Towards a general formula for redux

[Yollia]

I have some news that provides some hope on the prospect of finding a formula that calculates redux given a character's level, redux points, and number of spells known.

If you look at the Krakiipedia page on redux, it has a chart with some data for level 66 and level 52 characters. The X-axis is redux points and the Y-axis is redux. It states that the curve is approximately logarithmic. Try as I might, I can't fit a logarithmic curve to the data. It seemed likely to me that the curve was actually a hyperbola, which has an equation of the form (x-A)(y-B)=C. I reasoned that this would make sense because there would then be an upper limit to redux that you could never reach; with a logarithmic curve, the number would grow to infinity, which doesn't make sense.

I tested this theory by fitting a hyperbolic curve to the data on Krakiipedia. I obtained the unlikely-looking formula:

redux = 0.7265813392-75.27997877/(x-8.533398206), (FOR A LEVEL 66 WITH NO SPELLS)

where x is the number of redux points. On the face of it, the numbers are unenlightening. However, the curve fits the data beautifully:

http://i1312.photobucket.com/albums/t538/mattjsam/reduxdata_zpsecdb4fda.png

It's so close that we can safely assume that this is the correct formula for level 66; the deviations can be attributed to roundoff error.

I'll keep you posted on further progress. If you happen to be a level 66 with redux and spells, perhaps you could contact me so I can see how that factors in.

-Yollia

[Bobmuhthol]

Where is the data? I could only find the graph at Krakiipedia.

[Yollia]

I actually used the graph. I copied it into mspaint and scaled it based on pixel coordinates.


Where is the data? I could only find the graph at Krakiipedia.

[senorgordoburro]

Durfin did an absurd amount of research on this topic before he left. I still talk to him regularly and I will see if he has anything next time we talk.

[Latrinsorm]

I am so pleased that the data is still proving useful to someone.

It is almost certainly not a logarithm, but I think not for the reasons you state: redux points cannot technically go to infinity. There are only so many skills, so many trains per level. My (very rusty) calcs put redux points max at 1414, which is well beyond the domain of the graph but logarithms run like ol' black water. As I said in the beginning, I was almost certainly wrong with the logarithm, and a hyperbola makes a lot of sense (especially since that pesky 0-10 amount of redux points is annihilated by the 108 or whatever requirement for generating redux at all).

Have you tried hyperbole on the (regrettably limited) level 52 data? It would be very helpful for identifying which parameter contained the level effect. I would expect that the GS formulae used slightly more agreeable numbers than tenth-of-billionths.

[Latrinsorm]

Here is an astonishingly well-formatted c/p of the data:


110 118 126 134 142 150 158 166 174 182 190 198 206 214 222 230 238 246 254 262 270 278 286 294 302 310 318 326 334 342 350 358 366 374 382 390 398 406 414 422 430 438 446 454
0.000 0.039 0.108 0.158 0.183 0.232 0.257 0.292 0.315 0.332 0.355 0.373 0.384 0.395 0.418 0.423 0.435 0.447 0.456 0.473 0.482 0.482 0.489 0.501 0.511 0.510 0.515 0.529 0.525 0.538 0.541 0.541 0.546 0.548 0.557
0 0.043 0.098 0.144 0.169 0.203 0.239 0.268 0.298 0.316 0.333 0.357
No BS I took this directly from Excel... proof that we live under the aegis of a kind and loving God. First row is redux points, second row is level 66, third row is level 52. All praise be to the player of Satira; without her contributions there would be no data, and there would be great suffering in Guilder.

[Bobmuhthol]

I get redux = 0.713452 - 56.99461 / (points - 31.77197) but my fit looks pretty bad toward the end and pretty fucking good in the beginning. R^2 is 0.9978.

I'm sort of questioning that data though -- 302 <-> 0.511, 310 <-> 0.510, 326 <-> 0.529, 334 <-> 0.525... shouldn't this be strictly nondecreasing?

http://i39.tinypic.com/29w7jp4.png

[Yollia]

I'm using a least squares fit assuming it's of the form (x-A)(y-B)-C=0. To do this I set the partial derivatives of sum(((x[i]-A)(y[i]-B)-C)^2,i=1..numpoints) with respect to A, B, and C equal to 0 and solve the resulting system of equations.

I was off in my x indexing. I decided to round to hundredths since Latrinsorm is probably right. For level 66 I get

0.6840 - 46.38/(x-46.65)

which still looks good and makes a bit more sense. I'm guessing that the first number is the max. My fit is pretty chaotic though; for level 52 I got this:

0.8279 - 95.84/(x+4.93)

which fits well, but is again not particularly enlightening. I think more data is required.


I get redux = 0.713452 - 56.99461 / (points - 31.77197) but my fit looks pretty bad toward the end and pretty fucking good in the beginning. R^2 is 0.9978.

I'm sort of questioning that data though -- 302 <-> 0.511, 310 <-> 0.510, 326 <-> 0.529, 334 <-> 0.525... shouldn't this be strictly nondecreasing?

http://i39.tinypic.com/29w7jp4.png

[Archigeek]

What sort of parameters did you use for the hits originally? In an effort to confirm any hypothesis? I would assume a very standard base weapon swung at a very standard set of armor under the most blah conditions possible? So, no ambushing, no weighted or padded weapons/armor etc? That would seem to give the cleanest results when trying to confirm.

[Bobmuhthol]

The 52 data is way too limited. I find a t-stat of 1.23 for A.

[Yollia]

Unfortunately since hyperbolas change so little it seems like the initial curve (small redux points) is less important than the information that describes the asymptote (large redux points). Lots of hyperbolas are very close to the 52 data but approach different asymptotes, so we need large numbers to really know what's going on.


The 52 data is way too limited. I find a t-stat of 1.23 for A.

[Yollia]

I think there's a more meaningful way to interpret the formula (after rearranging):

y = ReduxCeiling * (x-ReduxThreshhold)/(x-FiddlingParameter)

ReduxCeiling is the horizontal asymptote, ReduxThreshhold is the X-intercept (min ranks required for redux), and we have to figure out what FiddlingParameter is. When I use this to fit level 66 I get

ReduxCeiling = 0.678
ReduxThreshhold = 116.56
FiddlingParameter = 51.92
(Level 66)

The first two numbers are believable. For the level 52 data we still get numbers that aren't great, but at least the threshhold makes sense:

ReduxCeiling = 0.7834 (eh)
ReduxThreshhold = 112 (believable)
FiddlingParameter = 8 (who knows)
(Level 52)



Unfortunately since hyperbolas change so little it seems like the initial curve (small redux points) is less important than the information that describes the asymptote (large redux points). Lots of hyperbolas are very close to the 52 data but approach different asymptotes, so we need large numbers to really know what's going on.

[Paradii]

This would be an ideal scenario to use GLMM with individual as a random effect.

[Yollia]

I don't know how to do that and the Wikipedia article, as usual, isn't very helpful. I'll have a PhD in math this year, but it's the wrong kind of math, so when it comes to analyzing data I'm probably pretty naive. Also, I'm using Maple, which sucks in pretty much every way.


This would be an ideal scenario to use GLMM with individual as a random effect.

[Latrinsorm]

I get redux = 0.713452 - 56.99461 / (points - 31.77197) but my fit looks pretty bad toward the end and pretty fucking good in the beginning. R^2 is 0.9978.

I'm sort of questioning that data though -- 302 <-> 0.511, 310 <-> 0.510, 326 <-> 0.529, 334 <-> 0.525... shouldn't this be strictly nondecreasing?Error bars, you black son of a... well, you can read the rest.
What sort of parameters did you use for the hits originally? In an effort to confirm any hypothesis? I would assume a very standard base weapon swung at a very standard set of armor under the most blah conditions possible? So, no ambushing, no weighted or padded weapons/armor etc?I may have open aim-bushed to avoid death critz, but certainly it was vanilla weapon vs. vanilla armor.
I think there's a more meaningful way to interpret the formula (after rearranging):Have you tried a constant (with respect to level) redux ceiling?

[Paradii]

Well, my suggestion only helps if you are incorporating data from numerous players. If its just one character then it's pointless. Basically, it would allow you to assess variation within an individual to between individuals. So if someone accidentally had a weighted weapon, or padded armor, or misclassified the weapon used, you could partition that away from the variance at a whole. In terms of data analysis, you might want to start looking into R. I personally haven't used maple but I've heard enough to avoid it. R is the rising star right now, tons of new packages being developed annually and enough people are using to appropriately vet the packages.

Plus, it's free. Takes a bit of a learning curve to get used to the coding though.

[Latrinsorm]

One player, two characters, I'll partition your face you biological son of a...

I preferred Matlab but didn't mind Maple. Haters gonna...

[Paradii]

You'll need more characters than that to make this a generalizable model. Gosh, you people in the 'hard' sciences just have no idea what its like working with unclean data.

[Yollia]

Holding the ceiling and threshhold constant gives us

FiddlingParameter = 294.8 + (-614.8+2.2*ReduxThreshhold)*ReduxCeiling (level 66)
FiddlingParameter = 175.29 + (-633.43+3.75*ReduxThreshhold)*ReduxCeiling (level 52)

to minimize the squared error. That almost convinces me that the FiddlingParameter can be derived from the ceiling and the threshhold.

[Yollia]

After doing lots of fiddling, I decided to cheat and guess that FiddlingParameter = ReduxThreshhold - Level. It looks like this may have been a good guess. Here's what we get:

Level 66:
ReduxCeiling = 0.681
ReduxThreshhold = 116

Level 52:
ReduxCeiling = 0.566
ReduxThreshhold = 116.68

These numbers fit the curves just as well, but the second one definitely looks a lot more like what we want. It's bad science, but luckily I'm not a scientist, so it's okay.

[Whirlin]

Hey everyone... Long time fan, first time poster in this thread...

But I just wanted to go ahead and challenge all of the minds on this thread on a most fundamental basis... but where was it ever documented the concept of Redux Points? The whole 1:.4:.3 thing seems a bit arbitrary to me, and I've never quite understood why it was set up in such a way... If those were inherently flawed, it could greatly jeopardize the integrity of any type of correlative equation that we're beginning to go down the rabbit hole on...

Kinda like assuming that dex is correlated to phantom damage... I mean... some stat... might... be...?

