadude Commander of the Forum

    This is why I suggested a dwarf in another thread - turrets don't crit and are essence efficient. A 1H dwarf using the same essence as the dk could just drop 1 and probably 2 mechanical turrets on mortis and forget about them, knowing that they won't crit and thus draw aggro from the DK.
     
  11. Zamvel7

    Zamvel7 Active Author

    Hi Everyone;

    I am here to follow the problem from our little bunny, it's seems we still have some trouble with how much mana do our "normal" bunny need to cast "n" strikes?

    [​IMG]

    Let me share with you my thinking;

    Our bunny has 211 mana in her pool; and she wants to cast "n" strikes (5 in this case); and she also has 14 Mana/sec reg, and 1.18 speed attack (that's what you need to fill in the excel)

    Now since we expect to use our regen skill to cast the last strike, we need "n-1" and "n-2".

    "n-1" is used to know how much mana is consumed before our last strike;
    n=5
    n-1=4
    mana consumes = 4*50 =200

    now how much mana do our "normal" bunny really do before the last strike; well for that we need "n-2"
    from bunny's first attack and penultimate one we have 4 strikes BUT the first one starts in 0 seconds!!!!

    1st attack 0 sec
    2nd 0+ cycle time (down below) .85
    3rd 0+.85+.85 = 1.7
    4th 0+.85+.85+.85 = 2.55

    So only 3 times i have been adding the cycle time; (n-2)

    so, how much time has passed from 1 attack to another, well we use attack speed (i am using what DR said before)
    cycle time= 1/speed attack = 1/1.18 = .85 (i rounded it)

    Ok, knowing our cycle time we must know how much time has been throught from bunny's first click and penultimate,
    cycle time * n-2 = .85 * 3= 2.55

    only 2.55 sec has passed, but how much much mana does the bunny has regened?
    I think and I may be wrong; but regen works in scale increments every one sec, in other words, our bunny after 1 sec will have 14, and after 2 ,28; BUT not 21 after 1.5 sec.

    So saying that; I use "2 seconds"

    Regened mana = Rounddown(n-2*cycletime) * 14 = 28

    Ok we are almost over;

    So do our bunny has enough mana to cast one final strike without waiting; let's see

    Mana pool - Mana consumes + Mana regened = Final mana
    211-4(50)-2(14) = 211-200+28=39

    if Final mana < 50 our bunny cant cast one more strike
    but if Final mana =>50 she can do it

    so she lacks Strike mana consumed - Final mana
    50-39= 11

    She just needs 11 more mana to cast 5 strikes in a row, using her regen stats at it's full potential.

    in other words, she needs 222!!!!

    Please tell me if you have further questions

    TEGAN
    Zamvel DK
    Diesam SM
     
    Last edited: Jul 26, 2015
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  12. silverseas

    silverseas Count Count

    Thank you Zam.

    ---

    For those who missed what happened, I followed Baragain's formulas above. Theoretically I should be able to cast 5x lightning strikes, but this was not the case, as there was a gap between #4 and #5. It appears Zam has solved it.

    Now I'll just make sure to never buy another sapphire in my life so I don't have to go through this mess again. XD
     
    Tigraine-Mantear likes this.
  13. DesertKoala

    DesertKoala Forum Pro

    Great posts guys. This obviously took a lot of time to figure out. Thank you.
     
  14. silverseas

    silverseas Count Count

    Indeed. I'm glad to have math nerd friends to pester. I wouldn't be able to figure out this kind of thing myself. xD
     
  15. _Baragain_

    _Baragain_ Living Forum Legend

    Thanks for pointing out that the mana replenishment happens in tics on the second. Not playing as a SW, I didn't consider when the replenishment would kick in in the grand scheme of things. I guess I'll have to go back and rethink my charts a bit.

    What could also be factoring in is attack speed breaks... but as silverseas has pointed out in the past, the charts don't go down to her attack speed and they don't include lighting strike either.
     
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