Mathematical analysis of Arrow, Rush, and Mist

[Vritra]

As I've been re-levelling my dragon, I've started figuring my potential maximum damage at certain MA benchmarks with different combinations of Mana Arrow, Arrow Rush, and Mist of Mana.

I apologize if this has been gone over before, but I thought it might be handy for those who want to understand just where the damage comes from.

Credits go to this guide entirely for all damage formulae and variables.

My current situation is this:

NeoVritra, Level 47/42 Dragon
Mana Arrow 1
Cure 10
Mana Bottle 1
Mist of Mana 1

20 TM points remaining, 28 will be available at TM 50

My question to myself was, "What combination of Mana Arrow, Arrow Rush, and Mist of Mana will give me the most potential damage for 28 TM?"

So I set 2 benchmarks: MA 100 (close to where I am now, MA 95), and MA 200 (down the road a ways, just to see if this 28 TM remains efficiently spent at later levels.)

Arrow 10, Rush 10, Mist 7

ASSUMPTION: MA before Mist = 100
(MA-49)*(Power/10)
((128-49)*(126.5/10)) * 6
(79 * 12.65) * 6
999.35 * 6
MAXIMUM POSSIBLE DAMAGE = 5996~5997

ASSUMPTION: MA before Mist = 200
(MA-49)*(Power/10)
((256-49)*(126.5/10)) * 6
(207 * 12.65) *6
2618.55 * 6
MAXIMUM POSSIBLE DAMAGE = 15711~15712

OPINION: Fairly beefy and it keeps all 3 skills at high levels. Should be good, right?


Arrow Master, Rush 10, Mist 5

ASSUMPTION: MA before Mist = 100
(MA-49)*(Power/10)
((122-49)*(138/10)) * 6
(73 * 13.8) * 6
1007.4 * 6
MAXIMUM POSSIBLE DAMAGE = 6042

ASSUMPTION: MA before Mist = 200
(MA-49)*(Power/10)
((244-49)*(138/10)) * 6
(195 * 13.8) * 6
2691 * 6
MAXIMUM POSSIBLE DAMAGE = 16146

OPINION: It gets a little better. Sure, the difference is only 47 points, but that's 47 stable points, since it applies to all six arrows.


Arrow 10, Rush Master, Mist 4

ASSUMPTION: MA before Mist = 100
(MA-49)*(Power/10)
((119-49)*(123.6/10)) * 7
(70 * 12.36) * 7
865.2 * 7
MAXIMUM POSSIBLE DAMAGE: 6056~6057

ASSUMPTION: MA before Mist = 200
(MA-49)*(Power/10)
((238-49)*(123.6/10)) * 7
(189 * 12.36) * 7
2336.04 * 7
MAXIMUM POSSIBLE DAMAGE: 16352~16353

OPINION: It can still get better, apparently, but this extra damage has a catch: you have to land the extra arrow to get it. As a result, it's unstable, and if you only land 6 arrows, your damage will be inferior to the last build's.


Arrow Master, Rush Master, Mist 2

ASSUMPTION: MA before Mist = 100
(MA-49)*(Power/10)
((113-49)*(134.9/10)) * 7
(64 * 13.49) * 7
863.36 * 7
MAXIMUM POSSIBLE DAMAGE: 6043~6044

ASSUMPTION: MA before Mist = 200
(MA-49)*(Power/10)
((226-49)*(134.9/10)) * 7
(177 * 13.49) * 7
2387.73 * 7
MAXIMUM POSSIBLE DAMAGE: 16714~16715

OPINION: Holy cow, we just hit the motherlode. Now, I personally was a bit surprised here - I thought sacking that much Mist for Arrow/Rush mastery would reduce my overall damage, but instead, it's increased it. You do lose out a bit at MA 100, compared to mastering JUST one of the two arrow skills, but down the road you'll outstrip the both of them, and to me, that's worth it. It's also fairly stable - the arrow mastery improves all seven arrows, and you have that potential to land the 7th arrow for extra pain. Now correct me if I'm wrong, but I'm not seeing a downside here.


So, judging from these numbers, a lot more damage comes from your Arrow/Rush skill level than I initially thought. Mist can play a big role, no doubt, but when it comes to choose which to pump/master first, fundamentals first, then buffs. Should save you on MP in the long run, too, since you're using a lower-levelled (and thus cheaper) variant of Mist.