[Latrinsorm]

You'll need more characters than that to make this a generalizable model. Gosh, you people in the 'hard' sciences just have no idea what its like working with unclean data.Without loss of generality I will assume that you are a big jerk. :grr:
After doing lots of fiddling, I decided to cheat and guess that FiddlingParameter = ReduxThreshhold - Level. It looks like this may have been a good guess.There was definitely a slight level dependence for the redux threshold insofar as "definitely" = "what I remember muddily and indistinctly". In a mirror darkly I remember it going the other way, though; lower levels had lower thresholds.

[Latrinsorm]

Hey everyone... Long time fan, first time poster in this thread...

But I just wanted to go ahead and challenge all of the minds on this thread on a most fundamental basis... but where was it ever documented the concept of Redux Points? The whole 1:.4:.3 thing seems a bit arbitrary to me, and I've never quite understood why it was set up in such a way... If those were inherently flawed, it could greatly jeopardize the integrity of any type of correlative equation that we're beginning to go down the rabbit hole on...

Kinda like assuming that dex is correlated to phantom damage... I mean... some stat... might... be...?Hey long time bow luster first time bow buyer last time Bowyer (X IS DISABLED)

The original testing was done by Porcell in the GS4 fever dream, who repeatedly swapped skills until he reached the magic threshold (as a function of his level at that time and price bracket). Obviously because I played in Gemstone negative 5 I understand this to be Porcell 3, not the original Porcell or even Porcell ][, but that's neither here nor there.

It is possible the points per skill also changes per level, but (only) in the same way that it is possible that apples might start to rise tomorrow, and that possibility does not merit equal time in phys-... strike that, Gemstawn classrooms.

[Yollia]

Life keeps getting in the way of this project, but I think that if we can find a formula for the redux threshold in terms of level, then we'll be almost done. Luckily, the threshold can be directly calculated, though it costs one fixskills. I'd wager that the dependence on level is simple and direct.

It is possible to do this stuff statistically without using fixskills. It would be great if we could estimate the mean and variance of the level and number of redux points of a character who doesn't know spells as well as the correlation between those two quantities. I could use that to build probability density functions of the unknown quantities and get tolerance estimates. This would unfortunately require annoying random surveys.

[Jhynnifer]

Well if it helps and you need a capped character that knows spells. I'd be happy to help out. =)

[Yollia]

Thanks for the offer. We'll be there soon.

After some analysis, I realized that it is important to know how much total damage the hit would have caused without redux in order to properly fit the curve. The harder the hit, the more accurate the reading. Also, higher numbers of redux points will also give more accurate readings. The error due to roundoff (assuming the curve is hyperbolic) is proportional to

1/(x^2*D)

where x is the number of redux points and D is the damage. I'm getting better numbers when I weight the derivatives by multiplying them by x^2, but hyperbolas are super picky. I think if I knew the total damage we'd be better off. Anyway, just to update my best guess so far for level 66 is
Redux ceiling = 0.68
Redux threshhold = 115

and for level 52 we have
ReduxCeiling = 0.573
ReduxThreshhold = 117.65

[Latrinsorm]

Oh I have some data for thresholds:

Level 16: 126.8
Level 17: 118 pts (confirmed)
Level 18: 117.2 pts
Level 20: 116.4 pts
Level 29, 20/10 spells: 111.2
Level 30, 31/? spells: 113
Level 83, 0-3 spells: 108.4

Looks like a logarithm to me. No! I kid. Also the data were collected from several different people, so feel free to throw any given one out if it doesn't fit.

[Yollia]

Oh I have some data for thresholds:

Level 16: 126.8
Level 17: 118 pts (confirmed)
Level 18: 117.2 pts
Level 20: 116.4 pts
Level 29, 20/10 spells: 111.2
Level 30, 31/? spells: 113
Level 83, 0-3 spells: 108.4

Looks like a logarithm to me. No! I kid. Also the data were collected from several different people, so feel free to throw any given one out if it doesn't fit.

Pretty sure that
ReduxThreshold = 106+(200/level)

Then
ReduxCeiling is about 0.675 (level 66)
ReduxCeiling is about 0.54 (level 52)

[Fortybox]

http://media.tumblr.com/tumblr_mamck5BmZC1qery84.jpg

[Latrinsorm]

Oh and I was also reminded last night by a dream that the figures I listed were weighted averages of redux factor (or WAoRFs, possibly my favorite coinage ever) that took into account the lower relative rounding uncertainty of higher endroll & damage hits.

[Yollia]

I think we have the spell-free formula, though I've only tested it for specimens of level 28, 31, 61, 67, 71, and 100. It fits the posted level 52 and 66 data and the thresholds are derived from what Latrinsorm posted. I'd say it works well enough that it would just take a few tweaks to make it absolutely correct. Since the fit is so insensitive to the data, that may never happen, but I'd trust this estimate (at least for levels 28+). More testing never hurts.

ReduxCeiling(level) = 0.716 - 2.7/(max(20,level)-19.12)
ReduxThreshold(level) = 106+200/level

I've been writing the formula in a bit of a nicer form:

Redux(reduxPoints,level) = max(0,ReduxCeiling/(1+level/(reduxPoints - ReduxThreshold)))


I have some ideas on calculating the redux hit due to spells, but unfortunately it's dependent on level AS WELL AS PROFESSION. The last part is annoying as fuck, but hey, so it goes.

[Yollia]

I think we have the spell-free formula, though I've only tested it for specimens of level 28, 31, 61, 67, 71, and 100. It fits the posted level 52 and 66 data and the thresholds are derived from what Latrinsorm posted. I'd say it works well enough that it would just take a few tweaks to make it absolutely correct. Since the fit is so insensitive to the data, that may never happen, but I'd trust this estimate (at least for levels 28+). More testing never hurts.

ReduxCeiling(level) = 0.716 - 2.7/(max(20,level)-19.12)
ReduxThreshold(level) = 106+200/level

I've been writing the formula in a bit of a nicer form:

Redux(reduxPoints,level) = max(0,ReduxCeiling/(1+level/(reduxPoints - ReduxThreshold)))


I have some ideas on calculating the redux hit due to spells, but unfortunately it's dependent on level AS WELL AS PROFESSION. The last part is annoying as fuck, but hey, so it goes.

So some good news and some bad news.

I've done a lot more testing, and I've come to expect the above formula to be correct to within 0.004...when I test by hitting the leg. I "tested" Nikhilan's abdomen (i.e. missed his leg) and the number was smaller by 0.03, which is comparatively huge. When I tested Roblar, I got a singificantly LARGER number for the neck than for the leg, but this was in the early stages and I dismissed it as a fluke.

There are (at least) two possible explanations for this:

1. There really are different redux factors for different body parts.
2. There are different redux factors for DF and for crit damage.

Explanation 2 would be much cleaner, nicer, and generally acceptable. However, I computed what the different factors would have to be for Nikhilan (level 79, 523.2 redux points) and Kupaka (level 100, 919.6 redux points):

Nikhilan DFredux: 0.6
Nikhilan crit redux: 0.3775

Kupaka DFredux: 0.6522
Kupaka crit redux: 0.3161

The problem with this picture is that Kupaka's crit redux is lower. This could be due to race or some other factors, but I doubt it. If you're worried about error margins, you probably shouldn't be; Kupaka's crit redux would almost surely be lower than Nikhilan's crit redux even when you account for roundoff error, despite the roundoff error conceivably being rather large. Even if you consider splitting up the redux points into points that count towards crit redux and points that count towards DFredux, it still doesn't make sense: Kupaka has more ranks in every relevant skill.


Explanation 1 is not horrible and may be correct, but I don't know yet. I'm sure there are other possibilities that I've missed, so if anyone can think of any please post them.

[Latrinsorm]

I remember that having a different ratio of crit damage to raw damage messed with things, and I also remember abdomen crits having more damage (rank to rank) than leg and much more than neck. This is functionally similar to but computationally and fundamentally distinct from explanation 1; for one thing, crit padding would skew the ratio even for same-location hits. I don't remember if those memories are true, or if we (meaning Mark) ever came up with a better description than "messed with things".

[Yollia]

So I've come to a realization: this is not really a curve-fitting problem. There is a level of error for each specific point that is unacceptable. It is in fact a nonlinear programming problem, which means minimizing a function subject to constraints that can't be violated. The constraint

((1-reduxApproximation)*RawDamage-RealDamage)^2<=0.25

must be satisfied for EVERY data point. What it means is that the given approximation of the redux gives the correct number of points of damage for the hit after rounding, although for that really to be true the inequality would have to be strict on one side...if we can satisfy this with a formula, we're in pretty good shape. The previously posted formulas aren't even close.


I was beginning to despair about a hyperbola being the correct kind of curve, because the math program I was using said the constraints weren't even close to being possible to meet. Instead of trying to find 3 specific values that minimized the error for all points, I decided that instead we should have the program pick one ceiling value but many different threshold and fiddling-parameter values; the function we would be trying to minimize then, since the error is already good enough when the constraints are met, is the sum of the absolute differences of the parameter values from each other. The goal is to see how close we can get the parameters to be to a single value, which is what we would want for a formula.

This wasn't working too well either, so I decided to raise the differences to the 6th power to emphasize to the fucking machine that they should be fucking small (trying to convey my mindset here; by the way, when I tried the 7th power it told me to go fuck myself). Using 6 data points for level 100, I found 3 numbers that satisfied all of the constraints...you'd think that'd be the redux formula for level 100, right? WRONG. It gave the exactly correct damage for the 6 data points, but none of them were anywhere near the threshold. I added a case with an extremely low number of redux points (for level 100) and the whole thing broke. I managed to pick up the pieces and got the following values of the threshold and the fiddling parameter for the various points (they're listed in reverse order):

(39.66,109)
(42.22, 106.4)
(42.22, 106.4)
(42.74, 105.8)
(41.6, 107)
(44.34,104.2)
(44.55,104)
(42.117,107.93)

What I noticed is this:
1. The numbers are pretty close to each other, but different enough that picking any given pair makes the formula fail to satisfy the constraints.
2. THE SUM OF EACH PAIR OF NUMBERS IS ALMOST EXACTLY THE SAME.

