Redux (Order of Operations)

[Riltus]

The purpose of this post is to explain how damage is reduced (order of operations) with the current redux model.

In the old model, DFredux, the weapon damage factor (DF) was reduced using a redux factor (RF) with the formula: .ceil((DF * (1-RF)) = DFr, where DFr is the reduced weapon DF. (DFr * endroll success margin) determined actual raw damage taken. The critical rank with corresponding damage was based on the reduced raw damage but there was no critical damage reduction. It has remained an open question whether or not there is just 1 or 2 redux factors used in the current model (answer is 1) and the order of operations for reducing damage.

The new model, total damage reduction, consists of two parts. Part I functions similarly to DFredux: the weapon damage factor is reduced by the redux factor and the resulting reduced raw damage determines the maximum critical rank. Part II includes an additional raw damage reduction bonus plus critical damage reduction.

Order of Operations

Part I (DFredux): Calculating the reduced weapon damage factor and reduced raw damage.
Note: This is calculated exactly as it was in the old DFredux model.

I'll designate the reduced weapon damage factor as DFr.

DFr = .ceil((DF * (1-RF))

Example using the following data (1st entry in the data set below)

Level 66 with 382 redux points (no spells)
ER success margin: 223
Weapon damage factor: .200 (broadsword vs plate)
Crit damage: 10
Redux factor: .353
DFr (reduced weapon DF): .130 [.ceil((.200 * (1-.353))]
Reduced raw damage: 29 [round(223 * .130)]
Total damage taken: 26

Note: The actual redux factor is greater than .352 and less than .355. Both .353 and .354 fit the data. I was able to back out the RF range from the data set.

The reduced raw damage determines the maximum critical rank. In the above example with 29 raw damage and the defender wearing plate armor, the maximum critical rank is 2 [trunc(29/11)].

Part II (Total Damage Reduction): Reduction of both reduced raw and unreduced crit damage.

Formula:

Total damage taken = (Reduced raw damage + Crit damage) - trunc((reduced raw + crit) * RF))

Example:

Reduced raw damage: 29
Crit damage: 10
Redux factor: .353

Calculated damage taken = (29 + 10) - trunc((29 + 10) * .353))
Calculated damage taken = 26
Actual damage taken (from 1st data entry) = 26

The following is from a data set for a level 66 character with 382 redux points posted by Latrinsorm. The above example uses the first entry (ER 323 with 10 crit damage)


RP RF +/- CrDa ER D TD
382 0.527 0.005 10 323 26 55
382 0.560 0.005 5 323 22 50
382 0.535 0.006 5 292 20 43
382 0.531 0.006 10 293 23 49
382 0.553 0.007 5 265 17 38
382 0.553 0.006 3 275 17 38
382 0.569 0.005 3 338 22 51
382 0.533 0.006 7 292 21 45
382 0.558 0.006 3 302 19 43
382 0.531 0.006 10 295 23 49
382 0.537 0.006 5 279 19 41
382 0.559 0.007 1 265 15 34
382 0.542 0.005 3 327 22 48
382 0.553 0.005 1 330 21 47
382 0.545 0.005 3 306 20 44

RP = redux points
RF = redux factor (these values represent the percentage of damage taken/calculated damage.
CrDa = critical damage
ER = endroll
D = actual damage taken
TD = Total unreduced damage

Summary

1. The current redux model retains DFredux but also adds additional raw and crit damage reduction.
2. The actual redux factor is significantly lower (approximately 2/3rds) than the commonly calculated redux factor used to estimate reduced damage.
3. Using this order of operation has given exact results for all the data I have.
4. The redux factor for the level 66 character with 382 redux points is >.352 to <.355 and the broadsword's DF (.200) is reduced to .130.

Mark

[gilchristr]

So at a high level the redo of redux added a second layer, leaving the first layer unchanged? Kind of like some other redone systems like critical randomization.

[Danical]

Well done. Really great work.

This second reduction in damage explains why I was getting rank 1 criticals and resulting in rank 1 wounds when the raw damage would normally be less than sufficient to normally cause a rank 1 critical.

[Danical]

I wonder if this model is how Resistance is calculated.



A swirling sonic barrier partially deflects the onslaught of the shocking attack.
Rimalon hurls a powerful lightning bolt at you!
AS: +535 vs DS: +288 with AvD: +40 + d100 roll: +90 = +377
... and hits for 45 points of damage!
Heavy spark to back. Bet that hurts.
You are stunned for 1 rounds!

[Geijon Khyree]

How about a capped warrior with 25 spells?

[rolfard]

Is one spell a flat effect or somehow exponential?

[Geijon Khyree]

We need some help understanding how spells impact redux Mark. Please! :)

[Roblar]

I'm curious and can be available for test beatings.

At 83 spell ranks now, but haven't noticed anything really major for a redux drop (total anecdotal observation).

[Geijon Khyree]

I feel like I lost a tier of damage reduction going from no spells to 25 without the benefit of 430. I can check logs, but where bandits would hit me for 11 they now seem to do 13-15.

[Roblar]

Oh I'm sure there is an impact, but much less than I feared, especially when compared to the benefits reaped.