Any questions, thoughts, criticisms?

EDIT: Before I forget, I realize that some of the end values have a 1-point range listed. This is because I'm not sure whether the game rounds decimals down or up when determining damage.

ANOTHER EDIT: I should mention that the maximum possible damage rating does is before you apply the victim's MD/resistance/skill effects, and it does not consider the effects of crits. If you are prone to scoring criticals on an arrow rush, your end result damage will likely be higher than what's listed here, and you'd be better off with the builds that sport Rush Master, as this would give you an extra arrow, and thus an extra opportunity to crit. In summary? Your mileage may vary, these are just raw the raw numbers.

UPDATE! I've now reached the point where I can practice what I'm preaching. I went with master arrow and master rush, with 2 mist - I'm pleased to find that I can easily kill Tritches (L80 Power, Magic Weak) in one cast 90% of the time and Mimics (L71 Sense, Dark Weak) 75% of the time. Aposis (L80 Charm, Magic Resist) goes down in two rushes, DESPITE her magic resistance and charm type. With the 1432 build, I miss maybe 1 arrow out of every rush, on average, even on enemies nearly 20 levels above me. A little over a third of my rushes land without a single miss. The only things that give me any trouble are magic types with magic resistance, as their natural MD is nuts. I'll also enjoy a nice, steady increase in power with each TM level gained - I can just dump that point into Mist, and reap the bonus with each consecutive TM level.

[Rukia]

Ah such great information, thanks for compiling that up. But I went on and got Mastered Arrow and lvl 10 Mist and still adding Rush, blegh I should've went the way you did. But great info for people who are determined to be a rush dragon.

This should be in the guide section.

[Kenjii]

Good calculations. Too bad I'm too lazy to read all that. >_>

All I need to know is:
The higher your MA, the more damage.

[TMM]

In game tests please. Until then I'm still going with triple mastery :P

[Vritra]

Oh, don't get me wrong, TMM. I'm not recommending you AVOID mastering any of the three skills, if arrows are your goal. In fact, I encourage mastering arrow, rush, and mist as soon as you possibly can, as arrow rush is an always-handy damage staple and mist will benefit every single direct-damage spell you will ever cast. This is only a mathematical analysis of potential maximums, intended to help those with limited TM make informed decisions about what to improve, and maybe when.

[TMM]

Yeah I understand that. I'd just like to see some of the other combinations carried out by someone. They're good calculations, but e all know some damage formulas can be... well, decieving.

[Vritra]

Well, if you've re-read the first post, you'll see that I put my money where my mouth is, so to speak, and opted for the master arrow/master rush/2 mist build option.

My experiences with it are as follows (keep in mind I'm currently 63/51):

Good Experiences

1. Against Tritch, I can score one-cast kills about 90% of the time
2. Against Aposis, I can defeat her in two arrow rushes, despite her magic resistance
3. Mimic usually dies in a single rush, but escapes about a quarter of the time with a sliver of HP left (a point or two of MA or a level of Mist should solve that)
4. Galli is a one-cast kill more than 85% of the time (REVENGE!!)

Bad Experiences

1. I can't even damage Nora Big without using Mist, but when I do he takes only about 120 damage a hit from Rush.
2. Winged Salamander's high MD makes him a bit of a nuisance
3. Allowing Maro Toy or Aposis to get to melee range and cast Magic Reflector makes them very painful to fight
4. Super Golden Moles are frustrating - they don't take a lot of damage from an arrow rush and are fast enough and strong enough to close the gap and kill me before I can score enough rushes to slaughter them
5. Other magic types, in general, are annoying due to high MD.

Other Notes

1. I can kill Galli - other mages close to my level who opt to pump arrow and mist before developing rush cannot seem do so easily, especially if they have a weak (Level 3-5) rush.
2. The repeated hits from my seven-arrow rush tends to put monsters into about a .3-.5 second's worth of stunlock - this has proven handy when escaping from melee with Mimic.

If anyone else wants to take my calculations to test with a character of their own, feel free. Post your experiences here. I want the input.

UPDATE: Out of sheer boredom, I decided to do an in-depth analysis of Mist of Mana, especially regarding its efficiency at each level.

All numbers are taken from this guide, except where noted.

