Guide Calculating Effective Dps

Tl;dr: A research paper (post? thread?) detailing how to calculate effective DPS that includes using spells.

Calculating Effective DPS​

Introduction

With the introduction of Wynndata by @dukioooo, many players have used this tool to make their builds. This tool also allows players to view their average damage per spell and their average melee DPS assuming that players are able to obtain maximum IDs on all of their gear. However, what this tool really lacks is being able to calculate average DPS across both melee and spell damage. In this paper, I will introduce a formula on how to calculate this DPS, to which I will coin the term, “effective DPS.”

Spell Cycles

As coined by @Madkurre, spell cycles are a way to use spells efficiently without wasting mana [1]. To use this, we must first calculate a mana cycle. A mana cycle is the amount of mana regen over a period of 4 seconds [1]. Every build also has a natural mana regen of 5/4s [1]. When a build also includes mana regen from gear, this must also be added with natural mana regen to then calculate a mana cycle.

Once a mana cycle has been calculated, we then must calculate a combination of spells that will use up a whole mana cycle. For example, let’s assume that an archer build has 68 int, a mana cycle of 7/4s, bomb spell deals 5k damage, and arrow storm deals 15k damage. We can then make a spell cycle that consists of an arrow storm (3 mana) and a bomb spell (4 mana). This puts us at 20k damage over 4 seconds, which will put our DPS at 5k damage (1)(2)(3). Note that mana steal has not been accounted for and will be excluded from this paper due to a lack of information.

Methodology

In order to calculate effective DPS, I will introduce a build I have made (4). Listed below are the facts needed to calculate effective DPS. Note that all of these damage values are the average amount of damage.

• Mana Regen: 7/4s
• Poison: 0 dmg
• Melee DPS: 5,111 dmg
• Spells:
  • Bomb Arrow (4 mana): 12,509 dmg
  • Arrow Storm (3 mana): 33,088 dmg (5)(6)
  • Arrow Shield (5 mana): 11,921 dmg

Now let's calculate a mana cycle:

Code:

manaCycle = naturalManaRegen + manaRegen = 5/4s + 7/4s = 12/4s

With 12 mana every 4 seconds, we can have a spell cycle of a bomb arrow, arrow storm, and arrow shield (7). Spell only DPS can then be calculated by adding up all 3 of these spell damages and dividing it by 4 seconds:

Code:

spellOnlyDPS = (bomb + storm + shield)/4 = (12,509 + 33,088 + 11,921)/4 = 14,379.5

Now we need to combine both spell DPS and melee DPS into effective DPS. This is not simply just adding both spell and melee DPS together. In order to combine the two, we must first look at the time it takes to cast a spell. Based on @YYGAYMER's video of him soloing LI, we can roughly estimate that it takes 0.5 seconds to cast any spell (8)(9)[2]. Using the example build, casting 3 spells will take 1.5 seconds. Notice that in the video, once he casts a spell, he can then immediately switch back to melee damage, indicating that there is no cooldown after casting a spell. This leaves us with 2.5 seconds to do melee damage within a mana cycle. Take spell damage, poison, and melee DPS and combine them in the following way:

Code:

effectiveDPS = [((bomb + storm + shield) * totalSpellCastingTime) + (meleeDPS * (4 – totalSpellCastingTime))] / 4 + poison / 3 = [((12,509 + 33,088 + 11,921) * 1.5) + (5,111 * (4 - 1.5))]/4 + 0 / 3 = 24,763.625 dmg

So my build has an effective DPS of 24,763 damage. This is really high, almost 5 times higher than melee DPS. This leads to the final formula of:

Code:

effectiveDPS = [((spell1 + spell2 + … + spelln) * (n * 0.5) + (meleeDPS * (4 – (n * 0.5)))] / 4 + poison / 3

Where n is the number of spells to cast in a spell cycle, and it must be less than 9. We can only cast spells up to 8 times per mana cycle assuming that the spell casting time is 0.5 seconds per spell.

Conclusion

Calculating effective DPS can help determine whether a build is suitable or not. Using the formula,

Code:

effectiveDPS = [((spell1 + spell2 + … + spelln) * (n * 0.5) + (meleeDPS * (4 – (n * 0.5)))] / 4 + poison / 3 , n < 9 

effective DPS can be calculated. This can help close the gap in comparing different play styles, including the comparisons between spell spam builds and melee only builds.

However, this formula is still missing some parts. Further research is needed on the frequency of mana steal being triggered with various attack speeds in order to include this into the total spell cycle damage. Mana steal is unique in a way that more spells mean less mana steal and vice-versa, which will make the effective DPS formula more complicated. Powder spells have not been included into the formula as well (10)(11).

