Redux Research

[Fallen]

Yeah..I don't know or care about Redux, but this particular poster is a wiz with this stuff. I hope it is of use to someone...

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Good News and Bad News · on 5/2/2006 5:37:18 PM


Bad News: Redux can be very highly shifted depending on body part.
Worse News: This shift is not 100% reproducible.

Method: While testing a subject (level 52), I aimed for the limbs. However, I missed and hit the chest four (4) times. In two of these instances, redux % was comparable to limb hits. In the other two, redux was roughly 15% higher (that is to say, 45% to 30%). The subject was not wearing armor, and was being subjected to a storebought broadsword. Arms and legs appear to be consistent with each other. Hands might not be consistent with limbs. The only other two areas I accidentally hit were back and neck. Back was not consistent, but happened to be a very low endroll hit, so it is very inconclusive. Neck appeared roughly consistent.

Good News: Redux sure goes up quick. Limb hits only, weighted average to follow:

RP R%
109.2 0.07%
117.2 5.77%
125.2
133.2 20.69%
141.2 23.90%
149.2 29.28%
157.2 32.44%
165.2 38.09%


I don't have uncertainties because I don't know how to calculate the uncertainty of a weighted average. The uncertainties on the individual hits (due to rounding in raw damage) ranged from 0.85 redux% to 2.78 redux% (again, meaning that a hit of 22% redux would be between about 19% and 25%). This fits pretty well to a linear regression, but obviously we don't expect that to continue. I'll have more data later.

-Anathemus' player


First thing: redux has a peculiar habit of leaping at times. At 173.2 redux points (level 52), I established a pretty good baseline of 40% for the arm region, and then on one hit I got 62.64%. So I don't know what that's about.

Secondly: I'm pretty sure I'm right on the body area thing. At 173.2 redux points, I have the following weighted averages (number of hits in parentheses):

Arm: 43.11% (8)
Leg: 45.70% (4)
Hand: 35.54% (5)

Worth noting is that the arm drops to about 40% if I change the 62% I mentioned before to 40%. Again, if anyone knows how to calculate the uncertainty of a weighted average, that would be very fulfilling.

Anyway, those are significant gaps IMO.

Recommendations:

All redux testing should be done sans armor.
All redux testing should be done with the most powerful (non-damage-weighted, non-forged) weapon available.
All redux testing should be done against the same area, for comparison's sake. I recommend arm.
All previous redux data should be discarded. We probably should have done this after the low-DF wackiness showed up, but we definitely should now.
Anyone doing redux testing now, keep track of the body part and crit type as well as all the other pertinent info.

Further plans:

I'm going to be doing some more testing on the subject I have until I return em to eir original plan. Then I plan on getting my warrior beaten up a lot to establish exactly how redux varies by body part (and from hit to hit, for that matter). Hopefully then I'll be able to go back to my first set of data and get more of a feel for how redux points to redux % works.

Note:

I hypothesized that perhaps the crit TYPE affected redux %. This does not appear to be the case. For arm at 181.2 redux points, I recorded the following data:
Crush 41.18
Puncture 40.51
Slash 39.74
Slash 43.15
Slash 45.58
Slash 39.74

By no means conclusive, but it's not as striking as hand/arm/leg is. I must note that I also have data sets that do seem to show a striking effect between crit types. I'll keep an eye on it, anyway.

What would help:

If anyone has a fixskills to burn on a redux-having character, here's what I could use. Grab a weapon that does only one kind of crit, or precision one into existence. This isn't necessary, but it would be helpful. Bring the character to 109 redux points with fixskills (or thereabouts) and add redux points until ey gets redux. Hit em in the arm twice. Add a goodly number of redux points (8-10 would be good). Repeat until you get em to eir original level of redux points. If you don't want to hit em in the arm, pick whichever body part you'd like but keep it constant.

-Anathemus' player

Okey dokey.