Your example itself is something anyone should be able to live with.

[Geijon Khyree]

Oh I'm sure there is an impact, but much less than I feared, especially when compared to the benefits reaped.

Your example itself is something anyone should be able to live with.

Agreed ;)

[Riltus]

I should be able to back out, within a narrow range, your current redux factors.

What I'll need. At least two sets of 10 attacks, preferably with critical damage. Low level crits are fine (ranks 1 and 2). For each set a different known weapon damage factor that are not integer multiples of each other. For example handaxe (DF .210) and scimitar (DF .165) vs plate would be fine. No damage weighting or padding. I'll also need character level, redux points, and spell ranks.

In addition to the spell penalty there are still other redux unknowns.

1. Level 100 redux point threshold (108??)
2. Level penalty?
3. Linear or nonlinear

It has been commonly accepted that the redux function is nonlinear. I'm not sure that is accurate. It could be a series of additive bonus. For example, the first 10 points above the threshold add .005 per point. The next 30 points add .003 per point. The next 30 points add .002 per point etc. With 70 effective redux points the redux factor would be (.05 + .09 + .06) = RF 0.200. This is yet to be determined.
4. Redux cap. Is there either a redux factor or redux points cap?

Guesstimates

Geijon : 8-10% redux factor penalty
Roblar: 28-30% redux factor penalty

Mark

[Riltus]

I have a rough estimate of ~60% penalty for a capped character with 305 effective redux points (413 actual points) and 126 spell ranks.. Expected redux factor without spells ~0.36. Actual RF with 126 spell is ~0.14

Note: Effective redux points = (total redux points - redux threshold)

Mark

[Roblar]

Level: 100
Redux points: 1,258.3 (pretty sure)
Spell ranks: 83


Relevant unenhanced skills:

Two Weapon Combat..................| 302 202
Armor Use..........................| 403 303
Shield Use.........................| 403 303
Combat Maneuvers...................| 302 202
Edged Weapons......................| 302 202
Blunt Weapons......................| 302 202
Two-Handed Weapons.................| 201 101
Ranged Weapons.....................| 201 101
Thrown Weapons.....................| 302 202
Polearm Weapons....................| 201 101
Brawling...........................| 302 202
Ambush.............................| 140 40
Multi Opponent Combat..............| 302 202
Physical Fitness...................| 403 303
Dodging............................| 403 303


11 with unweighted maul:

Geijon looks determined and focused.
In an awe inspiring display of combat mastery, Geijon engages you in a furious dance macabre, spiralling into a blur of strikes and ripostes!
Geijon swings a gleaming rune-scribed maul at you!
AS: +679 vs DS: +462 with AvD: +39 + d100 roll: +59 = +315
... and hits for 44 points of damage!
Mighty blow cracks several of your ribs.
Geijon swings a gleaming rune-scribed maul at you!
AS: +679 vs DS: +462 with AvD: +39 + d100 roll: +88 = +344
... and hits for 57 points of damage!
Your stomach is ripped open by a mighty blow!
You are stunned for 3 rounds!

Geijon looks determined and focused.
In an awe inspiring display of combat mastery, Geijon engages you in a furious dance macabre, spiralling into a blur of strikes and ripostes!
Geijon swings a gleaming rune-scribed maul at you!
AS: +679 vs DS: +447 with AvD: +39 + d100 roll: +76 = +347
... and hits for 53 points of damage!
Your shield arm is mangled horribly.
You are stunned for 3 rounds!
Geijon looks determined and focused.
In an awe inspiring display of combat mastery, Geijon engages you in a furious dance macabre, spiralling into a blur of strikes and ripostes!
Geijon swings a gleaming rune-scribed maul at you!
AS: +663 vs DS: +462 with AvD: +39 + d100 roll: +82 = +322
... and hits for 46 points of damage!
Smash to the kneecap.
Geijon swings a gleaming rune-scribed maul at you!
AS: +663 vs DS: +450 with AvD: +39 + d100 roll: +74 = +326
... and hits for 49 points of damage!
Respectable shot to your back.
You are stunned for 1 rounds!

Geijon looks determined and focused.
In an awe inspiring display of combat mastery, Geijon engages you in a furious dance macabre, spiralling into a blur of strikes and ripostes!
Geijon swings a gleaming rune-scribed maul at you!
AS: +663 vs DS: +437 with AvD: +39 + d100 roll: +50 = +315
... and hits for 44 points of damage!
Left elbow smashed into a thousand pieces.
You are stunned for 2 rounds!

Geijon looks determined and focused.
In an awe inspiring display of combat mastery, Geijon engages you in a furious dance macabre, spiralling into a blur of strikes and ripostes!
Geijon swings a gleaming rune-scribed maul at you!
AS: +637 vs DS: +464 with AvD: +39 + d100 roll: +7 = +219
... and hits for 26 points of damage!
Torn muscle in your right leg!
Geijon swings a gleaming rune-scribed maul at you!
By amazing chance, you evade the attack!
Geijon swings a gleaming rune-scribed maul at you!
AS: +637 vs DS: +452 with AvD: +39 + d100 roll: +14 = +238
... and hits for 29 points of damage!
Bones in right arm crack.