Spoiler: Footnotes

(1) @Madkurre posted his findings on Spell DPS in the second reply to his thread before I did [1].
(2) More complicated spell cycles such as an under-using mana cycle to then be compensated by a over-using mana cycle is also possible to calculate, although this makes the formula unnecessarily complicated.
(3) Freestyle mana usage is ignored.
(4) https://wynndata.tk/s/2Q6ysi
(5) As @dukioooo pointed out, I am assuming that all arrows will hit the target.
(6) This damage does not include the fact that as of July 27, 2018, arrow storm deals double damage than before.
(7) When casting the same spell consecutively, the second spell’s mana price increases by 1.
(8) As @dukioooo pointed out, spell casting times may vary from player to player.
(9) As @dukioooo pointed out, if meteor spells are casted consecutively and before the first meteor falls, the second meteor will override the damage of the first meteor, which effectively makes the first meteor deal no damage at all.
(10) I clearly have too much time huh...
(11) If you are going to ask for permission, @dukioooo, to use this on Wynndata, I allow you to do so.

Spoiler: Works Cited

[1] @Madkurre, "Introducing Spell Cycles." 25 July

2018. https://forums.wynncraft.com/threads/introducing-spell-cycles.230841/​

[2] @YYGAYMER, "Wynncraft Legendary Island (Archer/no pots)." 21 May 2018.

​

Spoiler: References

@dukioooo, "Wynndata." https://wynndata.tk
@motoki1, "How Damage Is Calculated." Edited 19 March

2018. https://forums.wynncraft.com/threads/how-damage-is-calculated.176082/​

@Rikio, "The Unofficial Identification Thread." 8 Feb 2018.

https://forums.wynncraft.com/threads/the-unofficial-identification-thread.124127/​

 

Spell cast time depends on player.... it might take 100ms or 1000ms ...
Meteors have a wait time after casting for the meteor to fall, if you recast it the first meteor will not make damage
Arrow storm .... you most likely wont hit all the 60 arrows

 

That's true. I should add that I am assuming that cast time is 0.5 seconds and that all 60 arrows from arrow storm will hit the target.

As for the meteors, I guess I'll add a footnote on that.

 

good shit

spell cycles are totally possible with mana steal, it's just a pain to write about so ive been putting it off.

how mana steal should be handled for cycles depends on the build's attack speed, i propose. if you have a slow speed with a higher chance of ms triggering consistently, it can be added to your current mana cycle (natural + mr id) and you can base your spell cycles on that

on higher speeds, mana regen and steal should be seen as separate pools from my viewpoint. since your mana regen id will likely be smaller, you'll use spell cycles of lesser mana cost, then switch to melee and in case mana steal triggers, then you spend that. theres so much fimmickyness with putting these theories into practice but trust me it'll work

ngl this should get tested whether it's possible for all 60 arrows to hit when shot at point-blank, since from what ive heard the invincibility frames of mobs will waste some of the arrows even if they should hit
get the average amount of arrows that hit and work out a multiplier you can use on your storms to get the actually accurate damage

 

You also assume that travel time = 0 on all archer abilities and arrow rain missed, those should probably be accounted for or addressed as well, overall, pretty nice though

 

I have tested this on villagers on multiple occasions (for stealing of course :P) and I noticed that all arrows hit the villagers and reduced their health by ~62k dmg (of course, with the arrow storm buffed to deal x2 damage).

 

I'm 99% sure that "buff" isn't intentional.

 

(it was intentional but rushed, so arrow storm will get buffed at least somewhat in any case)
but doesnt matter for these purposes as everything is the way it's supposed to be

 

So basically it was just stupidity.

And that still doesn't make the double damage intentional.

 

Not sure whether travel time should be accounted for, and if so, how it should be accounted for. As for arrow rain, I noticed that arrow rain misses about 90% of the time so I didn't include it for that reason. However, if we do find the % chance that an arrow from arrow rain will hit the target, I will include it in the arrow shield damage.

 

Travel time should be accounted for, since there can't be two spells from the same player at once.

 

no but it's still intentional in the way that the devs knowingly made the damage doubled, and that's how it is in-game as seen from op's testing
so it's working the way it's supposed to, although that way might not be the best balancing-wise

 

"Might"

 

You can have 2 spells still travelling that have not yet hit their target yet. For example, lets say I cast 2 bomb arrows. The first one didn't even hit the target yet and I already casted another one. Both bomb spells will still hit the target for their respective damages.

There may be other spells that follow this rule though. Take a look at meteor spell. If 2 is casted consecutively, the first one may not even do damage at all. This implies that the player must be able to efficiently use their spells accordingly in order to maximize DPS. There may be other spells similar to meteor that I am not aware of since I mainly play archer only.

 

they will not. you cant have 2 of the same spell running at the same time, no matter the spell. i personally got on just to confirm this with arrow bombs, and the first one disappears as soon as you cast a second one

 

Random info : You can melee while firing the arrow storm

not helpful?
Ik :(

 

You're right... I need to revise my methodology then. I am going to need help on finding the duration it takes for each spell to damage the target before casting another spell. For example, how long does it take for arrow storm to shoot out all the arrows?

However, melee still works while the spell is travelling to the target...

Oh I knew that one, thanks anyway.