At 181.2 Redux Points, weighted averages vs. Arm:

Crush: 43.24% (4 hits)
Puncture: 40.31% (3 hits)
Slash: 43.75% (7 hits)

Same vs. Hand:

Crush: 39.32% (6 hits)
Puncture: 39.18% (2 hits)
Slash: 37.02% (5 hits)

165.2 Redux Points, weighted avgs vs. Leg:

Crush: 40.38% (1 hit)
Puncture: 38.13% (3 hits)
Slash: 43.31% (2 hits)

Again, these aren't enough to satisfy me. I'll have more hits for my warrior, as this experiment was originally intended for the % to RP calculation. Until I'm satisfied with the crit type and body part effects, however, I'm not going to try to work that through. The data is just too diluted.

Incidentally, the crit type rate for broadswords looks like 5/3/2 slash/crush/puncture, though I'd want more samples before I said anything definitive there too.

-Anathemus' player

[Fallen]

>Maybe the different damage types (puncture, crush, slash) all have different DFs?

I was actually testing something else that I'll get to in a minute, but I took a non-redux character and smashed her hand over and over, checking the crits to see if they matched the table. They did, and while checking this I assumed a .450 DF at all times (broadsword vs. hand). It would not be possible for the DF to differ noticeably and generate those results.

I appear to have found a phantom crit.

You swing a broadsword at Anathemus!
AS: +153 vs DS: -47 with AvD: +36 + d100 roll: +63 = +299
... and hit for 46 points of damage!
Slash to Anathemus's left hand!
Several fingers fly!

If you have the same file I do, you will find no mention of this crit under left hand, slash or either of the other two tables. As I alluded to earlier, I checked the left hand out and crits 1-6 exist as listed in my chart. Namely:

1-Slash to the giant rat's shield arm. / Strike trims off a few fingernails.
3-Wild slash scratches the back of the giant rat's hand.
5-Slice to the giant rat's left fingers. / Nice move.
7-Deep cut to the giant rat's left hand! / Seems to have broken some fingers too.
9-Slash across back of hand, tendons sliced!
10-Rapped the knuckles hard! / Left hand sounds broken.

There is a right hand version of this crit (rank 4), good for 5 points of crit damage. However, over 9 hits of hand/slash, I have a weighted average of 63.31%. The two hits, assuming the message is worth 5 points of crit damage, generate redux values of ~54%. Whatever this message is worth, it's pretty clear it isn't 5.

I couldn't reproduce the phantom crit message on the non-reduxed character. My search thing seems to be broken, so I'll try that again tomorrow.

In any event, the body part dependent redux hypothesis is going strong. The crit type dependent redux hypothesis is lagging behind a little. I've only got 50 hits so far, I'll post again when I have better sample size.

>It's reading this folder and laughing at you all right this minute.

I non-mechanistically preen in the general direction of this alleged program.

-Anathemus' player

[Fallen]

I broke down and downloaded .qrs myself, and it is in fact worth 9 damage.

I have no doubt that redux is body part dependent.

The crit type dependence is a real pain. Versus hand I have 61, 59, 60 (s/c/p). Versus leg I have 67, 71, 67. Versus arm I have 65, 65, 64. I'm going to check through and make sure all my crits have the right values. If that leg crush starts coming down, that would be nice.

I happened to get a string of 7 hits in a row with 7 crit damage, endrolls ranging from 131 to 167. Redux values to follow:

61.54%
61.81%
60.20%
66.67%
60.32%
71.33%
62.96%

+/- 2% (the actual redux %, not parts per hundred) on each. Why do I bring this up? Whatever variations redux has, they are more than simply endroll or crit rank dependent. There could ALSO be those, but there is something more, probably a simple randomizer. Just something to keep in mind.

Also, I'm getting intervals of at least 10r% between min and max on a single body part and crit type. Standard deviations, however, are around 4.5r%.

The research continues!

-Anathemus' player

I had an error in my standard deviation values before.