Geijon looks determined and focused.
In an awe inspiring display of combat mastery, Geijon engages you in a furious dance macabre, spiralling into a blur of strikes and ripostes!
Geijon swings a gleaming rune-scribed maul at you!
AS: +688 vs DS: +449 with AvD: +39 + d100 roll: +38 = +316
... and hits for 44 points of damage!
Grazing blow to your stomach.
Geijon swings a gleaming rune-scribed maul at you!
AS: +688 vs DS: +435 with AvD: +39 + d100 roll: +29 = +321
... and hits for 45 points of damage!
Mighty blow cracks several of your ribs.
Geijon swings a gleaming rune-scribed maul at you!
AS: +688 vs DS: +435 with AvD: +39 + d100 roll: +65 = +357
... and hits for 55 points of damage!
Respectable shot to your back.
You are stunned for 1 rounds!

10 with unweighted war mattock:

Geijon looks determined and focused.
In an awe inspiring display of combat mastery, Geijon engages you in a furious dance macabre, spiralling into a blur of strikes and ripostes!
Geijon swings an enruned imflass war mattock at you!
AS: +626 vs DS: +462 with AvD: +35 + d100 roll: +78 = +277
... and hits for 34 points of damage!
Smash to the kneecap.
Geijon swings an enruned imflass war mattock at you!
AS: +626 vs DS: +450 with AvD: +35 + d100 roll: +80 = +291
... and hits for 35 points of damage!
Smash to the kneecap.
Geijon swings an enruned imflass war mattock at you!
AS: +626 vs DS: +450 with AvD: +35 + d100 roll: +7 = +218
... and hits for 23 points of damage!
Bones in right arm crack.

Geijon looks determined and focused.
In an awe inspiring display of combat mastery, Geijon engages you in a furious dance macabre, spiralling into a blur of strikes and ripostes!
Geijon swings an enruned imflass war mattock at you!
AS: +626 vs DS: +435 with AvD: +35 + d100 roll: +92 = +318
... and hits for 43 points of damage!
Solid blow gouges a chunk out of your right leg.
You are stunned for 1 rounds!
Geijon swings an enruned imflass war mattock at you!
AS: +626 vs DS: +372 with AvD: +35 + d100 roll: +51 = +340
... and hits for 50 points of damage!
Flesh ripped from your back, muscles exposed.
Geijon swings an enruned imflass war mattock at you!
AS: +626 vs DS: +372 with AvD: +35 + d100 roll: +82 = +371
... and hits for 54 points of damage!
Whoosh! Several ribs driven into your lungs.

Geijon looks determined and focused.
In an awe inspiring display of combat mastery, Geijon engages you in a furious dance macabre, spiralling into a blur of strikes and ripostes!
Geijon swings an enruned imflass war mattock at you!
AS: +610 vs DS: +464 with AvD: +35 + d100 roll: +95 = +276
... and hits for 37 points of damage!
Respectable shot to your back.
You are stunned for 1 rounds!
Geijon swings an enruned imflass war mattock at you!
AS: +610 vs DS: +444 with AvD: +35 + d100 roll: +45 = +246
... and hits for 29 points of damage!
Mighty blow cracks several of your ribs.
Geijon swings an enruned imflass war mattock at you!
AS: +610 vs DS: +444 with AvD: +35 + d100 roll: +93 = +294
... and hits for 36 points of damage!
Smash to the kneecap.

Geijon swings an enruned imflass war mattock at you!
AS: +705 vs DS: +455 with AvD: +35 + d100 roll: +6 = +291
... and hits for 34 points of damage!
Large gash to your right arm, several muscles torn.
You are stunned for 1 rounds!
The guiding force leaves Geijon.

[Geijon Khyree]

Level: 100
Redux ranks:

Geijon (at level 100), your current skill bonuses and ranks (including all modifiers) are:
Skill Name | Current Current
| Bonus Ranks
Armor Use..........................| 240 140
Combat Maneuvers...................| 307 207
Two-Handed Weapons.................| 327 227
Ambush.............................| 105 25
Multi Opponent Combat..............| 155 55
Physical Fitness...................| 403 303
Dodging............................| 302 202
Arcane Symbols.....................| 86 19
Magic Item Use.....................| 58 12
Harness Power......................| 25 5
Spiritual Lore - Summoning.........| 2 0
Survival...........................| 25 5
Perception.........................| 25 5
Climbing...........................| 64 13
Swimming...........................| 25 5
First Aid..........................| 25 5

Spell ranks: 25

10 with a handaxe

Roblar swings a radiant dark ora-bladed axe at you!
AS: +578 vs DS: +298 with AvD: +23 + d100 roll: +31 = +334
... and hits for 29 points of damage!
Bones in left arm crack.

Roblar swings a radiant dark ora-bladed axe at you!
AS: +568 vs DS: +298 with AvD: +23 + d100 roll: +10 = +303
... and hits for 23 points of damage!
Quick slash to your upper right arm!
Just a nick

Roblar swings a radiant dark ora-bladed axe at you!
AS: +568 vs DS: +298 with AvD: +23 + d100 roll: +46 = +339
... and hits for 28 points of damage!
Slash to your left leg hits high!
Kinda makes your knees weak, huh?