I deduced that I in fact do NOT have my head up my ass (at least not completely) and there IS a formula of the form

redux=ReduxCeiling * (reduxPoints - ReduxThreshold) / (reduxPoints - ReduxThreshold + FiddlingParameter)

The reason it isn't coming out to be exact for some fixed threshold and fiddling parameter is because THE CURRENT METHOD FOR CALCULATING REDUX POINTS, WHILE EXTREMELY CLOSE TO CORRECT, IS MISSING SOMETHING. There could be an additional skill that needs to be factored in, a skill that needs to be taken out, or maybe a stat or stat bonus...or maybe something else. I think if we can fix this then we can get an exact formula.

[Latrinsorm]

Well, there definitely is a different redux threshold at each level, which you seemed to have mapped out pretty convincingly a little while ago. It seems like using that as a control rather than having Mammon guess a redux ceiling would be more productive.

Have you looked into my awesome suggestion of crit damage ratio warping redux? Would it help if I said I hit my head on a DeLorean in the bathroom to come up with it? I remember Mark's theory having a second redux factor for the purposes of crit divisor deflation, you should find him. Find him!!!

I can try and find the raw data to-morrow, as I said I just took exquisitely refined averages of it to communicate the data most succinctly. It is possible that there is actually a point overlapped by all data that does not quite correspond to this pristine average, but from what I remember that (GS3 era) process didn't work too well for us either.

[Riltus]

I remember Mark's theory having a second redux factor for the purposes of crit divisor deflation, you should find him. Find him!!!

You may regret this after attempting to read through this post.

There is a fixed redux factor that I had initially labeled RF1 but, descriptively, it would be more appropriate to refer to it as RFc. RFc is used to determine the minimum damage at each critical rank threshold. This applies to all weapon DFs and all armor groups. Think of DF Redux. I also believe that RFc is the redux factor floor.


1. There really are different redux factors for different body parts.

No.


There could be an additional skill that needs to be factored in, a skill that needs to be taken out, or maybe a stat or stat bonus...or maybe something else.

You are not missing any skills, stat or stat bonuses. RFc is also the redux factor that applies to raw damage reduction below the rank 1 critical threshold so long as this is also before any double length endroll intervals.


Endroll Intervals:

No redux
Weapon DF: 0.100
Armor: Plate
Rank 1 critical divisor: 10.5 damage

Actual Dmg Taken|1|2|3|4|5|6|7|8|9|10|10.5
Endrolls|101-114|115-124|125-134|135-144|145-154|155-164|165-174|175-184|185-194|195-204|205** R1 crit
Interval size|15|10|10|10|10|10|10|10|10|10|critical

Intuitively, it would make sense that if a character had 50% redux, the number of endrolls for each point of damage would double and would look like this:

Weapon DF: 0.050
Armor: Plate
Armor critical divisor: 10.5

Actual Dmg Taken|1|2|3|4|5|6|7|8|9|10|10.5
Endrolls|101-129|130-149|150-169|170-189|190-209|210-229|230-249|250-269|270-289|290-309|310** (R1 crit)
Interval size|30|20|20|20|20|20|20|20|20|20|critical

The second table is representative of the old DF Redux model.

But is this how the endroll intervals look in the new model? The answer is no. We now encounter double size ER intervals. Periodically, an interval representing 1 point of damage expands.

Here are actual examples of the endroll intervals for a Level 27 character, 200.5 redux points and 0 spell ranks. This character has an RFc of ~.222 and an RF of ~.333. BTW the verified redux threshold for this character is 113.6 to 113.8. There was no redux at 113.5 points. Adding 1 additional weapon rank gained redux.

Since this character has an RFc of .222 it is possible to calculate the minimum endoll for any critical rank/armor/weapon combination.

For example

If I want to know the minimum endroll that will inflict a rank 4 critical while wearing full plate with a broadsword attack:

Rank 4 plate critical divisor: 43.5 damage
Broadsword DF vs plate: .200
Minimum endroll: 100 + round up((43.5/.200)/.778) = 380

or you could simply reduce the weapon DF.

Reduced DF = 1 - (weapon DF * RFc)

RFc is unaffected by the actual damage taken.
----------------------------------------------------------------

The next two tables compare the different endroll patterns for a non-redux character and the Level 27 character above.

Weapon DF: .150 (Jackblade vs Brig)
Rank 1 armor crit divisor: 6.5 (Brig)

No redux

Actual Dmg Taken|1|2|3|4|5|6|7|8(1)|9(1)|10(1)
Endrolls|101-109|110-116|117-123|124-129|130-136|137-143|X|144** (R1 crit) - 149|150-156|157-163
Interval size|10|7|7|6|7|7|X|6 (R1 crit)|7|7

Lev 27, 200.5 redux pts
Weapon DF: .150 (Jackblade vs Brig)
Rank 1 armor critical divisor: 6.5

Actual Dmg Taken|1|2|3|4*|5|6|7 (1)|8 (1)
Endrolls|101-112|113-121|122-129|130-147*|148-155|X|156** R1 crit -172|173-181
Interval size|13|9|8|18*|8|X|17* R1 crit|9|

* indicates a double interval
** indicates the minimum endroll required for a rank 1 critical

So what's going on?

In the example with redux, the 1st, 2nd and 3rd points of damage are all reduced with an RF of ~.222 the same as RFc. There is a significant increase in damage reduction at the end of the 4th damage point. ER 147 is just a bit less than 4.5 reduced damage but the unreduced damage is (47 * .150 = 7.05). The redux factor for this hit, therefore, is approximately 1 - (4.45/7.05) = RF .368

The minimum endroll for a rank 1 critical is 156. Since this is brig armor the minimum raw damage for a rank 1 critical is 6.5. ER 156 is, minimally, 6.5 reduced damage.

ER 155 = 8.25 unreduced damage (55 * .150)


Attacker swings with a jackblade at you!
AS: +186 vs DS: +148 with AvD: +19 + d100 roll: +98 = +155
... and hits for 5 points of damage!
Blow glances off your shoulder.

ER 156 = 8.4 unreduced damage (56 * .150)


Attacker swings with a jackblade at you!
AS: +209 vs DS: +148 with AvD: +19 + d100 roll: +76 = +156
... and hits for 7 points of damage!
Diagonal slash to your weapon arm.
Strike misses but bruises a few knuckles.

The min/max range for the redux factor at the critical divisor threshold is (1 - (6.5 reduced damage/8.4 unreduced damage = RFc .226. This is the maximum RFc. The minimum must be greater than ER 155 since there was no crit at this endroll. The minimum RFc (1 - (6.5/8.25)) = RFc .212. Therefore, the RFc range is >.212=<.226

By using different combinations of weapon DFs and armor this range can be narrowed.
-------------------------------------------------------------------

At endroll 156 there is also a minimum of 1 critical damage which I indicated in the table with (1). All attacks with endrolls 156 to 172 will result in 7 total damage if the critical damage is 1.

If you were to calculate the redux factor for each of these attacks independently, without knowing the damage interval or their position within the interval, these would be the results:

Endroll 156


Attacker swings with a jackblade at you!
AS: +209 vs DS: +148 with AvD: +19 + d100 roll: +76 = +156
... and hits for 7 points of damage!
Diagonal slash to your weapon arm.
Strike misses but bruises a few knuckles.

DF: .150
ER success margin: 56
Raw damage: 8.4
Crit damage: 1
Total unreduced damage: 9.4
Actual damage: 7
Redux Factor: 1 - (7/9.4) = RF .225

Compare that RF to ER 172 which is in the same damage interval with 1 critical damage.

Enroll 172


Attacker swings with a jackblade at you!
AS: +233 vs DS: +166 with AvD: +19 + d100 roll: +86 = +172
... and hit for 7 points of damage!
Diagonal slash to your weapon arm.
Strike misses but bruises a few knuckles.

DF: .150
ER success margin: 72
Unreduced raw damage: 10.8
Critical damage: 1
Total unreduced damage: 11.8
Actual damage: 7
Redux Factor: 1 - (7/11.8) = RF .406

Even though the ERs are in the same damage interval, the calculated RFs are vastly different. At endroll 156 (the lowest endroll in the interval) the calculated RF is .225 and jumps to .406 at ER 172 (the highest endroll in the interval).

However, these calculations don't take into account that the actual reduced raw damage for the 156 endroll is not 6, but equal to or slightly greater than 5.5 and the 172 endroll is slightly less than 6.5. Adjusting for their position, the calculated RFs are approximately:

ER 156: (1 - (6.55/9.4) = RF ~.303
ER 172: (1 - (7.45/11.8) = RF ~.368

The location of the double intervals will change depending on the characters RFc and the amount of critical damage.

For this same character, wearing plate vs jackblade (DF .110), and a rank 1 crit divisor of 10.5

At ER 222 (ER success margin 122) no critical
At ER 223 (ER success margin 123) (rank 1 crit)

Lev 27, 200.5 redux pts
Weapon DF: .110 (Jackblade vs Plate)
Rank 1 armor critical divisor: 10.5

Actual Dmg Taken|1|2|3|4*|5|6|7*|8|10(1)|11*(1)
Endrolls|101-117|118-129|130-140|141-163*|164-175|176-187|188-210*|211-222|223**-233 (1)|234-256?*
Interval size|18|12|11|23*|12|12|23*|12|11|23?

In the above table I'm missing ERs 254 and 255 with 1 critical damage so, I can't confirm the exact interval length but it is a double interval.

RFc calculations:

Minimum unreduced raw damage for a rank 1 crit: >13.42 (122 * .110)
Minimum RFc: 1 - (10.5/13.42) >.217
Maximum unreduced raw damage for a rank 1 crit: <=13.53 (123 * .110)
Maximum RFc: 1 - (10.5/13.53) <= .224

RFc range: >.215<=.224

Not only is the calculated RF affected by the location of the endroll within an interval but, as Latrinsorm has posted, it is also affected by the CDR. RF (not RFc) increases as the ratio of total damage to crit damage increases. If you could convert redux points to RFc you could eliminate redux factor variability. But gathering this data is near impossible. With CDR adjustment it can be approximated from a character's average RF (RFc = adjusted RF * 2/3) or rearranged (adjusted RF = RFc * 3/2).