Level 1:

• 160 MP Cost
• Duration 100s
• +10% bonus

MP-to-Duration Efficiency: .625
MP-to-MA-Bonus Efficiency: .0625


Level 2:

• 180 MP Cost
• Duration 105s
• +13% bonus

MP-to-Duration Efficiency: .583
MP-to-MA-Bonus Efficiency: .072


Level 3:

• 200 MP Cost
• Duration 110s
• +16% bonus

MP-to-Duration Efficiency: .55
MP-to-MA-Bonus Efficiency: .08


Level 4:

• 220 MP Cost
• Duration 115s
• +19% bonus

MP-to-Duration Efficiency: .5227
MP-to-MA-Bonus Efficiency: .863


Level 5:

• 240 MP Cost
• Duration 120s
• +22% bonus

MP-to-Duration Efficiency: .5
MP-to-MA-Bonus Efficiency: .0916


Level 6:

• 260 MP Cost
• Duration 125s
• +25% bonus

MP-to-Duration Efficiency: .4807
MP-to-MA-Bonus Efficiency: .0961


Level 7:

• 280 MP Cost
• Duration 130s
• +28% bonus

MP-to-Duration Efficiency: .4642
MP-to-MA-Bonus Efficiency: .1


Level 8:

• 300 MP Cost
• Duration 135s
• +31% bonus

MP-to-Duration Efficiency: .45
MP-to-MA-Bonus Efficiency: .103


Level 9:

• 320 MP Cost
• Duration 140s
• +34% bonus

MP-to-Duration Efficiency: .4375
MP-to-MA-Bonus Efficiency: .1062


Level 10:

• 340 MP Cost
• Duration 145s
• +37% bonus

MP-to-Duration Efficiency: .4264
MP-to-MA-Bonus Efficiency: .1088


MASTER LEVEL:

• 380 MP Cost
• Duration 180s
• +45% bonus

MP-to-Duration Efficiency: .4736
MP-to-MA-Bonus Efficiency: .1184


CONCLUSIONS: For the most part, levels 1-10 didn't surprise me much. I figured that the MA-bonus efficiency would rise, while the efficiency of the duration would drop. Master level was a pleasant surprise, considering both efficiency rates rose, rather than one rising and one dropping. Master Mist is well worth getting, for that reason alone. The only problem is getting the selinolites to do it, which is a pain in the rear.

EDIT: Found a typo in FrozenFlame's guide regarding the duration of Master Level Mist. It's 180 seconds, not 120. I confirmed this in-game as well. My conclusions have changed, and the calculations for master level mist has been fixed.

ANOTHER EDIT: Thanks to Sherlock2100, a mistake in the Lv.10 Mist calculations has been fixed.

YET ANOTHER EDIT: Fixed a typo.

[samilbz]

can u help me???


T_T

[Vritra]

Do the tutorial if you don't know how to play the game.

[sherlock2100]

i dont get this calculation. i did it, they were different from urs. where is ur mist of mana bonuses to magic ability? mist of mana increase ur magic ability not the power of the spell.
where did u get the information about arrow rush and mana arrow? (their power at each level)
-------------------------------------------------
u did a typo or a calculation error on MP-MA bonus, at lvl 10, its 37/340=.1088

[Vritra]

I included Mist in the MA value.

For instance:

Arrow Master, Rush Master, Mist 2

ASSUMPTION: MA before Mist = 100 <--- Assumed MA of the caster BEFORE Mist
(MA-49)*(Power/10) <--- The spell's formula
((113-49)*(134.9/10)) * 7 <--- Bolded number: Assumed MA (100) + bonus from Mist (13)
(64 * 13.49) * 7
863.36 * 7 <--- Bolded number: Expected base damage per individual arrow
MAXIMUM POSSIBLE DAMAGE: 6043~6044 <--- Expected base damage if all arrows land normally

I get my formulas from here, as I mentioned in the first post.

Credits go to this guide entirely for all damage formulae and variables.

And you're right about the mistake on my Lv.10 mist calculation. I'll fix that.

[Gametime]

wow neo ya did ya homework eh btw man whats up its me Gametime that buff ne ways im lv 90 on him 4132 all ap and i made a mage 2 test this out ign MaximumPower and ill b using the double mastery tech u got up there only thing stopping me is tm lvls heh

OH WOW, how old is this thread. Don't bump 2 year old threads.

[bladedfury]

i recommend just mastering AR, Mana Arrow, and Mist A.S.A.P.
way more dmg than just mastering 1 or 2 of them >.>

[No14]

Great guide, who would've expected this?