Roblar swings a radiant dark ora-bladed axe at you!
AS: +568 vs DS: +291 with AvD: +23 + d100 roll: +96 = +396
... and hits for 37 points of damage!
Feint to the left goes astray as you dodge!
Deep gouge to your back!

Roblar swings a radiant dark ora-bladed axe at you!
AS: +691 vs DS: +298 with AvD: +23 + d100 roll: +87 = +503
... and hits for 54 points of damage!
Diagonal slash leaves a bloody trail across your torso.
You are stunned for 3 rounds!

Roblar swings a radiant dark ora-bladed axe at you!
AS: +691 vs DS: +298 with AvD: +23 + d100 roll: +70 = +486
... and hits for 46 points of damage!
Left elbow smashed into a thousand pieces.
You are stunned for 2 rounds!

Roblar swings a radiant dark ora-bladed axe at you!
AS: +691 vs DS: +278 with AvD: +23 + d100 roll: +91 = +527
... and hits for 55 points of damage!
Deft slash to your left leg digs deep!
Bone is chipped!

Roblar swings a radiant dark ora-bladed axe at you!
AS: +626 vs DS: +298 with AvD: +23 + d100 roll: +45 = +396
... and hits for 37 points of damage!
Smash to the kneecap.

Roblar swings a radiant dark ora-bladed axe at you!
AS: +626 vs DS: +291 with AvD: +23 + d100 roll: +52 = +410
... and hits for 38 points of damage!
Banged your right shin.
That'll raise a good welt.

Roblar swings a radiant dark ora-bladed axe at you!
AS: +626 vs DS: +298 with AvD: +23 + d100 roll: +55 = +406
... and hits for 36 points of damage!
Large gash to your left arm, several muscles torn.
You are stunned for 1 rounds!

Falchion base

Roblar swings a mirror-edged brushed silver khopesh at you!
AS: +681 vs DS: +291 with AvD: +21 + d100 roll: +10 = +421
... and hits for 34 points of damage!
Banged your left shin.
That'll raise a good welt.
The guiding force leaves Roblar.

Roblar swings a mirror-edged brushed silver khopesh at you!
AS: +606 vs DS: +268 with AvD: +21 + d100 roll: +85 = +444
... and hits for 35 points of damage!
Glancing slash to your shield arm!
You are stunned for 1 rounds!

** Roblar's brushed silver khopesh releases a spray of acid! **

... 30 points of damage!
Acid hits you full in the left eye! Nothing left but a smoking socket!

Hehe

Roblar swings a mirror-edged brushed silver khopesh at you!
AS: +655 vs DS: +271 with AvD: +21 + d100 roll: +23 = +428
... and hits for 35 points of damage!
Downward slash across your left thigh
Gouges bone!
You are stunned for 1 rounds!

Roblar swings a mirror-edged brushed silver khopesh at you!
AS: +655 vs DS: +242 with AvD: +21 + d100 roll: +31 = +465
... and hits for 38 points of damage!
Banged your right shin.


Roblar swings a mirror-edged brushed silver khopesh at you!
AS: +655 vs DS: +272 with AvD: +21 + d100 roll: +1 = +405
... and hits for 31 points of damage!
Hesitant slash to your upper right arm!
Just a scratch.


Roblar swings a mirror-edged brushed silver khopesh at you!
AS: +655 vs DS: +266 with AvD: +21 + d100 roll: +16 = +426
... and hits for 34 points of damage!
Banged your left shin.
That'll raise a good welt.

Roblar swings a mirror-edged brushed silver khopesh at you!
AS: +655 vs DS: +274 with AvD: +21 + d100 roll: +29 = +431
... and hits for 35 points of damage!
Banged your left shin.
That'll raise a good welt.


Roblar swings a mirror-edged brushed silver khopesh at you!
AS: +655 vs DS: +244 with AvD: +21 + d100 roll: +71 = +503
... and hits for 40 points of damage!
Glancing slash to your shield arm!
You are stunned for 1 rounds!


Roblar swings a mirror-edged brushed silver khopesh at you!
AS: +655 vs DS: +244 with AvD: +21 + d100 roll: +99 = +531
... and hits for 43 points of damage!
Powerful slash just cracks your weapon arm!
You are stunned for 2 rounds!

Roblar swings a mirror-edged brushed silver khopesh at you!
AS: +653 vs DS: +275 with AvD: +21 + d100 roll: +27 = +426
... and hits for 33 points of damage!
Glancing slash to your shield arm!
You are stunned for 1 rounds!

[Riltus]

I'm banging my head against the wall.

Is this a perfect maul with a non-standard DF?
gleaming rune-scribed maul

Looks like it based on the AvD. Before I continue can you confirm?

Mark

[Geijon Khyree]

It's a 10x perfect maul with t3 ensorcell

[Geijon Khyree]

We can test Roblar with a different weapon if it's causing headaches.

[Riltus]

We can test Roblar with a different weapon if it's causing headaches.