Mark

[Yollia]

I can try and find the raw data to-morrow, as I said I just took exquisitely refined averages of it to communicate the data most succinctly. It is possible that there is actually a point overlapped by all data that does not quite correspond to this pristine average, but from what I remember that (GS3 era) process didn't work too well for us either.

WANT MORE DATA WANT WANT. From now on I think any redux testing should at least keep track of the number of points of damage for each hit as well as the raw damage rather than just the reduction factor.



Anyway, I take back the redux points being off thing because I decided to do my optimization programming approach to determine a single character's redux precisely from many hits...it didn't quite work. It was not possible that a single redux factor was explaining the damage reduction in all of the hits EXACTLY. However, if you were happy to be correct to within 1.934 points of damage, his redux was 54.19%, no questions asked. This doesn't mean the redux is random, however...this inaccuracy could be accounted for by rounding two ways.

[Yollia]

New theory:

Mean redux for a level 100 that has redux is computed as follows:

meanRedux(x) = 0.6576*(x-109.25)/(x-44.35)

On each hit the mean redux is deviated by a random number, uniformly distributed between -0.02 and 0.02 (or at least as close as a computer can get to simulating that).

[Latrinsorm]

RP RF +/- CrDa ER D TD
110 0.000 0.014 5 179 21 21
110 0.000 0.009 7 227 32 32
118 0.037 0.011 7 202 26 27
118 0.071 0.010 5 216 26 28
118 0.000 0.019 5 157 16 16
118 0.000 0.014 7 177 22 22
118 0.040 0.010 3 211 24 25
118 0.000 0.019 3 160 15 15
118 0.000 0.019 1 160 13 13
118 0.056 0.013 1 185 17 18
118 0.042 0.010 1 214 23 24
118 0.043 0.011 3 201 22 23
126 0.097 0.009 7 222 28 31
126 0.108 0.008 10 234 33 37
126 0.095 0.014 5 181 19 21
126 0.094 0.009 7 227 29 32
126 0.118 0.007 3 253 30 34
126 0.095 0.011 1 202 19 21
126 0.095 0.011 1 202 19 21
126 0.136 0.011 1 203 19 22
126 0.108 0.007 7 249 33 37
126 0.129 0.008 3 240 27 31
126 0.105 0.006 3 277 34 38
126 0.105 0.006 3 276 34 38
126 0.109 0.005 7 340 49 55
134 0.158 0.007 5 263 32 38
134 0.129 0.008 5 232 27 31
134 0.179 0.010 5 213 23 28
134 0.143 0.010 5 215 24 28
134 0.150 0.007 7 266 34 40
134 0.138 0.009 5 219 25 29
134 0.154 0.010 3 216 22 26
134 0.171 0.008 7 239 29 35
134 0.146 0.006 7 272 35 41
134 0.161 0.008 3 239 26 31
134 0.189 0.006 1 279 30 37
134 0.172 0.008 1 239 24 29
134 0.171 0.007 3 262 29 35
134 0.138 0.008 3 231 25 29
134 0.150 0.006 5 277 34 40
142 0.176 0.008 7 234 28 34
142 0.190 0.007 10 258 34 42
142 0.195 0.007 10 253 33 41
142 0.171 0.007 5 250 29 35
142 0.171 0.008 7 239 29 35
142 0.200 0.013 3 185 16 20
142 0.160 0.010 3 211 21 25
142 0.167 0.008 7 246 30 36
142 0.167 0.013 1 186 15 18
142 0.192 0.009 1 225 21 26
142 0.200 0.008 1 246 24 30
142 0.174 0.012 5 190 19 23
142 0.186 0.006 7 279 35 43
142 0.194 0.007 3 265 29 36
142 0.179 0.009 3 224 23 28
150 0.226 0.009 5 230 24 31
150 0.233 0.007 10 263 33 43
150 0.231 0.012 7 195 20 26
150 0.226 0.009 7 218 24 31
150 0.225 0.007 10 250 31 40
150 0.243 0.007 5 259 28 37
150 0.222 0.010 5 212 21 27
150 0.250 0.009 3 223 21 28
150 0.238 0.006 7 274 32 42
150 0.240 0.010 3 208 19 25
150 0.200 0.013 3 187 16 20
150 0.200 0.013 3 185 16 20
150 0.229 0.007 3 261 27 35
150 0.217 0.010 1 212 18 23
150 0.231 0.009 1 225 20 26
150 0.242 0.007 1 262 25 33
158 0.255 0.006 10 286 35 47
158 0.258 0.009 5 230 23 31
158 0.229 0.008 7 242 27 35
158 0.238 0.006 5 287 32 42
158 0.267 0.006 10 273 33 45
158 0.256 0.006 7 280 32 43
158 0.258 0.008 3 242 23 31
158 0.257 0.007 3 262 26 35
158 0.261 0.005 5 306 34 46
158 0.259 0.008 1 231 20 27
158 0.250 0.009 1 217 18 24
158 0.275 0.006 5 273 29 40
158 0.261 0.005 5 305 34 46
158 0.241 0.008 1 240 22 29
158 0.273 0.007 1 259 24 33
166 0.282 0.006 5 272 28 39
166 0.296 0.010 5 209 19 27
166 0.298 0.006 10 284 33 47
166 0.278 0.007 5 257 26 36
166 0.298 0.006 7 299 33 47
166 0.270 0.007 7 250 27 37
166 0.281 0.008 3 246 23 32
166 0.300 0.008 3 234 21 30
166 0.270 0.007 7 252 27 37
166 0.300 0.006 3 283 28 40
166 0.310 0.005 1 303 29 42
166 0.286 0.008 1 237 20 28
166 0.294 0.007 1 263 24 34
166 0.306 0.007 3 263 25 36
166 0.293 0.006 1 300 29 41
174 0.295 0.007 10 270 31 44
174 0.325 0.006 5 273 27 40
174 0.296 0.010 5 209 19 27
174 0.313 0.005 7 303 33 48
174 0.286 0.010 5 215 20 28
174 0.278 0.008 7 247 26 36
174 0.313 0.008 3 243 22 32
174 0.306 0.005 7 308 34 49
174 0.333 0.007 3 249 22 33
174 0.310 0.006 3 296 29 42
174 0.323 0.007 1 250 21 31
174 0.353 0.007 1 263 22 34
174 0.333 0.007 1 259 22 33
174 0.320 0.009 1 218 17 25
174 0.318 0.005 3 304 30 44
182 0.314 0.008 5 248 24 35
182 0.333 0.008 5 238 22 33
182 0.340 0.005 5 308 31 47
182 0.308 0.006 5 272 27 39
182 0.310 0.009 5 222 20 29
182 0.351 0.007 3 269 24 37
182 0.341 0.005 3 304 29 44
182 0.349 0.006 3 298 28 43
182 0.333 0.007 3 263 24 36
182 0.311 0.006 7 291 31 45
182 0.308 0.007 7 262 27 39
182 0.346 0.009 1 224 17 26
182 0.333 0.007 3 251 22 33
182 0.333 0.006 3 280 26 39
182 0.349 0.006 3 298 28 43
190 0.367 0.009 5 224 19 30
190 0.370 0.005 5 305 29 46
190 0.350 0.004 10 350 39 60
190 0.370 0.005 5 307 29 46
190 0.356 0.006 5 299 29 45
190 0.340 0.005 10 314 35 53
190 0.351 0.005 8 344 37 57
190 0.350 0.007 7 267 26 40
190 0.354 0.005 7 305 31 48
190 0.333 0.008 5 238 22 33
190 0.371 0.007 3 258 22 35
190 0.357 0.008 1 236 18 28
190 0.364 0.005 3 303 28 44
190 0.333 0.008 3 237 20 30
190 0.357 0.008 1 235 18 28
198 0.354 0.006 10 288 31 48
198 0.367 0.009 5 224 19 30
198 0.386 0.006 5 293 27 44
198 0.359 0.006 5 272 25 39
198 0.359 0.006 5 272 25 39
198 0.364 0.007 3 251 21 33
198 0.393 0.009 3 224 17 28
198 0.386 0.005 3 303 27 44
198 0.367 0.008 3 235 19 30
198 0.364 0.007 3 250 21 33
198 0.393 0.008 1 236 17 28
198 0.371 0.007 3 262 22 35
198 0.387 0.007 1 249 19 31
198 0.375 0.007 1 255 20 32
198 0.391 0.010 1 209 14 23
206 0.371 0.007 5 250 22 35
206 0.378 0.006 5 301 28 45
206 0.361 0.007 5 256 23 36
206 0.367 0.006 10 294 31 49
206 0.364 0.008 5 242 21 33
206 0.370 0.006 10 281 29 46
206 0.364 0.006 7 287 28 44
206 0.385 0.006 3 281 24 39
206 0.409 0.005 3 303 26 44
206 0.388 0.005 7 308 30 49
206 0.370 0.006 7 296 29 46
206 0.407 0.009 3 219 16 27
206 0.400 0.006 5 273 24 40
206 0.406 0.007 1 253 19 32
206 0.400 0.006 3 286 24 40
206 0.400 0.008 1 243 18 30
206 0.394 0.007 1 259 20 33
206 0.391 0.010 1 210 14 23
214 0.385 0.010 3 215 16 26
214 0.357 0.010 7 206 18 28
214 0.419 0.006 3 300 25 43
214 0.393 0.010 5 214 17 28
214 0.391 0.005 5 304 28 46
214 0.385 0.007 5 269 24 39
214 0.385 0.007 7 259 24 39
214 0.386 0.006 7 284 27 44
214 0.396 0.005 7 303 29 48
214 0.385 0.007 7 261 24 39
214 0.379 0.008 3 231 18 29
214 0.429 0.008 1 235 16 28
214 0.389 0.007 3 263 22 36
214 0.385 0.009 1 227 16 26
214 0.407 0.008 1 232 16 27
214 0.421 0.006 3 273 22 38
222 0.379 0.009 5 219 18 29
222 0.387 0.009 7 218 19 31
222 0.409 0.006 10 271 26 44
222 0.422 0.006 5 302 26 45
222 0.400 0.008 7 240 21 35
222 0.429 0.006 3 294 24 42
222 0.432 0.007 3 270 21 37
222 0.407 0.009 3 222 16 27
222 0.400 0.008 3 237 18 30
222 0.432 0.005 3 303 25 44
222 0.425 0.006 1 294 23 40
222 0.417 0.010 1 213 14 24
222 0.405 0.006 3 272 22 37
