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Old 06-06-2010, 10:26 PM   #1
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Lightbulb Damage Value and Damage Multiplier

Code:
                          (Reroll 100-200)                (Crit dmg ~50)             (Reroll 0-100, crit dmg ~25)                
Team type:    |        LS-heavy nin        |        LS-heavy tai        |       Hybrid Seal (3-3)     |         High Seal          |All
Stat               |Dmg value    Reroll bonus    |Dmg value    Crit bonus    |Dmg value    Reroll bonus    |Dmg value    Crit bonus    |Dmg multiplier
----------------+-------------------------------+-------------------------------+-------------------------------+-------------------------------+--------------
Tai                | 0.563                   | 0.628                   | 0.531                   | 0.5                       |
crit_dmg    |                        |            0.005       |                       |                       |
crit_chance    |                        |                        |                        |            0.0025       |
Nin                | 0.659                   | 0.563                   | 0.532                   | 0.5                     |
attack reroll    |            0.00158     |                       |            0.00317      |                       |
Stamina     |                        |                        |                        |                        |(0.007)
Endurance          |                        |                       |                       |                       | 0.005
Resist            | Undef                       |                       |                       |                       |
EI                 | Undef                       |                       |                       |                       |
Attack             | 1                       | 1                       | 1                       | 1                      |
minus e.atk        | 0.5*                     | 0.5*                      | 0.5*                     | 0.5*                      | 
TI                 | 0.6**                     | 0.6**                    | 0.6**                    | 0.6**                    |
NI                 | 0.6**                     | 0.6**                    | 0.6**                    | 0.6**                    |
Spec. ele. adv. |                        |                        |                        |                        |[0.0035]
ele. adv.    |                        |                        |                        |                        |[0.0035]
spec. ele. dmg    |[1]                     |[1]                    |[1]                    |[1]                    |
                                    
Ninja exp          Undef                                
L5 Death           Undef                                
Ryo gain           Undef                                
Item finding       Undef                                

Empty entries are equal to 0 or have such a limited effect that it might as well be 0.
Numbers in () are only applicable if the ninja in question is short on stamina.
Numbers in [] are only applicable if the elements in question are correct.
*Minus e.atk have values that are highly dependent on situation, typically ranging from 0.1 to 1.0
*TI/NI have values that are highly dependent on situation, typically ranging from 0.4 to 0.8

Abbreviatoins:

LS = low seal
HS = high seal
DV = damage value
DM = damage multiplier
Tai = taijutsu
crit dmg = critical hit damage
Nin = ninjutsu
EI = elemental immunity
minus e.atk = minus enemy attack
spec. ele. adv. = specific elemental advantage (i.e. fire advantage, water advantage, etc.)
ele. adv. = elemental advantage
spec. ele. dmg = specific elemental damage (i.e. fire damage, water damage, etc.)
TI = taijutsu immunity
NI = ninjutsu immunity
LW = legendary weapon

Preface

I have decided to compile my own ratings for LW attributes. The final results are in the table above. All values listed in the table are for progression only. As such I have decided to name these values "damage value" (DV) and "damage multiplier" (DM) to set them apart from "attack value", since you are literally doing damage to your opponent's HP on the world map.

I try my best to account for differences across different difficulties but for the most part these values are geared toward higher difficulties because you spend more time there. As such, the values are most accurate for Hard+ but are still somewhat useful for Medium and Easy. I didn't really bother with Beginner since progression really starts at Easy. Most baseline and reference values come from my observations and results of tens of hours of simming with Aenonar's Kyuubi Basher.

The damage value of attributes are highly team-type specific due to various synergy that exist between stats. Thus I list different values for different progression team types. I have listed values for low seal heavy nin, low seal heavy tai, hybrid seal 3-3 (not hybrid damage), and high seal. To estimate the value for low seal hybrid damage, just average the two values across LS-nin and LS-tai. Crit bonus for hybrid seal is the same as crit bonus for LS tai because crit dmg is a linear increasing attribute. Reroll bonus is different for hybrid seal than LS-nin because reroll has a saturation effect, which will be explained later. Lastly, all team types are affected by the damage multiplier. Since the exact total damage of a ninja varies greatly in progression, a multiplier is more descriptive of the effect of certain attributes. A ninja's total damage is simply increased by (1 + total(DM)).