ArmS ArmC ArmP LegS LegC LegP HandS HandC HandP
R% 64.39% 64.56% 63.74% 66.89% 69.67% 67.44% 60.69% 60.03% 60.06%
n 32 19 7 24 19 12 41 13 13
Range 16.23% 14.23% 11.35% 12.43% 11.82% 9.60% 13.05% 16.93% 7.17%
Stdev 3.63% 3.91% 3.92% 3.92% 3.25% 2.97% 2.69% 4.19% 2.15%


All % mean "redux %" and not "parts per hundred". R% is the weighted average. n is the number of hits I have (total of 190ish I think). As you can no doubt see, the crit type is barely distinguishable on arm and hand. Leg remains troublesome (doesn't it always?), but unless someone else has something to note, I feel confident stating that crit type does not affect redux (though I will continue to segregate data by crit type until that doggone leg crush value gets in line). These ranges are pretty crazy though. In the same vein as the redux leaps I noticed before, perhaps it's possible to get redux fumbles(!) as well.

I decided to subtract the average value from the actual value for each hit, round it to the nearest percentage point, and graph the distribution. It can be seen here:
http://img.photobucket.com/albums/v456/johnnyoldschool/dist.jpg

It looks pretty good to me. Sorta jagged, but the general shape looks right for a normal-esque randomizer thingie.

-Anathemus' player

Eureka · on 5/9/2006 2:52:41 PM

This has been staring me in the face for months, it's unbelievable I haven't seen it yet.

We've been operating on the assumption that DF redux is just that, a reduction in DF. As such, it would have no effect on crit damage, only raw damage.

I propose that this is no longer the case; that DFredux can be more accurately called Total Damage Reduction. Take how much total damage we should have been hit with and reduce it by a percentage directly. I have 264 hits against constant redux points. When I run this new paradigm through my spreadsheets, I get results as follows:

ArmS ArmC ArmP LegS LegC LegP HandS HandC HandP
R% 50.65% 50.66% 49.84% 51.65% 52.35% 52.08% 49.23% 48.92% 48.94%
n 40 29 13 35 31 16 52 21 14
Range 7.19% 19.33% 6.60% 5.50% 7.25% 8.99% 7.95% 9.95% 6.46%
Stdev 1.73% 3.48% 2.04% 1.38% 1.73% 2.08% 1.55% 2.19% 1.72%
Avg 51.21% 50.91% 50.72% 51.99% 52.95% 52.98% 49.30% 49.48% 49.63%


There's still one oddball in ArmC, and we don't quite have agreement between the body parts, but everything's a lot neater now (stdevs are clearly smaller). Of course, things were pretty neat before, so why do I think this new theory is the case?

Recall the bizarre examples that spawned the "low-DF wonkiness" theory. Specifically:

Stunseed swings an eahnor-set ivory vultite dagger at you!
AS: +512 vs DS: +181 with AvD: +0 + d100 roll: +64 = +395
... and hits for 26 points of damage!
Damaging strike to chest, several ribs shattered!
You are stunned for 5 rounds!
The guiding force leaves Stunseed.

Stunseed thrusts with a rapier at you!
AS: +442 vs DS: +183 with AvD: +15 + d100 roll: +96 = +370
... and hits for 25 points of damage!
Well placed strike to back shatters vertebrae!
You are knocked to the ground!
You are stunned for 5 rounds!
The guiding force leaves Stunseed.

Stunseed thrusts with a rapier at you!
AS: +437 vs DS: +183 with AvD: +15 + d100 roll: +81 = +350
... and hits for 21 points of damage!
Diagonal slash leaves a bloody trail across your torso.
You are stunned for 3 rounds!

These are incredibly impossible in the classic redux understanding of GS3. I even suggested crit damage reduction at the time (low-DF wonkiness), but that didn't really help much. Let's apply my new theory (the holistic theory).

Dagger and rapier vs. MBP are .075 DF weapons. On the first hit, Jolena should have had 22 raw damage and 25 crit damage, or 47 damage total, so she has 55% damage reduction +/- a little.

Will the second hit be consistent?

.

270*.075 = 20 rd, 25 cd, 45 td, 56% damage reduction.