222 0.412 0.007 3 255 20 34
222 0.439 0.006 3 289 23 41
230 0.412 0.008 7 236 20 34
230 0.417 0.008 7 246 21 36
230 0.405 0.007 7 252 22 37
230 0.412 0.008 5 247 20 34
230 0.407 0.010 5 212 16 27
230 0.421 0.006 3 276 22 38
230 0.441 0.007 3 253 19 34
230 0.444 0.009 3 218 15 27
230 0.429 0.009 3 224 16 28
230 0.432 0.007 3 269 21 37
230 0.435 0.011 2 205 13 23
230 0.417 0.010 1 215 14 24
230 0.424 0.007 1 260 19 33
230 0.429 0.011 1 200 12 21
230 0.435 0.010 1 210 13 23
238 0.417 0.007 5 257 21 36
238 0.424 0.008 5 240 19 33
238 0.414 0.009 5 221 17 29
238 0.400 0.010 7 215 18 30
238 0.408 0.006 10 297 29 49
238 0.432 0.006 3 272 21 37
238 0.452 0.008 3 240 17 31
238 0.432 0.007 3 270 21 37
238 0.457 0.007 3 259 19 35
238 0.455 0.008 3 248 18 33
238 0.455 0.007 1 260 18 33
238 0.452 0.007 1 251 17 31
238 0.455 0.007 1 260 18 33
238 0.444 0.006 1 276 20 36
238 0.429 0.006 3 297 24 42
246 0.423 0.011 5 203 15 26
246 0.455 0.008 5 241 18 33
246 0.447 0.007 5 267 21 38
246 0.429 0.010 7 207 16 28
246 0.455 0.008 5 240 18 33
246 0.458 0.010 3 206 13 24
246 0.435 0.011 3 201 13 23
246 0.423 0.009 3 217 15 26
246 0.455 0.007 3 250 18 33
246 0.407 0.009 3 222 16 27
246 0.458 0.005 1 334 26 48
246 0.455 0.007 1 261 18 33
246 0.469 0.007 1 254 17 32
246 0.438 0.009 7 225 18 32
246 0.480 0.009 1 218 13 25
246 0.429 0.006 10 295 28 49
254 0.429 0.007 5 251 20 35
254 0.459 0.007 5 259 20 37
254 0.444 0.007 5 257 20 36
254 0.426 0.006 10 287 27 47
254 0.459 0.008 7 248 20 37
254 0.463 0.006 3 291 22 41
254 0.463 0.006 3 288 22 41
254 0.455 0.006 7 284 24 44
254 0.465 0.006 3 298 23 43
254 0.460 0.005 3 336 27 50
254 0.475 0.006 3 285 21 40
254 0.435 0.006 10 280 26 46
254 0.465 0.005 1 310 23 43
254 0.471 0.007 1 264 18 34
254 0.462 0.006 3 279 21 39
262 0.474 0.007 5 265 20 38
262 0.474 0.007 5 263 20 38
262 0.477 0.006 5 294 23 44
262 0.447 0.007 7 253 21 38
262 0.460 0.006 10 301 27 50
262 0.460 0.005 7 315 27 50
262 0.488 0.006 3 302 22 43
262 0.483 0.008 3 231 15 29
262 0.475 0.006 3 283 21 40
262 0.452 0.008 3 241 17 31
262 0.489 0.005 1 318 23 45
262 0.500 0.008 1 245 15 30
262 0.500 0.008 1 243 15 30
262 0.457 0.006 10 279 25 46
262 0.469 0.007 1 253 17 32
270 0.468 0.006 7 300 25 47
270 0.457 0.007 5 251 19 35
270 0.471 0.008 5 245 18 34
270 0.457 0.007 5 252 19 35
270 0.488 0.006 5 281 21 41
270 0.483 0.008 3 231 15 29
270 0.489 0.005 3 318 24 47
270 0.467 0.008 3 235 16 30
270 0.476 0.006 7 273 22 42
270 0.488 0.006 3 288 21 41
270 0.481 0.009 1 228 14 27
270 0.500 0.005 3 345 26 52
270 0.487 0.006 3 280 20 39
270 0.486 0.006 1 272 18 35
270 0.487 0.006 3 279 20 39
278 0.486 0.007 5 260 19 37
278 0.472 0.007 5 256 19 36
278 0.476 0.006 5 285 22 42
278 0.481 0.005 10 312 27 52
278 0.467 0.009 5 225 16 30
278 0.487 0.006 3 280 20 39
278 0.490 0.005 7 312 25 49
278 0.486 0.007 3 270 19 37
278 0.464 0.009 3 227 15 28
278 0.467 0.008 3 234 16 30
278 0.468 0.006 10 284 25 47
278 0.500 0.006 1 275 18 36
278 0.477 0.005 3 307 23 44
278 0.500 0.009 1 224 13 26
278 0.500 0.007 1 256 16 32
286 0.500 0.008 5 233 16 32
286 0.485 0.008 5 240 17 33
286 0.469 0.008 5 237 17 32
286 0.474 0.007 7 257 20 38
286 0.452 0.009 7 222 17 31
286 0.486 0.006 3 272 19 37
286 0.486 0.006 3 272 19 37
286 0.480 0.009 1 221 13 25
286 0.500 0.007 3 264 18 36
286 0.487 0.006 3 279 20 39
286 0.512 0.006 3 291 20 41
286 0.500 0.005 3 306 22 44
286 0.500 0.007 1 264 17 34
286 0.467 0.006 10 273 24 45
286 0.500 0.009 1 225 13 26
294 0.487 0.007 7 261 20 39
294 0.486 0.007 3 258 18 35
294 0.475 0.007 7 266 21 40
294 0.478 0.006 7 297 24 46
294 0.500 0.006 5 274 20 40
294 0.483 0.009 3 229 15 29
294 0.500 0.009 3 224 14 28
294 0.511 0.005 3 310 22 45
294 0.500 0.006 3 276 19 38
294 0.512 0.006 3 298 21 43
294 0.511 0.005 1 318 22 45
294 0.536 0.008 1 233 13 28
294 0.487 0.006 3 281 20 39
294 0.523 0.005 1 314 21 44
294 0.511 0.005 3 318 23 47
302 0.500 0.006 5 283 21 42
302 0.478 0.006 7 296 24 46
302 0.500 0.007 5 264 19 38
302 0.513 0.007 7 258 19 39
302 0.484 0.008 5 232 16 31
302 0.514 0.006 3 271 18 37
302 0.522 0.005 3 314 22 46
302 0.522 0.005 3 314 22 46
302 0.513 0.006 3 280 19 39
302 0.512 0.006 3 290 20 41
302 0.516 0.007 1 252 15 31
302 0.515 0.007 1 261 16 33
302 0.524 0.005 1 304 20 42
302 0.528 0.006 1 276 17 36
302 0.512 0.005 1 310 21 43
310 0.490 0.006 10 294 25 49
310 0.490 0.005 10 304 26 51
310 0.510 0.005 7 319 25 51
310 0.484 0.009 6 226 16 31
310 0.500 0.006 9 286 23 46
310 0.531 0.008 3 243 15 32
310 0.500 0.007 3 255 17 34
310 0.512 0.006 3 298 21 43
310 0.531 0.008 3 244 15 32
310 0.500 0.005 7 305 24 48
310 0.516 0.007 1 252 15 31
310 0.535 0.005 1 311 20 43
310 0.528 0.006 1 275 17 36
310 0.514 0.006 1 272 17 35
310 0.516 0.007 1 249 15 31
318 0.500 0.007 5 267 19 38
318 0.525 0.006 5 273 19 40
318 0.486 0.007 7 252 19 37
318 0.513 0.007 5 268 19 39
318 0.511 0.005 5 312 23 47
318 0.519 0.009 3 222 13 27
318 0.533 0.008 1 243 14 30
318 0.500 0.005 7 307 24 48
318 0.516 0.008 3 239 15 31
318 0.500 0.006 3 276 19 38
318 0.525 0.006 3 284 19 40
318 0.522 0.005 3 316 22 46
318 0.514 0.007 1 270 17 35
318 0.541 0.006 1 280 17 37
318 0.528 0.006 1 276 17 36
326 0.500 0.008 5 236 16 32
326 0.533 0.006 5 299 21 45
326 0.516 0.009 5 229 15 31
326 0.529 0.008 5 244 16 34
326 0.522 0.005 5 303 22 46
326 0.500 0.006 7 286 22 44
326 0.528 0.007 3 267 17 36
326 0.548 0.008 3 239 14 31
326 0.538 0.006 3 279 18 39
326 0.526 0.006 3 275 18 38
326 0.535 0.006 3 302 20 43
326 0.524 0.006 3 297 20 42
326 0.536 0.008 1 235 13 28
326 0.543 0.007 1 269 16 35
326 0.545 0.005 3 303 20 44
334 0.514 0.007 5 252 17 35
334 0.512 0.006 7 282 21 43
334 0.510 0.005 9 310 25 51
334 0.500 0.007 7 267 20 40
334 0.500 0.006 10 289 24 48
334 0.532 0.005 3 321 22 47
334 0.520 0.005 7 315 24 50
334 0.542 0.006 10 289 22 48
334 0.519 0.005 7 325 25 52
334 0.515 0.007 3 251 16 33
334 0.529 0.005 3 340 24 51
334 0.542 0.005 1 337 22 48
334 0.531 0.007 1 256 15 32
334 0.542 0.005 1 335 22 48
334 0.541 0.006 1 280 17 37
342 0.514 0.008 5 248 17 35
342 0.500 0.007 7 263 20 40
342 0.537 0.004 5 347 25 54
342 0.526 0.007 5 267 18 38
342 0.531 0.005 7 311 23 49
342 0.538 0.006 3 281 18 39
342 0.521 0.005 7 305 23 48
342 0.538 0.006 3 280 18 39
342 0.537 0.005 7 336 25 54
342 0.529 0.007 3 253 16 34
342 0.550 0.006 1 295 18 40
342 0.553 0.005 1 330 21 47
342 0.563 0.007 1 254 14 32
342 0.556 0.005 1 318 20 45
342 0.545 0.005 1 315 20 44
350 0.533 0.004 10 348 28 60
350 0.521 0.005 7 303 23 48
350 0.538 0.005 5 334 24 52
350 0.526 0.007 5 267 18 38
350 0.549 0.005 5 331 23 51
350 0.553 0.005 3 320 21 47
350 0.515 0.007 3 251 16 33
350 0.543 0.005 5 304 21 46
350 0.543 0.007 3 260 16 35
350 0.523 0.006 7 287 21 44
350 0.568 0.006 1 279 16 37
350 0.564 0.006 1 288 17 39
350 0.543 0.005 1 326 21 46
350 0.540 0.005 3 337 23 50
350 0.545 0.007 1 261 15 33
358 0.538 0.007 5 270 18 39
358 0.528 0.008 7 246 17 36
358 0.540 0.005 7 315 23 50
358 0.510 0.005 10 304 25 51
358 0.510 0.005 10 307 25 51
358 0.528 0.007 3 266 17 36
358 0.543 0.007 3 260 16 35
358 0.553 0.005 3 322 21 47
358 0.558 0.004 3 347 23 52
358 0.540 0.005 5 327 23 50
358 0.548 0.006 3 293 19 42
358 0.511 0.006 9 291 23 47
358 0.568 0.005 1 315 19 44
358 0.548 0.006 3 295 19 42
358 0.563 0.005 3 323 21 48
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

Go crazy!