It shouldn't be necessary. I can use those attacks, if I need them, with a .318 DF. Thanks for confirming.

Mark

[gilchristr]

I noticed you said relevant unenhanced skills

Were you wearing your enhancives when you took those shots?

[Geijon Khyree]

Roblar posted skill base. Mine is skill but my armor and a bunch of enhances were off. It shouldn't matter.


For reference though:
Geijon (at level 100), your base skill bonuses, ranks and goals are:
Skill Name | Actual Actual
| Bonus Ranks Goals In-Game Time to Goal
Armor Use..........................| 240 140 140
Combat Maneuvers...................| 302 202 202
Two-Handed Weapons.................| 302 202 202
Ambush.............................| 102 24 24
Multi Opponent Combat..............| 155 55 55
Physical Fitness...................| 403 303 303
Dodging............................| 302 202 202
Arcane Symbols.....................| 86 19 19
Magic Item Use.....................| 58 12 12
Harness Power......................| 25 5 5
Survival...........................| 25 5 5
Perception.........................| 25 5 5
Climbing...........................| 50 10 10
Swimming...........................| 25 5 5
First Aid..........................| 25 5 5

>exp
Level: 100 Deeds: 0
Experience: 9001054 Death's Sting: None
Exp. to next TP: 1446 Recent Deaths: 3
Mental TPs: 0 Fame: 38077286
Physical TPs: 8 Mana: 25/25 max
(432 Phy converted to Mnt)

I'm at the very edge of non-gimp to achieve 425.

[Riltus]

Roblar, Level 100, 83 spell ranks, ~1210 effective redux points

Redux Factor: .272 (this is the exact value)

Maul DF: .318
Reduced Maul DFr: .232

War Mattock DF: .275
Reduced War Mattock DFr: .201
---------------------------------------

Geijon, level 100, 25 spell ranks, ~500 effective redux points

Redux Factor: .310/.311/.312 (each of these RFs fit the data provided)

Handaxe DF: .210
Reduced Handaxe DFr: .145

Falchion DF: .175
Reduced Falchion DFr: .121
----------------------------------------

All the DFs are exact values.

Estimated redux factors without spells (this is a semi-educated guess) lol

Roblar: ~.390
Geijon: ~.370

Estimated RF spell penalties

Roblar: ~30%
Geijon: ~16%

I'll add more info tomorrow with comparisons of damage with/without spells etc.

Mark

[Geijon Khyree]

Exciting! You work so fast!

Am I suffering because I've got less primary training stats compared to Roblar and it's inflating my spell penalties? This is great stuff. Your cracked the code on this!

I did the simple math on the maul since you reacted. Your surprise and clarity question seemed to be why my maul had 39 avd and not 36 = (cause it's perfect), but everything else is normal, ya?

[Roblar]

I noticed you said relevant unenhanced skills

Were you wearing your enhancives when you took those shots?

Technically yes, but I had all enhancives turned off during those shots.


Riltus, thanks for the calculations! Does CON bonus and its natural padding impact anything?

[Riltus]

Exciting! You work so fast!

Am I suffering because I've got less primary training stats compared to Roblar and it's inflating my spell penalties? This is great stuff. Your cracked the code on this!

I did the simple math on the maul since you reacted. Your surprise and clarity question seemed to be why my maul had 39 avd and not 36 = (cause it's perfect), but everything else is normal, ya?

The difference in redux points is not affecting the spell penalty. The spell penalty is based on the percentage of spells per level but it is not strictly linear. Roblar would have the same ~16% penalty to his redux factor with 25 spell ranks since you are both level 100.

I started doing the calculations without having first checked the maul AvD. That was an oversight on my part. Using a DF of .300 was causing havoc when applied to the Order of Operations formula.

To accurately calculate the spell penalty we would also need to calculate the redux factor without spells (while maintaining the same number of redux points. This would require a fixskill.

Mark

[Riltus]

Technically yes, but I had all enhancives turned off during those shots.


Riltus, thanks for the calculations! Does CON bonus and its natural padding impact anything?

It doesn't affect redux factor calculations.

Mark

[Geijon Khyree]

I was trying to fish up my training from about a month ago before I skilled into spells. You would need a fixskill and the same 10 attacks with different weapon modifiers?

I had 100 MOC, 30 ambush, and 202 brawling as redux stats at the time.

[Geijon Khyree]

I wonder what Drangell's Redux is as an NPC.

You swing a gleaming rune-scribed maul at Drangell!
AS: +803 vs DS: +520 with AvD: +41 + d100 roll: +68 = +392
... and hit for 91 points of damage!
A mighty hit turns Drangell's insides to outsides!

* Drangell drops dead at your feet!

[Riltus]

I wonder what Drangell's Redux is as an NPC.

You swing a gleaming rune-scribed maul at Drangell!
AS: +803 vs DS: +520 with AvD: +41 + d100 roll: +68 = +392
... and hit for 91 points of damage!
A mighty hit turns Drangell's insides to outsides!

* Drangell drops dead at your feet!