:)

#3?

19 rd, 20 cd, 39 td, 54% damage reduction.

Lookin' sharp!

This explains why I thought different body areas had different redux values; leg offers more crit damage than arm which offers more crit damage than hand. It's tempting to just say that the highest avg. crit damage would logically have given the highest numbers before, but I want to be pretty rigorous about this. For any hit of x success margin, we have the following under the classical approach:
(x * DFr) + Crit = Total Reduced Damage
Redux % = 1 - (DFr/DF)

For comparison's sake, under the holistic approach, we have:
(x * DF + Crit) * Redux Factor = Total Reduced Damage
Redux % = Redux Factor

From the first equation:
DFr = (TRD - Crit)/x

Crit can never be more than TRD, so the larger the crit, the closer the numerator gets to 0, the smaller DFr gets. The smaller DFr gets, the bigger R%1 gets. Larger crit ==> larger R%1.

This explanation isn't perfect. I've got over 80 hits for arm, leg, and hand, and the holistic approach gives numbers of 50.5%, 52.0%, and 49.1% respectively (stdevs of 2.53%, 1.7%, 1.83%). Not near as big gaps as before, but I'd rather they be pretty much dead-on together. Deleting the bizarro hit from before brings arm up to 50.7% and more importantly reduces its stdev to 1.68% and drops its range to 1/3 of the previous value, but it wouldn't be very scientific to just discard information that doesn't agree with my hypothesis. Furthermore, I'm not sure how crit rank would be calculated in this environment. There must be some crit divisor deflation, or else we'd be getting wounds all the time on like 5 or 6 raw damage. I'm going to try to catch up with Stun and see if he remembers his dex bonus at the time and if he was ambushing on those Jolena hits, and then we'll be able to quantify this a bit.

-Anathemus' player


>Crit can never be more than TRD

Addendum: Unless lots of crit weighting is present (c.f. claidhmores). Lots of crit weighting was not present in the tests I did.

-Anathemus' player

[Drew]

Testing redux without armour is a no-no in my mind, introduces too much possible wonkiness. Kinda like the old higher DS with no weapon training bug.

[Stunseed]

Over in the dux folder, alot of people ( myself included, obviously ) have been putting alot of effort into finding out the formulae involved. Anathemus and Gibrecful ( sp ) have aded alot of numbers to help solidify the ideas stated. It's a good read if you're into that kinda thing.

[Jolena]

The hits that Jolena took were AIMed ambush to the chest, torso and back, just for further information. :)

[Fallen]

I hope you guys plaster your findings everywhere once you are finished. I always look to conserve information like this when I come across it. You never know who you might help, including yourself when you get this information to as large an audience as possible.

Definitely look into Krakiipedia as well, once you have everything you are testing compiled.

[Jolena]

I've offered over on the officials to be a test subject once more since the shots I took seem to be the most puzzling to Anathemus. Hopefully, there will be more #'s to post soon.

[Latrinsorm]

An excerpt from a Warden post in the warrior boards:

"I think quite a few players knew how DF Redux worked in GS3. For GS4, however, not only did the formula change, but also the specifics of how it was applied (which is part of the reason for us calling it Damage Reduction now). The latter change is what causes players using the GS3 concept to arrive at seemingly inexplicable results."

This, to my mind, shows that my holistic theory of redux (or something like it, at least) is definitely the way to go from now on. It's also just more convenient from what I've seen.

Jolena: your hits were vital to show that the GS3 concept must be abandoned. The only explanatory gap in my theory is that the crit divisor deflates *somehow*. I was hoping to get an exact bead on how much crit weighting Stun was using and try to get a rough estimate that way, but with ambush AND Dex bonus factoring in, it's just too much uncertainty to be worth the trouble.

What I really need from someone is a character with 0 dex bonus. The AS doesn't have to be really high (and in fact it'd be better if it's not), about 50 should be plenty. What I'll have you do is take a shot at my warrior, let him acantha up, and repeat a good 5 or 6 times. From that, I should be able to piece together a good understanding of crit divisor deflation.