[Whirlin]

http://i0.kym-cdn.com/entries/icons/original/000/000/559/iconric.jpg

[Yollia]

Go crazy!

So the nonlinear programming shit worked. I fed the program your massive chunk of data. If we say that

meanRedux66(x) = 0.71354*(x-112.42)/(x-33.03)

then this gives the correct redux factor for ALL of the data you gave me with a maximum error of 1.5 points of damage.

[Latrinsorm]

But did you do Mark's thing? That thing I think would thing the thing.

[Yollia]

But did you do Mark's thing? That thing I think would thing the thing.

When I split the data by crit rank, in all cases the fit became accurate to within at most 1.4 points of damage (so 1 point of damage after rounding)! I think if I had the exact raw damage instead of the rounded raw damage the fit could be better (as in maybe exact).

[Latrinsorm]

The unreduced damage factor in all cases was .200, so you can get the unrounded raw damage that way.

[Yollia]

To Riltus:

Here is a possible explanation of the inflated intervals:

Notice that the intervals aren't exactly always doubled. For example, the first interval you show is 18, then 12, then 11, then 23. Even if the real interval size is 11.5, doubling doesn't explain the interval of length 18. I did some tests myself and it didn't seem that any intervals were doubles of any others, but I definitely agree that there were some intervals that were much larger than others.

Especially for low endrolls, the effective DF (meaning (weapon damage)/(endroll-100)) is likely not a good approximation of the "real" DF because the denominator is too small. Here's what happens as the endrolls increase by 1:

1. If the damage stays the same, then the effective DF decreases (by a relatively small amount).
2. If the damage increases, then the effective DF increases (by a more significant jump).

The situation could be that they decided that straight rounding, which would give intervals of a regular size, is too unforgiving, giving damages that are too high for lower endrolls. Thus they would hold the damage constant until the effective DF drops low enough that increasing the damage by 1 will yield an effective DF that isn't too much higher than the real thing. Also, rather than going endroll by endroll they probably just have a criterion like

If damage/(endroll-100)>realDF*1.05 then damage = damage - 1.


I could be wrong, but I see this as a likely explanation because whatever they do is unlikely to be a whole lot more complicated than a few truncations, subtractions, divisions, etc. It would be too much work for virtually no benefit.

Without knowing exactly what they're doing, we can apparently turn the redux points into a number that's close enough to the real thing that if we multiply the raw damage by (1-the number) and round we're off by no more than 2 points of damage for every hit. Of course, this is huge for low endrolls.

If your goal is to have an extremely good estimate of how much your damage is reduced by for each hit, then we're almost there. If your goal is to compute everything exactly, then the easiest thing to do is bribe one of the GMs with a chocolate bar to let us look at the code.

[Riltus]

To Riltus:

Here is a possible explanation of the inflated intervals:

Notice that the intervals aren't exactly always doubled. For example, the first interval you show is 18, then 12, then 11, then 23. Even if the real interval size is 11.5, doubling doesn't explain the interval of length 18. I did some tests myself and it didn't seem that any intervals were doubles of any others, but I definitely agree that there were some intervals that were much larger than others.

Especially for low endrolls, the effective DF (meaning (weapon damage)/(endroll-100)) is likely not a good approximation of the "real" DF because the denominator is too small. Here's what happens as the endrolls increase by 1:

1. If the damage stays the same, then the effective DF decreases (by a relatively small amount).
2. If the damage increases, then the effective DF increases (by a more significant jump).

The situation could be that they decided that straight rounding, which would give intervals of a regular size, is too unforgiving, giving damages that are too high for lower endrolls. Thus they would hold the damage constant until the effective DF drops low enough that increasing the damage by 1 will yield an effective DF that isn't too much higher than the real thing. Also, rather than going endroll by endroll they probably just have a criterion like

If damage/(endroll-100)>realDF*1.05 then damage = damage - 1.


I could be wrong, but I see this as a likely explanation because whatever they do is unlikely to be a whole lot more complicated than a few truncations, subtractions, divisions, etc. It would be too much work for virtually no benefit.

Without knowing exactly what they're doing, we can apparently turn the redux points into a number that's close enough to the real thing that if we multiply the raw damage by (1-the number) and round we're off by no more than 2 points of damage for every hit. Of course, this is huge for low endrolls.

If your goal is to have an extremely good estimate of how much your damage is reduced by for each hit, then we're almost there. If your goal is to compute everything exactly, then the easiest thing to do is bribe one of the GMs with a chocolate bar to let us look at the code.

I'm going to break up my response into a couple of posts to avoid eyes glazing over.

PART 1

1. Reduced critical damage formula:


Reduced crit damage = round(crit damage * (1 - RFc)

2. RFc = Redux Factor floor.

a. It serves to reduce raw damage up to the first double endroll interval
b. It determines the reduced critical damage taken
c. It can also be used to determine the endroll at each critical rank threshold for all armor groups and weapon DFs.

2. Endroll Intervals

Number of endrolls in a standard interval = 1/weapon DF
Number of endrolls in a double interval = 2/weapon DF

Note: the first interval is unique since damage less than 0.5 rounds up to 1. Therefore, it contains approximately 1.5x the number of endrolls as a standard interval.


Lev 27, 200.5 redux pts
RFc: .222
Weapon DF: .110 (Jackblade vs Plate)
Reduced DF: 0.86
Rank 1 plate critical divisor: 10.5

Actual Dmg Taken|1|2|3|4*|5|6|7*|8|10(1)|11*(1)
Endrolls|101-117|118-129|130-140|141-163*|164-175|176-187|188-210*|211-222|223**-233 (1)|234-256?*
Interval size|18|12|11|23*|12|12|23*|12|11|23?

Endrolls per standard interval: 1/.086 = 11.6279
Endrolls per double interval: 2/.086 = 23.2558

Any difference in the number of endrolls, between either standard or double intervals, is due to rounding.

This becomes apparent if you multiply the reduced RFc damage factor by the lowest and highest ER success margins in each interval.

Interval 1:

ER 101 (1 * .086) = 0.086 rounds UP to 1
ER 117 (17 * .086) = 1.462 rounds to 1

Interval 2:

ER 118 (18 * .086) = 1.548 rounds to 2
ER 129 (29 * .086) = 2.494 rounds to 2

Interval 3:

ER 130 (30 * .086) = 2.58 rounds to 3
ER 140 (40 * .086) = 3.44 rounds to 3

Interval 4: Double Interval

ER 141 (41 * .086) = .3526 rounds to 4
ER 163 (63 * .086) = .5418 rounds to 4

END PART 1

Mark

[Yollia]

The level 66 formula was almost a perfect fit thanks to Latrinsorm's data. Hyperbolas are assholes in that they can be so close yet so far. I suspect that in our formula:

redux=C*(x-T)/(x-A)

we have that A=level/2. Even if this is correct, we don't know how to calculate C. My provisional formulas have given really good estimates for various levels, but they blow up at low levels. Also, I WANT EXACT FORMULAS.

The solution is clearly to gather another assload of data, with multiple hits on characters with the same number of redux points and the same level. I was relying on using just hard hits before because they give more accurate estimates. Having a wide range of hits, though, hard or not, is the way to go, because we don't want to measure an estimate, we want to measure the real thing.

[Yollia]

I have a massive test scheduled in Shattered, but I also released a lich script called rdxpoints which seems to come pretty close to calculating your redux if you don't know spells. I took the two formulas that work for levels 66 and 100 and I used them to do some extrapolation. It probably works so well because the effect of the level is kind of small. The syntax is

;rdxpoints person

It uses lnet, so they have to allow you to view their skills and info. Of course it always works on yourself. Enjoy.

[Yollia]

After several hours of scripting the redux test in shattered, I parsed the data and fit a hyperbola to it. The formula for level 29 is (almost)

redux29(x)=0.703268*(x-113.4)/(x-14.5),

or at least this curve fit the 1838 usable data points to within 1.69 points of damage. I had to throw some of the data out because the crit messages were ambiguous.

It's not quite right because you DO have some redux at 113.4; that is in fact the lowest number of redux points for which I no longer saw the "insufficient bonus for redux" message. But you have almost no redux at that point.

[Yollia]

I wanted to share an image of the latest fit, since it might look like I'm just throwing functions at you.

http://i1312.photobucket.com/albums/t538/mattjsam/redux29fit_zpsbfe2b745.png

[Snoopy Dogg]

completely off topic, but your avatar made me laugh

[Yollia]

completely off topic, but your avatar made me laugh

That is off-topic. How dare you.

[Yollia]

Oh I have some data for thresholds:

Level 16: 126.8
Level 17: 118 pts (confirmed)
Level 18: 117.2 pts
Level 20: 116.4 pts
Level 29, 20/10 spells: 111.2
Level 30, 31/? spells: 113
Level 83, 0-3 spells: 108.4

Looks like a logarithm to me. No! I kid. Also the data were collected from several different people, so feel free to throw any given one out if it doesn't fit.