This is interesting. Backing out the RF range yields the following:

Order of Operations Formulas:


DFr = .ceil((DF * (1-RF))


Total damage taken = (Reduced raw damage + Crit damage) - trunc((reduced raw dmg + crit dmg) * RF))

Unreduced weapon DF: .450 (perfect maul vs scale) trunc[.425 * 1.06]
Unreduced raw damage: 131.4 (292 * .450)
Estimated RF: .406
DFr w/.406 redux factor: .268 [.ceil(.450 * (1-.406))]
Endroll success margin: 292
Reduced raw damage: 78 [round(292 * .268)]
Crit damage: 75 (R9 crush - abdomen)
Total reduced raw + crit dmg: 152

Using the total damage taken formula:


152 - trunc(152 * .406) = 91 which matches the actual damage taken

It turns out the following redux factors and their corresponding reduced weapon damage factors each satisfy the actual result of 91 damage.

RF .406 w/DFr .268
RF .407 w/DFr .267
RF .408 w/DFr .267
RF .409 w/DFr .266
RF .410 w/DFr .266
RF .411 w/DFr .266

Assuming that there is no damage padding and that Drangell has max skills (~1450 total redux points) then the theoretical maximum redux factor is within the range .406 to .411 without enhanced stats.
-----------------------------------------------------------------------------------------------------------
Using the common method for calculating damage reduction:

1 - (total unreduced damage/actual damage)

Total unreduced damage: 206.4 (131.4 raw + 75 crit)
Actual damage: 91

1 - (91/206.4) = .559 or 55.9% redux
and adjusting for CDR = .589

Mark

[Geijon Khyree]

Awesome. I'm glad you could go where I thought you could with that!

[Riltus]

An approximate redux factor can be calculated by using the coefficients and constant of a quadratic equation in the standard form ax^2 + bx + c = 0

x = redux factor, a = raw damage, b = (2a + crit damage) and the constant c = the sum of (raw damage + crit damage - actual damage + 0.5).

What's needed? Approximately 6 to 10 attacks with decent raw and critical damage. A weapon with a known damage factor and the attack's critical damage. Do not use damage weighted weapons or damage padded armor. Crit weighting and padding are acceptable.

a = raw damage (do not round): Quadratic Coefficient
b = 2a + crit damage (always enter this as a negative value): Linear Coefficient
c = a + crit damage - actual damage + 0.5: Constant

Note: raw damage is (endroll - 100) * weapon damage factor

If you don't have quadratic equation calculator handy one can found at:

http://www.math.com/students/calculators/source/quadratic.htm

Simply enter the A, B, C values and click SOLVE. The redux factor is X2.

Example:

You swing a gleaming rune-scribed maul at Drangell!
AS: +803 vs DS: +520 with AvD: +41 + d100 roll: +68 = +392
... and hit for 91 points of damage!
A mighty hit turns Drangell's insides to outsides!

Weapon DF: .450 (perfect maul vs scale)
Raw damage: 131.4 (292 * .450)
Crit damage: 75 (R9 crush - abdomen)
Actual damage: 91

a = 131.4 (raw damage)
b = 337.8 (raw damage * 2) + crit damage
c = 115.9 (raw damage + crit damage + 0.5 - actual damage)

Redux Factor: ~.408 (0.4077873841171237 is the X2 value from the online calculator).


Mark

[Latrinsorm]

Very nice :D

[gilchristr]

So I did this and x1 is reported as -0.26515886314965686, and x2 was reported as -2.2177956823048888.

Whats my redux? Is it a value in that range, or is it the absolute value of x2? (which would put my redux at 2.22%, this was at 34 trains with 25 spells and 117.4 redux ranks NOT COUNTING ENHANCIVES WORN, 127.7 redux points if you count enhancives worn)

[Riltus]

So I did this and x1 is reported as -0.26515886314965686, and x2 was reported as -2.2177956823048888.

Whats my redux? Is it a value in that range, or is it the absolute value of x2? (which would put my redux at 2.22%, this was at 34 trains with 25 spells and 117.4 redux ranks NOT COUNTING ENHANCIVES WORN, 127.7 redux points if you count enhancives worn)

Can you post a log of the attack and the values that you used? I'll need the endroll, weapon DF, crit messaging and actual damage taken. X1 and X2 should be positive. Your enchancives should be counting toward redux points.

It should look something like this:

A: 24 (raw damage)
B: -55 ((2 * raw damage)+ crit damage)
C: 2.5 (raw damage + crit damage + 0.5) - actual damage taken

X1: 2.24527290016323
X2: 0.04639376650343641

Although B has a positive value when calculated, it is necessary to enter it with a minus sign.

X2 is the redux factor but it is only an approximate value because the damage formula includes both rounding and truncation.

Mark

[gilchristr]

Mark - would you like me to do some testing on enhancives and redux? I have low redux and I think I just picked up some +14 PF fodder, between that and my CM enhancives, there should be a not insignificant difference between hits with the enhancives on and without them, for comparison to confirm that enhancives affect redux calculations.