Also, I made a change in a later post, from

"(x * DF + Crit) * Redux Factor"

to

"(x * DF + Crit) * (1 - Redux Factor)

The reason is just to make it line up better with the oldstyle redux percentages. Now a redux factor of 1 is complete damage reduction, rather than a redux factor of 0. I also think to make the split totally clear it'd be best to refer to redux factor the way we refer to damage factor, i.e. .604 instead of 60.4%. These two changes are purely cosmetic, but I think they're good ideas.

I'm *very* confident this is the way to go about things. Thanks for the repost, Fallen. :)

[AestheticDeath]

Anyone found out the maximum amount of redux you can get? I had thought for some reason redux was capped somewhere.

[Latrinsorm]

Redux % was supposed to cap somewhere (80% maybe?). It stands to reason that redux factor also caps somewhere. I'm pretty sure that we've been in the redux factor paradigm since the 3/4 switch, so any numbers given since then have been suspect as to establishing a max (or anything else, for that matter).

The maximum number of redux *points* is primary: 3 * 101 + secondary: (3 + 2 + 2 + 2 + 2 + 3 + 3) * .4 * 101 + tertiary: 7 * .3 * 101 = 303 + 686.8 + 212.1 = 1201.9. The maximum number of redux points for a feasible plan by cap is around 800 somewhere, I imagine. My warrior's got one of the best possible redux plans and he's at about 7.8 per level, by cap he could probably be knocking on 8.

[Shari]

Wow, that is a LOT of math.

[MrFeature]

Worthless, your math is all wrong.

[mgoddess]

Worthless, your math is all wrong.

So, if their math is all wrong, what's the right math?

[StrayRogue]

I doubt him.

[Drew]

Definitely look into Krakiipedia as well, once you have everything you are testing compiled.


I'd edit krakiipedia if it was an actual wiki, and didn't have approved accounts.

[Fallen]

Alright then. I'm going to review what we've got so far.

1) DF Redux no longer exists the way it did in GS3.
2) It is now referred to by Warden as "Damage Reduction".
3) This change in terminology, along with irreconcilable hits, suggested to me that both raw damage and crit damage are reduced.
4) To this end, I proposed a new model, which I have designated the Holistic Model.

GS3 Model:
(Endroll - 100) * Damage Factor * (1 - Redux %) = Reduced Raw Damage
where Redux % = (DF - Reduced DF)/DF
Reduced Raw Damage / Crit Divisor = Crit Rank
Crit Rank --> Crit Damage
Reduced Raw Damage + Crit Damage = Total Reduced Damage

Holistic Model:
(Endroll - 100) * (Damage Factor) * (1 - Redux Factor) = Reduced Raw Damage
where Redux Factor = 1 - Reduced Raw Damage / Unreduced Raw Damage
Crit Divisor * (1 - Crit Divisor Deflation Factor) = Deflated Crit Divisor
where Crit Divisor Deflation Factor = 1 - Deflated Crit Divisor / Crit Divisor
Raw Damage / Deflated Crit Divisor = Max Crit Rank
Max Crit Rank --> Unreduced Crit Damage
Unreduced Crit Damage * (1 - Redux Factor) = Reduced Crit Damage
Reduced Raw Damage + Reduced Crit Damage = Total Reduced Damage

What prompted this flurry of research in the first place were hits that apparently showed 0 and 1 raw damage leading to rank 5 crits. Further, hits were shown where less than 11 raw damage led to rank 1 crits. The second class still showed less than 11 raw damage following the application of the Holistic Model without crit divisor deflation, thus my introduction of the crit deflation factor.

I haven't checked thoroughly, but it doesn't look like people without redux are having crit divisor problems. Therefore, it must in some way be related to the redux factor. My recent redux testing was all done versus skin. I compiled a table of the crit values and reduced raw damages and found that the overwhelming majority (98.5%) fell within expected ranges. The few that didn't were easily explained with crit weighting and padding from Con and Dex stats. This could be a problem, as you'll see at the **.