Each team type has certain baseline assumptions:

LS-nin is assumed to have reroll just above 100, which is generally true for higher difficulty teams but less so for lower diff. Lower diff teams should actually use hybrid seal value since hybrid seal ninjas are assumed to have lower than 100 reroll. But since you spent a good deal more time on higher diff than lower diff I decided to go with the assumption of 100+ reroll. For the purpose of calculating the value of nin, LS-nin ninjas are assumed to have a reroll of 100.

LS-tai is not actually very useful for progression on higher diff. However, I included it because LS-hybrid damage can be calculated by average LS-nin and LS-tai, and hybrid seal use the same values for crit bonus as LS-tai. The base assumption is that you can average a total crit damage of 50 on your ninjas, which correspond to a Hachibi of lv 12-ish.

Hybrid seal assumes 3 high seal ninja, 3 low seal ninja. You can kind of guess how other mix of seals might behave by interpolating between hybrid seal, LS, and HS. Hybrid seal does not make any assumptions about whether the LS ninjas are nin or tai, but it does assume that a given ninja is either nin-heavy or tai-heavy and that you equip your LW appropriately (i.e. reroll LW goes on nin-heavy, crit dmg LW goes on tai-heavy).

HS just high seal, plain and vanilla.
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Old 06-06-2010, 10:27 PM   #2
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In-depth Explanation

Here I will explain in details how each and every value is derived, making proper references as appropriate. Remember that all values are based on world map behavior, so certain formulas are appropriately simplified.

Taijutsu

The value of taijutsu comes direct from a statistical average of the taijutsu part of the damage formula, which goes as,

0.5 * (taijutsu * (1 + (crit_dmg/100))), if critical
0.5 * (taijutsu), if no critical

Since we know the chance of a critical happening, we can write a formula to calculate the average damage,

0.5 * (taijutsu * (1 + (crit_dmg/100) * (crit_chance/100)))

For LS-nin, crit_dmg ~25, crit_chance = 50, so DV of 1 tai is 0.563
For LS-tai, crit_dmg ~50, crit_chance = 50, so DV of 1 tai is 0.625
For hybrid seal, the DV of 1 tai is 0.563 for a LS ninja but 0.5 for a HS ninja, so the average is 0.531
For HS, the DV of 1 tai is 0.5 because crit_chance = 0.

Crit_dmg

Critical damage applies a direct multiplier to base tai damage. For a ninja with 50% crit_chance, the average multiplier is,

(crit_chance/100) * (crit_dmg/100) = 0.005 * crit_dmg

For LS-nin, crit_dmg has almost no effect because we're assuming these ninjas have negligible tai.
For LS-tai, crit_dmg applies a multiplier of 0.005 per point.
For hybrid seal, the effect is the same as for LS-tai.
For HS, crit_dmg has no effect because crit_chance = 0.

Crit_chance

Critical chance also applies a direct multiplier to base tai damage but is only applicable to high seal ninjas. Assuming the ninja has 25% crit_dmg, the average multiplier is,

(crit_chance/100) * (crit_dmg/100) = 0.0025 * crit_chance

For LS-nin and LS-tai, crit_chance has no effect because crit_chance is capped at 0.5, which is already provided by the LS bonus.
For hybrid seal, the effect is a multiplier of 0.0025 for HS ninjas and no effect for LS ninja. We can estimate this as simply half effective, or 0.00125 per point. (this value is not written into the table)
For HS, crit_chance applies a multiplier of 0.0025.

Ninjutsu

The value of ninjutsu can also be calculated via statistical averaging. I've already done an in-depth analysis of nin-reroll synergy and posted the formula at http://www.ninjamanager.net/showpost...7&postcount=12.

For LS-nin, we assumed reroll ~100, plugging into the formula gives a multiplier of 1.317 so the effective DV of 1 nin is 0.5 * 1.317 = 0.659
For LS-tai, we assume a reroll of 40 (base LS bonus), which gives a DV of 0.563
For hybrid seal, the DV of 1 nin is 0.563 for a LS ninja but 0.5 for a HS ninja, so the average is 0.532 (there's some round off)
For HS, the DV of 1 nin is 0.5 because reroll has little effect on HS ninjas.

Attack Reroll

The same formulas from my nin-reroll analysis can also be used to calculate the effect of reroll.

For LS-nin, since we're assuming 100+ reroll, the formula for reroll of 100-200 applies and gives a multiplier of 0.00158 per point.
For LS-tai, the effect is small since we're assuming heavy tai.
For hybrid seal, since we're assuming 100- reroll, the formula for reroll of 0-100 applies and gives a multiplier of 0.00317 per point.
For HS, reroll has negligible effect.