Thanks, I bet I forgot to enter B as a negative. I used the values from the first of three hits that I previously recorded in this thread.

http://forum.gsplayers.com/showthread.php?96598-damage-reduction-at-34th-train-bard


I took a 188 endroll with a scythe in brig (I have no damage padding abilities... im in voln, and a bard, brig is crit padded), and got the crit "right kneecap smashed into pulp" ... total damage 49

I have the bonus damage from that crit as 17, which means the damage before the bonus was 32.
but 88*.4 = 35.2

Took a 243 endroll with the crit "shield arm is mangled horribly" for 67 total damage, which means damage before the bonus was 52
but 143*.4 = 57.2

took a 213 endroll with the crit "right kneecap smashed into pulp" for 58 total damage, which means damage before the bonus was 41
but 112*.4 = 45.2


a = raw damage (do not round): 88*.4=35.2Quadratic Coefficient
b = 2a + crit damage (always enter this as a negative value): -70.4-17=-87.4Linear Coefficient
c = a + crit damage - actual damage + 0.5: 35.2-32+0.5=3.7Constant

x2=0.043 ... SO 4.3% REDUX

calculated again from the third shot and got 4.49%, as you said these are approximate values since there is rounding and truncating

Thank you Mark!

[gilchristr]

Ok, took some shots tonight from a halberd again, and its pretty clear to see that enhancives are changing redux. First I manipulated my CM ranks so that my total redux points were almost identical to the total redux points with enhancives from my earlier numbers. Worked out two shots at 4.1%

Then I put on 12.4 worth of redux points (31 CM ranks), took a couple more shots, did calculations and got 7.9% and 8.9%.

[Riltus]

Ok, took some shots tonight from a halberd again, and its pretty clear to see that enhancives are changing redux. First I manipulated my CM ranks so that my total redux points were almost identical to the total redux points with enhancives from my earlier numbers. Worked out two shots at 4.1%

Then I put on 12.4 worth of redux points (31 CM ranks), took a couple more shots, did calculations and got 7.9% and 8.9%.

That's great to now have it confirmed! Thanks for testing it.

Mark

[Khariz]

Here's something fun to calculate redux from. Drangell hitting you!

Drangell looks determined and focused.
In an awe inspiring display of combat mastery, Drangell engages you in a furious dance macabre, spiralling into a blur of strikes and ripostes!
Drangell swings a huge glowing white axe at you!
Some damascened black rolaren plate partially deflects the onslaught of the slashing attack.
AS: +996 vs DS: +475 with AvD: +23 + d100 roll: +70 = +614
... and hits for 40 points of damage!
Hard slash to belly severs a few nerve endings.
You are stunned for 3 rounds!
Drangell swings a huge glowing white axe at you!
Some damascened black rolaren plate is overwhelmed by the onslaught of the crushing attack.
AS: +996 vs DS: +465 with AvD: +23 + d100 roll: +37 = +591
... and hits for 55 points of damage!
Your left leg is mangled horribly.
You are knocked to the ground!
Drangell swings a huge glowing white axe at you!
Some damascened black rolaren plate partially deflects the onslaught of the slashing attack.
AS: +996 vs DS: +393 with AvD: +23 + d100 roll: +16 = +642
... and hits for 42 points of damage!
Slash along your lower back.
Drangell swings a huge glowing white axe at you!
Some damascened black rolaren plate is overwhelmed by the onslaught of the crushing attack.
AS: +996 vs DS: +393 with AvD: +23 + d100 roll: +75 = +701
... and hits for 64 points of damage!
Whoosh! Several ribs driven into your lungs.
!SPJR>

[Roblar]

Me too! Maybe not enough hits but look at that damn hidden kroderine or whatever he has - did not know it could take that many spells.


Drangell looks determined and focused.
In an awe inspiring display of combat mastery, Drangell engages you in a furious dance macabre, spiralling into a blur of strikes and ripostes!
Drangell swings a huge glowing white axe at you!
With extreme effort, you beat back the attack with your waraxe!
Drangell swings a huge glowing white axe at you!
AS: +956 vs DS: +534 with AvD: +23 + d100 roll: +24 = +469
... and hits for 51 points of damage!
Right elbow smashed into a thousand pieces.
You are stunned for 2 rounds!
Drangell swings a huge glowing white axe at you!
AS: +956 vs DS: +502 with AvD: +23 + d100 roll: +68 = +545
... and hits for 63 points of damage!
Eye crushed by a hard blow to the face!

** Drangell's glowing white axe glows brightly for a moment, consuming the magical energies around you! **

The deep blue glow leaves you.
Deep blue motes swirl away from you and fade.
You are coated in a hazy film.
The very powerful look leaves you.
The white light leaves you.
The dull golden nimbus fades from around you.
The brilliant aura fades away from you.
The layer of protection fades away.
Your intensity and fervor recedes.
You feel the inner strength leave you.
Your boosted confidence and fearlessness fade.
The light blue glow leaves you.
You feel less confident.
The powerful look leaves you.
You feel the extra courage wane.
A dark shadow seems to detach itself from your body, swiftly dissipating into the air.
The brilliant luminescence fades from around you.
Drangell swings a huge glowing white axe at you!
You stumble dazedly, somehow managing to block the attack with your rolaren waraxe!

[Aganii]

That is what Spell Cleave needs to be, good lord.