How was the threshold for level 17 confirmed?

[Latrinsorm]

Two good and upstanding men swore to it. The rest...

[Yollia]

I have some mathematical and practical reasons to believe that the ceiling is always 70%.

First let's look at the mathematical reasons. We know the fit for level 29 is good, and the ceiling might as well be 70% in that case. Let's assume that if the number of redux points stays the same, then the redux always increases (or stays the same) when the level increases, which makes sense because the threshold decreases. This leads us to the inequality

-C'(L)<-T'(L)*C(L)/(x-T(L))+C(L)/(2(x-L/2))

which must be valid for all x. If C'(L)<0 for some L, then the left-hand side is greater than 0. The right-hand side goes to 0 as x goes to infinity, so this is not possible. We can conclude that C'(L)>=0 for all L, so the ceiling must either increase or stay the same as the level increases. A redux function with a ceiling of 70% can be fitted to Latrinsorm's level 66 data quite well...just as well as what I posted earlier. So it is reasonable to assume that the ceiling always stays the same.

Now the practical reason: it's much easier on Simu's end to always have a ceiling of 70% than to come up with some wonky formula for the ceiling as a function of the level.



If this reasoning is correct, we basically just need to figure out a formula for the threshold to finish this thing.

[Yollia]

I have some mathematical and practical reasons to believe that the ceiling is always 70%.

First let's look at the mathematical reasons. We know the fit for level 29 is good, and the ceiling might as well be 70% in that case. Let's assume that if the number of redux points stays the same, then the redux always increases (or stays the same) when the level increases, which makes sense because the threshold decreases. This leads us to the inequality

-C'(L)<-T'(L)*C(L)/(x-T(L))+C(L)/(2(x-L/2))

which must be valid for all x. If C'(L)<0 for some L, then the left-hand side is greater than 0. The right-hand side goes to 0 as x goes to infinity, so this is not possible. We can conclude that C'(L)>=0 for all L, so the ceiling must either increase or stay the same as the level increases. A redux function with a ceiling of 70% can be fitted to Latrinsorm's level 66 data quite well...just as well as what I posted earlier. So it is reasonable to assume that the ceiling always stays the same.

Now the practical reason: it's much easier on Simu's end to always have a ceiling of 70% than to come up with some wonky formula for the ceiling as a function of the level.



If this reasoning is correct, we basically just need to figure out a formula for the threshold to finish this thing.

Also, theoretically the only thing you need to do to measure the threshold is accurately calculate the redux of someone of that level who has redux and solve for the threshold. But you'd need 3 or 4 decimal places of accuracy.

[Tenlaar]

So I don't know what any of this stuff really means, I just want to say that I got to punch Yollia. A lot.

[Yollia]

So I don't know what any of this stuff really means, I just want to say that I got to punch Yollia. A lot.

1,964 times, to be exact. I had plans to do it again sometime...

[SpiffyJr]

I'm 48 if someone wants to punch me

[Tenlaar]

1,964 times, to be exact. I had plans to do it again sometime...

I'm up for it whenever, assuming at some point my computer decides to stay connected to shattered for more than a couple of hours at a damned time.

[Yollia]

I just had Azanoth punch me a bunch of times (I'm level 31 now in Shattered) so I could try to compute the threshold. Taking the average gave a threshold of 118ish. If I postulate that the threshold is around what I want it to be (113.2), then everything is perfect except for hits with high rank crits, which are off by 1-2 points of damage. Indeed, the error seems to depend on the rank and NOT on the crit damage.

[Yollia]

A graduated redux scale is looking good. LIKE TAXES, RIGHT? It doesn't totally resolve the discrepancies for rank 1 crits in the level 29 data, but it reduces the maximum error to 1 point of damage BEFORE rounding. Using one redux factor for raw damage and one for crit damage reduces the maximum error to 1.3 points of damage for all of the level 29 data. I suspect a graduated scale could reduce the error for every rank to 1 point of damage, but verifying this will require reorganizing my program a bit and doing some manual data entry, and I'm lazy when it comes to that sort of thing.

I apologize to Riltus for taking so long to come around to considering these things, but I find that I have to investigate things my own way.

[Riltus]

A graduated redux scale is looking good. LIKE TAXES, RIGHT? It doesn't totally resolve the discrepancies for rank 1 crits in the level 29 data, but it reduces the maximum error to 1 point of damage BEFORE rounding. Using one redux factor for raw damage and one for crit damage reduces the maximum error to 1.3 points of damage for all of the level 29 data. I suspect a graduated scale could reduce the error for every rank to 1 point of damage, but verifying this will require reorganizing my program a bit and doing some manual data entry, and I'm lazy when it comes to that sort of thing.

I apologize to Riltus for taking so long to come around to considering these things, but I find that I have to investigate things my own way.

Hey, no need to apologize. It took me quite some time to grasp and verify this. It only became apparent when I mapped out (several times with different weapon/armor combinations) the endrolls up to and above the rank 1 critical divisor.

There are two parts to redux.

1. The formula for the translation of level/redux points/spell penalty to a redux factor.

and

2. The application of the redux factor to:

a. Maximum reduced critical rank determination.

b. Critical damage reduction.

c. Raw damage reduction.

I can contribute some insight to part 2. I know the formulas for 2a/2b and have some understanding of the underlying mechanics of 2c but the formula has been quite elusive.

There are, for each character of Lev x, Redux pts y, and spell ranks z, both a non-variable primary (pRF) and non-variable secondary (sRF) redux factor. The graph that you posted has the primary values represented in the y-axis, however, they are inflated ~50%. The secondary redux factor is derived from the first. The following table contains a partial list of primary redux factors and their secondary counterparts.


Primary RF|Secondary RF|50% Inflation**
.010|.505|.015
.020|.510|.030
.030|.515|.045
.040|.520|.060
.050|.525|.075
.100|.550|.150
.150|.575|.225
.200|.600|.300
.250|.625|.375
.300|.650|.450
.350|.675|.525
.360*|.680*|.540*
.400|.700|.600


*Indicates Latrinsorm's level 66 (382 redux pts) approximate primary, secondary and inflated redux factors.

**The inflated column is the approximate calculated value when averaging several attacks under normal conditions ie., no crit weighting or padding. This is the approximate values that you are using for the redux factor.

All critical and raw damage with a standard ER interval length are reduced by the pRF. sRF only applies to the double length intervals.

Secondary RF (sRF) formula:


[1 - ((1- pRF)/2)]

How is this calculated? I'll use the broadsword (DF 0.200). For non-reduxed characters each endroll adds 0.200 pts of damage. Latrinsorm with a pRF of .36 has a reduced weapon Df of 0.128. His character will take .128 damage per endroll when there is a standard interval. When there is a double interval the weapon damage factor is halved from .128 to .064. For each endroll in the double interval his character is taking .064 damage. Compare that to the unreduced damage per ER of .200 and calculate the redux factor [1 - (.064/.200)] = sRF 0.68 or expressed another way, DFredux 68%. Keep in mind that standard intervals and double intervals each represent 1 pt of damage.

Latrinsorm's character has two distinct redux factors: pRF 0.36 and sRF 0.68.

Why does he have a caculated RF of 0.54? Imagine that pRF (.36) is a can of white paint and sRF (.68) is a can of black paint. We place one ounch of white paint into an empty can for each point of critical damage and for each point of standard interval length raw damage. But that still leaves us at 36% damage reduction. Periodically, double intervals occur. Whenever there is a double interval we add one ounch of black paint to the mix. What we now have is gray paint. As the percentage of black to white paint increases, the shade of gray darkens (an increase in overall damage reduction).

I strongly recommend that you map out the endrolls up to the rank 1 critical divisor for your research character. It is very helpful to see this laid out. Take note of the highest and lowest endrolls for each damage point and at the critical divisor itself. To limit critical damage, you can set it up so that you will only take a critical at the highest d100 rolls. You can then calculate the reduced weapon DF within a small range and then use that to calculate an approximate value of pRF (1 - (reduced DF/unreduced DF).

For example, have your character wear brig armor and the attacker use a dagger (DF 0.100). Minimum damage for a rank 1 crit in scale is 6.5. The minimum endroll success margin is calculate by dividing the crit divisor by the weapon DF and rounding up.

(6.5/0.100) = 65 endroll success margin (non-redux character)

After many attacks you finally determine that the highest endroll that didn't cause a crit was ER 187 (success margin 87) and the lowest endroll that did inflict a critical was ER 188. You can now calculate the approximate weapon DF by 6.5/88 = .074. At endroll 87 there was no crit (87 * .074 = 6.438) which is insufficient to have cause a crit. What about DF .075 will that work? No, because if the DF was .075 there would have been a crit at ER 187 (87 * 0.075) = 6.25 damage.

You've now established that the reduced weapon DF is .074. Now use the formula 1 - (reduced DF/ unreduced DF) to determine the approximate pRF. From the example, pRF = 1 - (.074/0.100) = .26. You can then calculate sRF [1 - ((1- .074)/2)] = 0.630

Critical Damage Reduction

Critical damage is reduced by the primary redux factor.

Formula:

[Indent]round[(1 - Primary RF) * Unreduced Critical Damage] = Reduced Critical Damage taken

For Latrinsorm's Lev 66 char (382 redux pts) the Primary RF is ~0.36, therefore, critical damage taken is [round(0.64 * unreduced critical damage)].

Maximum Critical Rank

Formula


trunc[(ER - 100) * weapon DF)/(armor crit divisor) = Maximum crit rank

For characters with redux the weapon DF is the reduced weapon DF obtained from the primary redux factor.

Example:

Non-redux character, broadsword vs plate DF 0.200, ER 300

trunc[(300 - 100) * 0.200)]/11 = 3

Latrinsorm's character pRF 0.360
Reduced broadsword DF ( 1 - .36) * 0.200 = 0.128

Reduced max crit rank

trunc[(300 - 100) * 0.128]/11 = 2

Note: Once pRF is known, it is then possible to calculate (in the absence of crit weighting/padding) the minimum endroll required for any critical rank/weapon/armor combination.

Mark

[Yollia]

There's a bit of a problem. We've sort of gone from no formula to too many formulas. Let me explain.