Stamina

Stamina applies a global damage multiplier to the ninja's total damage by increasing the number of hits it does as well as the overall damage for hit number 2 and on. However, the effect of stamina is capped at 100 for ninjas that are not mis-slotted, (I will not give a treatment of mis-slotted ninjas here) thus only the amount of stamina added up to 100 is effective.

To analyze the effect of stamina mathematically, you need a good understanding of geometry or integral calculus. Neither of which I will talk about here. Instead I will provide a simplified approach to calculate the effect of stamina. We begin by assuming ninja A has 100 stamina and ninja B has 50 stamina. They both have the same peak damage and they face an enemy on the world map who, on the average, does half as much damage as they do. In this scenario, ninja A does 5 hits and ninja B does 4. Using the stamina formula in the tutorial, we find that the total damage dealt by ninja A is ~1.35 times that of ninja B. Thus 50 stamina gave a DM of 0.35, or ~0.007 per stamina. The real value of stamina varies by about +- 0.001 per stamina so its not too far off from this value.

Stamina applies a global bonus and so is not team-type specific.

Endurance

Similar to stamina, an analysis of endurance requires either geometry or integral calculus, which I have already performed in this post http://www.ninjamanager.net/showpost...2&postcount=87. The results is very simple,

DM = endurance/200 = 0.005 * endurance

This DM bonus of 0.005 per point is global.

Resist and Elemental Immunity

Resist and EI both defies mathematical analysis for progression because almost everyone simply chance their element when the opponent has an elemental advantage. For this reason, resist and EI are arguably of negligible value. However, there are rare situations where a high resist or EI item can allow you to tremendously extend a ninja's life and total damage. Since these two stats are highly situation and worthless most of the time, they are left as undefined.

Attack

The DV of attack is 1 for all team-types, plain and simple.

Minus Enemy Attack, Taijutsu Immunity, Ninjutsu Immunity

-e.atk, TI, and NI have unique effects on the world map in that they lower the cutoff threshold at which your ninjas get knocked out. However, they do not add any damage and only serves to prolong a ninja's life. I have ran a number of plausible scenarios involving different cutoff points and found that the value of -e.atk tend to vary from 0.1 to 1.0 depending on the peak ninja damage versus the enemy's average damage. In particular, ninjas on lower difficulty tends to receive a higher DV bonus while ninjas on higher difficulty tends to receive a lower DV bonus. This disparity comes from the fact that enemy HP is increased by 40% per diff but enemy damage only increase by 15% per diff. So at higher difficulties your ninja's initial damage is higher than the enemy's average damage than on lower difficulties. By the time, your ninja's damage decayed to the cutoff point, it is already a small fraction of his initial damage, so that further hits are very weak in comparison. I have, for the time being, assigned a value of 0.5 DV for -e.atk.

I have also completed a set of analysis for TI/NI involving rather complicated math, which the average forum users are unlikely to be interested in. So I won't be posting the derivation. PM me if you are interested in seeing the derivation. Instead I will simply say that I found the average DV of TI/NI is ~0.6, having greater worth when your ninja's damage is only a bit greater than the enemies' average damage, and less worth when your ninja's damage is much greater than the enemies' average damage.

Specific Elemental Advantage, Elemental Advantage, Specific Elemental Damage

Specific elemental advantage is tricky to analyze because it only applied to ninjas of one specific element against enemy of another specific element. When it is working, it applies a global damage multiplier to the ninja's total damage. For world map fights, the bonus is 35% per 100 elemental advantage, or 0.0035 per point. However, since the application of this damage is highly conditional, it is left in [] in the table.

Elemental advantage is a straight out DM of 0.0035 per point against an elemental enemy, and 0 against a non-elemental enemy, as such it is also left [].

Specific elemental damage is less stringent than specific elemental advantage because your ninja does not have to have the right element, but the enemy does. It applies a straightforward DV of 1 when the conditions are met and is left in [].
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Old 06-06-2010, 10:28 PM   #3
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Closing Remarks

I intend to use these values to give each LW ratings that are tailored to specific progressin team types. Hopefully, this will help you all decide which LW is better for a particular type of teams. I know the table of values look complicated at the moment but it can be used produce a single LW DV value for each team-type and a global multiplier. After applying it to a small sample of LWs, I found some interesting trends that I intend to share once I've finish a complete analysis.