[Riltus]

Here's something fun to calculate redux from. Drangell hitting you!

Drangell looks determined and focused.
In an awe inspiring display of combat mastery, Drangell engages you in a furious dance macabre, spiralling into a blur of strikes and ripostes!
Drangell swings a huge glowing white axe at you!
Some damascened black rolaren plate partially deflects the onslaught of the slashing attack.
AS: +996 vs DS: +475 with AvD: +23 + d100 roll: +70 = +614
... and hits for 40 points of damage!
Hard slash to belly severs a few nerve endings.
You are stunned for 3 rounds!
Drangell swings a huge glowing white axe at you!

Drangell axe: standard handaxe DF of .210 vs plate
Redux Factor: ~.391
Slash Resistance: 25%
Crush Vulnerability: 10%

Redux reduced the weapon DF from .210 to DFr .129

Success Margin: 514
DFr: .129
Raw damage: 66 (514 * .129)
Crit damage: 15 (Rank 3 w/3 round stun, L2 abs and L1 nerve injuries)
Slash Resistance 25%: -16 dmg [trunc(66*.25)]
Modified raw damage: 50 (66 - 16)
Total actual damage: 40 (50 mod dmg + 15 crit) - trunc((50 mod + 15 crit) * .391 redux factor)

Expected result without redux and slash resistance using averaged critical rank outcome after randomization.

Raw damage: 108
Crit damage: 50 (Rank 7 slash crit w/8 round stun, L3 abs and L2 back injuries)
Total calculated damage: 158

Effective damage reduction with redux and 25% slash protection: 74.6% (40 actual dmg/158 calculated dmg)


Some damascened black rolaren plate is overwhelmed by the onslaught of the crushing attack.
AS: +996 vs DS: +465 with AvD: +23 + d100 roll: +37 = +591
... and hits for 55 points of damage!
Your left leg is mangled horribly.
You are knocked to the ground!
Drangell swings a huge glowing white axe at you!


Success Margin: 491
DFr: .129
Raw damage: 63 (491 * .129)
Crit damage: 20 (Rank 5 crush w/5 round stun, knockdown, L2 leg injury)
Crush vulnerability 10%: +6 damage (63 * .10)
Modified raw damage: 69 (63 + 6)
Total actual damage: 55 (69 mod dmg + 20 crit) - trunc((69 mod + 20 crit) * .391 redux factor)

Expected result without redux and crush vulnerability

Raw damage: 103
Crit damage: 30 (Rank 7 crush w/8 round stun, limb loss, L3 leg injury)
Total calculate damage: 133

Effective damage reduction with redux and 10% crush vulnerability: 58.6% (55 actual damage/133 calc damage)

Note: The effective damage reduction percentages will vary with individual attacks.

Mark

[Riltus]

Me too! Maybe not enough hits but look at that damn hidden kroderine or whatever he has - did not know it could take that many spells.


Drangell looks determined and focused.
In an awe inspiring display of combat mastery, Drangell engages you in a furious dance macabre, spiralling into a blur of strikes and ripostes!
Drangell swings a huge glowing white axe at you!
With extreme effort, you beat back the attack with your waraxe!
Drangell swings a huge glowing white axe at you!
AS: +956 vs DS: +534 with AvD: +23 + d100 roll: +24 = +469
... and hits for 51 points of damage!
Right elbow smashed into a thousand pieces.
You are stunned for 2 rounds!

This is estimated since there are two unknowns, the redux factor and spell penalty%, but it should be fairly close to the actual values.

Estimated redux factor without spell penalty: .410
Estimated redux factor with spell penalty of ~37%: .259
Reduced weapon damage factor (DFr): .156 (standard handaxe DF .210)

Success Margin: 369
DFr: .156
Raw damage: 58 [round(369 * .156)]
Crit damage: 10 (R4 crush)
Total actual damage: 51 (58 raw + 10 crit) - trunc((58 raw + 10 crit) * RF .259)

Expected result without redux using averaged critical rank outcome after randomization.

DF: .210
Raw damage: 77
Crit damage: 17 (avg rank 4,5,6,7)
Total calculated damage: 94

Effective damage reduction: 45.7% (51 actual dmg/94 calculated dmg)


Drangell swings a huge glowing white axe at you!
AS: +956 vs DS: +502 with AvD: +23 + d100 roll: +68 = +545
... and hits for 63 points of damage!
Eye crushed by a hard blow to the face!


Success Margin: 445
DFr: .156
Raw damage: 69 [round(445 * .156)]
Crit damage: 15 (R5 crush)
Total actual damage: 63 (69 raw + 15 crit) - trunc((69 raw + 15 crit) * RF .259)

Expected result without redux using averaged critical rank outcome after randomization.

DF: .210
Raw damage: 93 (445 * .210)
Crit damage: 20 (R6 crush)
Total calculated damage: 113

Effective damage reduction: 44.2% (63 actual dmg/113 calculated dmg)


Mark

[Khariz]

Thanks, man! I appreciate it!

[Roblar]

Thanks again.

100 spell ranks and more redux factor/skills than last time! Not in game to count all that but it's ok.