I also saved three sets of hits from back when this mess started. One from Atlanteax, one from Jolena, and one from Anathemus. All three were wearing plate armor, and all three had unexplainably low amounts of raw damage given an 11 (or 9, in some cases) crit divisor. All but two of the hits also happened to be rank 1 crits. Here's a breakdown of each set.

Jolena:
4 dagger hits.
Redux factors of .522, .478, .478, and .563.
Reduced raw damages of 10, 9, 9, and 7.
Crits of 1, 1, 1, and 0.
Hits on chain, plate, plate, and plate.

I noted that the crit divisor deflation was less than the damage reduction by about a factor of 3. I then assumed that a Crit Deflation Multiple existed that connected Redux Factor to Crit Divisor Deflation Factor. Working through some algebra, we can calculate this CDM exactly as Unreduced Crit Divisor * (1 - RF) / (Unreduced Crit Divisor - Reduced Crit Divisor).

We know the Chain CD is 9, so the first hit is ok so long as the Crit Divisor isn't reduced to 2.5 or lower (which would cause a rank 4 max assuming no padding or weighting which would make a rank 1 crit impossible). This is fine by me, as a Crit Divisor Deflation Factor of .75ish implies a Redux Factor of 2.25ish, which is obviously not possible.

The second hit is on Plate CD which is 11, but we only have Raw Damage of 9 (which could have been anywhere from 8.5 to 9.5). 11 / (11 - 9.5) = 22 / 3. We also have a built-in uncertainty to the redux factor related to the endroll which in this case is .022. Therefore, the absolute higheset the Crit Deflation Multiple could be is (22/3) * (1 - RF + Uncertainty), which in this case works out to 3.985. We can't establish a lower limit that a priori reasoning can't give us for the same reason we showed above.

Continuing in like manner, we note that the third hit has the same RF and leads to the same limits. The fourth hit we can only establish a lower limit on, because as far as we know from this rank0 hit the Reduced Crit Divisor could be infinity. Anyway, the lower limit we establish is 1.277. This is a pretty big range. Luckily, we have more hits to help us out.

Jolena also posted 3 rapier hits. One of those chain coulda-been-rank-1s-anyway, a plate CBR1A, and a plate of .520 RF that only showed 10 reduced raw damage. As you might guess, the CDM can be awful high in this case as the reduction in Crit Divisor is pretty tiny. It turns out it's 11, which doesn't constrain our range any.

Atlanteax had 5 rapier hits, 4 to a Chain CD and 1 to a Plate CD, all producing rank 1 crits. Unfortunately only 2 prove useful to us: a 9 reduced raw damage versus Plate and an 8 reduced raw damage versus Chain, which establish upper bounds of 3.483 and 8.591 respectively.

Finally, my set of hits had three closed fists, two blackjacks, and three daggers. None provide any useful upper bounds, but one of the closed fist hits tell us the lower bound is 1.800.

So, to sum up:

1) Crit Divisor is deflated when Damage is reduced.
2) This is accomplished by multiplying Crit Divisor by (1 - Crit Divisor Deflation Factor).
3) The CDDF is derived by dividing Redux Factor by a Crit Deflation Multiplier.
4) The Crit Deflation Multiplier is a number somewhere between 1.800 and 3.483. Hopefully this number is constant across adventurers and not based on Logic stat at level 23 or something.

** Here's the problem. Reducing the Crit Divisor versus Skin should only require an RF of about .500, which my warrior has. I'm going to go through the numbers again tomorrow to see if I'm confusing myself in this half-awake haze. If all else fails, I'll claim that the Skin Crit Divisor is simply exempt from reduction because it's already so tiny.

Why this post is titled "Request":

I need redux hits. The hits I require have the following characteristics:

1) Rank 1 crit.
2) Versus chain or plate armor.
3) No damage padding or damage weighting.

Any and all hits that could be provided would be super. We've almost got redux figured out (possibly)! :)

-Anathemus' player