There are a number of attributes with values that are either undefined or ill-defined. I welcome you all to debate the correct value to use though I do ask that you provide some supporting evidence for your choice of value.

And in case anyone is wondering, yes, I wrote this table of values because I'm annoyed with Lunar2's treatment of attack values and his attempt to average out the effects of attribute across BA and WM. I applaud him for his effort, but that does not change the fact that his results are outdated and do not work when applied to progression, and I'm going to prove it.

Credit

udon, for making this awesome game, I'm definitely sinking more time into this than I originally intended.
Teamish, for getting me fire up enough about this to actually write a new table of values.
Aenonar, for programming Kyuubi Basher.
The LW guide crew, for providing invaluable data for me to process. In particular, Reversal for starting that guide, Minaro and dist for doing a fine job maintaining it. Let me know if I missed anyone who is also maintaining it. You can find the LW guide at the following http://www.ninjamanager.net/showthread.php?t=487.

Updates:
2010-6-7, changed HS crit_chance bonus back to 0.0025 because I forgot that tai to total ratio is something taken care in the final calculation, and not within the table of value itself.
2010-6-29, changed the value of TI/NI from 0.5 to 0.9 based on new analysis
2010-6-30, changed the value of TI/NI from 0.9 to 0.6 because of a coefficient I missed in my previous analysis; what do you know, my original arbitrary guess wasn't too far off
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Old 06-06-2010, 10:29 PM   #4
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Old 06-06-2010, 10:32 PM   #5
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alright, read it, liked it, gonna try to help with things if possible

you mentioned in certain situations concerning elem adv. as .0035 worth, wouldnt it be .35? 100 adv = 35% increase of base dmg added on, 35/100 = .35 (unless im missing something)

also you mentioned the trend of changing elements to avoid being disadvantaged, would it be fine to assume that someone would change the element when given the chance to have adv? and could easily set specific values for Elem. Adv/ Elem. Dmg values in these cases, each of course being reduced at each higher difficulty, since the WM enemies have specific Resist values

edit: regarding specific resist values, checked the tutorial to fact check myself, but for some reason I cant find it, and Im pretty sure Ive heard or seen it before... hmm
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Old 06-07-2010, 02:58 AM   #6
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I wrote ele adv in multiplier form as in,

100 ele adv -> 100*0.0035 = 0.35 so a global damage multiplier of (1+0.35) = 1.35

So its in decimal form, not percentage.

I was thinking maybe I should write a separate multiplier for LWs with elemental attributes basically saying this is the max bonus you get out of this LW when the elements are aligned properly. And put this value in [] to set them apart. Some LWs are element heavy and would appear to have low DV/DM when their true utility is element. Having an extra value could show that.

I would love to see these resist values, they could go a long way to capture the effect of elements. But yea, can't find them.
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Old 06-07-2010, 11:13 AM   #7
udon
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Awesome guide.... I think! :D

I think we need some examples to really understand how this differ from the currently known and used atk values. I know YOU know your stuff, but I don't really follow yet.

Can you give some examples how you would evaluate some LWs (that Teamish value differently for example, and not those with itemfind and ryo etc ;))

Also, Resist Values? I don't think WM enemies RES is modified at all for higher diffs. Just enemy E.Adv.
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Old 06-07-2010, 11:43 AM   #8
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Yea, I'm going to do that as soon as I get some time to process the remaining LWs. I only have the LWs that I plan on using processed so far, that's why I haven't posted the actual guide yet. But I figure I post the basis for the guide first to get some feedback.

Edit: anybody knows how to make spoiler tags?
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Old 10-25-2010, 05:01 PM   #9
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Quote:
Originally Posted by Firehydrant View Post
Yea, I'm going to do that as soon as I get some time to process the remaining LWs. I only have the LWs that I plan on using processed so far, that's why I haven't posted the actual guide yet. But I figure I post the basis for the guide first to get some feedback.

Edit: anybody knows how to make spoiler tags?
check it out.

Spoiler:
Use these tags >> [ SPOILER ] [ / SPOILER ]
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Old 10-25-2010, 06:11 PM   #10
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Quote:
Originally Posted by udon View Post
Also, Resist Values? I don't think WM enemies RES is modified at all for higher diffs. Just enemy E.Adv.
Udon ain't sure about his game^^ Or did Madara send a body-double?

Anyways, another fine guide, even though I couldn't understand much.
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