We have 1,818 relevant data points. For a given number of redux points, there are almost always 5 corresponding data points; I had to throw some out because of ambiguous crit messages. That's a shitload of data, right? Surely enough to make it very hard to find a fit.

From what you said, a simple multiplication using two factors won't get us the exact reduced damage. That's fine; let's say we're happy if we're at least within 1 point of damage after rounding. Pretty strict, right? We'll really be hard-pressed to find numbers that work, especially for ALL 1,818 data points...right?

Let's go even farther. Let's say that if the weapon DF is reduced by the factor C1 (including the sporadic extra reducton, so sort of an average) and the critical damage is reduced by C2, then we'll insist that C1=1-(1-C2)/2. You wouldn't expect the computer to even find ONE fitted curve that satisfies ALL of these conditions for 1,818 data points.

For problems like this, if there's one solution then there are infinitely many, so it's not so strange that there are infinitely many solutions. The problem is that there's at least a 3.7% variation in the feasible solutions. You might think this isn't so bad, but it grates on my heart.

Anyway, for level 29 if we say that the primary redux factor is

0.535*(x-113.4)/(x-14.5)

and we assume that the entirety of the raw weapon damage is reduced by the secondary redux factor, but the crit damage is reduced by the primary redux factor, then we will always be within 1 point of damage of the correct answer after rounding, at least for all of the 1,818 usable data points Tenlaar, Empath and I collected. Indeed, the answer is exactly correct for more than 75.3% of the data points. So this isn't bad as far as solutions go.

So, uh, let's do more testing so we can get the thresholds and scale factors for other levels.

[Yollia]

Also, I'll figure out the endroll to damage map for this character for some weapon. Just have to have someone hit me dozens, possibly hundreds of times.

[Yollia]

Okay...after this test I did I feel a bit better about our formula.

Level 32 Yollia hunted in Shattered all night last night and most of today. She's hunting arctic titans, which have war hammers. I used my program to pull out the relevant data from them hitting her. For each point, I added (crit damage*primary redux factor), where primary redux factor is quoted above (but I guessed the threshold; three levels away isn't really far enough for the difference to matter that much), then subtracted what the actual crit damage would have been. The first thing I noticed was that the sequence of numbers I got, when ordered by endroll, was increasing. This was encouraging; it's supposed to be the raw weapon damage with the reduced DF. After dividing by (1-secondary redux factor), which should inflate the numbers to what you'd normally get with a war hammer, then by endroll-100, which should give you the DF, the resulting numbers are about the same as the DF of the war hammer. This is the most we can really hope for. The actual damage from a war hammer doesn't quite match, but it's almost the same...it's just that the length of the intervals is different.

[Riltus]

Now it's my turn to apologize. After reviewing some data it became evident that there are two unique DFredux factors.

Level 27, 200.5 redux points

pRF (critical damage): ~.22
sRF (raw damage): ~.393

With a jackblade vs brig (DF .150) the reduced weapon DF for critical damage is .117 and the raw damage DF is .091. The DFs are exact for this weapon but I'll need to look at other weapon/armor combos to see if I can measure the redux factors more precisely.

Calculations for redux factors:

Critical damage: 1 - (.117/.150) = .220
Raw damage: 1 - (.091/.150) = .393

Interestingly, the expression (pRF * (1 + pRF compliment) yields sRF for this character. Might be a longshot but you may want to see if this fits your data.

pRF: .22
sRF: .393
pRF Compliment: .78
1 + pRF comp: 1.78

(pRF * (1 + pRF compliment) = sRF??


(.22 * 1.78) = .392


Mark

[Yollia]

Now it's my turn to apologize. After reviewing some data it became evident that there are two unique DFredux factors.

Level 27, 200.5 redux points

pRF (critical damage):
sRF (raw damage): ~.393

With a jackblade vs brig (DF .150) the reduced weapon DF for critical damage is .117 and the raw damage DF is .091. The DFs are exact for this weapon but I'll need to look at other weapon/armor combos to see if I can measure the redux factors more precisely.

Calculations for redux factors:

Critical damage: 1 - (.117/.150) = .220
Raw damage: 1 - (.091/.150) = .393

Interestingly, the expression (pRF * (1 + pRF compliment) yields sRF for this character. Might be a longshot but you may want to see if this fits your data.

pRF: .22
sRF: .393
pRF Compliment: .78
1 + pRF comp: 1.78

(pRF * (1 + pRF compliment) = sRF??


(.22 * 1.78) = .392


Mark

Those numbers jibe with the formula I posted, but one thing I posted was erroneous: I didn't set srf=(1+prf)/2. Rather, the scale factor for srf is (1+0.535)/2 instead of 0.535.

[Yollia]

Those numbers jibe with the formula I posted, but one thing I posted was erroneous: I didn't set srf=(1+prf)/2. Rather, the scale factor for srf is (1+0.535)/2 instead of 0.535.


Just to clarify, let's say your character were level 29 instead of 27. Then the formula says

pRF = 0.535*(200.5-113.4)/(200.5-14.5) ~ 0.251

and

sRF = (1+0.535)/2*(200.5-113.4)/(200.5-14.5) ~ 0.359

This gives a reduced raw weapon damage factor of 0.09615...not very far off from what you posted. The "critical damage factor" as you call it would then be 0.11235. The differences would only be seen in actual calculations with large numbers and could plausibly be explained by the level difference.

[Riltus]

Just to clarify, let's say your character were level 29 instead of 27. Then the formula says

pRF = 0.535*(200.5-113.4)/(200.5-14.5) ~ 0.251

and

sRF = (1+0.535)/2*(200.5-113.4)/(200.5-14.5) ~ 0.359

This gives a reduced raw weapon damage factor of 0.09615...not very far off from what you posted. The "critical damage factor" as you call it would then be 0.11235. The differences would only be seen in actual calculations with large numbers and could plausibly be explained by the level difference.

If the formula's output you are using is correct, then I don't see how these are accurate.


pRF = 0.535*(200.5-113.4)/(200.5-14.5) ~ 0.251

and

sRF = (1+0.535)/2*(200.5-113.4)/(200.5-14.5) ~ 0.359

For my character the scale factor, using the formulae above, would need to be ~.476 to match my actual redux factors, and I would need to modifiy the sRF formula.

pRF = 0.476 * (200.5 - 113.6)/(200.5 - 13.5) = .221

sRF =

1- [1- (0.476 * (200.5 - 113.6)/(200.5 - 13.5))]²
1 - [(1 - (.476 * .465)]²
1 - (1 - .221)² = .393

Note: pRF (crit damage redux factor), sRF (raw damage redux factor)

If the character's level increases to 29 and the redux points remain the same then both crit and raw damage factors will increase, albeit a relatively small amount. Your calculations have my character's sRF decreasing with a level increase. That's not possible.

Let:

a = crit damage redux factor
b = raw damage redux factor
c = crit damage weapon DF multiplier
d = raw damage weapon DF multiplier

Lvl 27, 200.5 redux points

a = .221
b = .393
c = .779
d = .607

Note: RF 'a' margin of error +/- .001

Weapon DF calculations

Unreduced weapon DF: .150
Crit damage weapon DF: .117 (.150 * .779)
Raw damage weapon DF: .091 (.150 * .607)

These are the character's precise weapon DFs.

Table I

The table below shows each value expressed in terms of the other three.


a =.221|b =.393|c =.779|d =.607
1-c|1-d|1-a|1-b
1-√d|1-c²|√(1-b)|c²
1-√(1-b)|1-(1-a)²|√d|(1-a)²

These expressions can be used to find corresponding values for ANY/ALL redux factors.

If a = .300

b = 1-(1-.300)² = .510
c = 1 - .300 = .700
d = (1 - .300)² = .490

Also, the 1 point discrepancies (calculated damage 1 less than actual damage taken) seem to be related to damage thresholds and the standard/double length intervals. Initially, raw damage is reduced by the critical RF and its correspondingly higher weapon DF.

Mark

[Yollia]

If the formula's output you are using is correct, then I don't see how these are accurate.



For my character the scale factor, using the formulae above, would need to be ~.476 to match my actual redux factors, and I would need to modifiy the sRF formula.

pRF = 0.476 * (200.5 - 113.6)/(200.5 - 13.5) = .221

sRF =

1- [1- (0.476 * (200.5 - 113.6)/(200.5 - 13.5))]²
1 - [(1 - (.476 * .465)]²
1 - (1 - .221)² = .393

Note: pRF (crit damage redux factor), sRF (raw damage redux factor)

If the character's level increases to 29 and the redux points remain the same then both crit and raw damage factors will increase, albeit a relatively small amount. Your calculations have my character's sRF decreasing with a level increase. That's not possible.

Let:

a = crit damage redux factor
b = raw damage redux factor
c = crit damage weapon DF multiplier
d = raw damage weapon DF multiplier

Lvl 27, 200.5 redux points

a = .221
b = .393
c = .779
d = .607

Note: RF 'a' margin of error +/- .001

Weapon DF calculations

Unreduced weapon DF: .150
Crit damage weapon DF: .117 (.150 * .779)
Raw damage weapon DF: .091 (.150 * .607)

These are the character's precise weapon DFs.

Table I

The table below shows each value expressed in terms of the other three.


a =.221|b =.393|c =.779|d =.607
1-c|1-d|1-a|1-b
1-√d|1-c²|√(1-b)|c²
1-√(1-b)|1-(1-a)²|√d|(1-a)²

These expressions can be used to find corresponding values for ANY/ALL redux factors.

If a = .300

b = 1-(1-.300)² = .510
c = 1 - .300 = .700
d = (1 - .300)² = .490

Also, the 1 point discrepancies (calculated damage 1 less than actual damage taken) seem to be related to damage thresholds and the standard/double length intervals. Initially, raw damage is reduced by the critical RF and its correspondingly higher weapon DF.

Mark

Say pRF=C*(x-T)/(x-L/2), where T is the threshold, L is the level, and C is the scale factor. This is an increasing function with level because the numerator gets larger and the denominator gets smaller.

Consider 1-(1-pRF)^2. If you take the derivative, you get -2(1-pRF)*(-prF')=(prF')*(1-pRF)>0, so if that's how you define the secondary redux factor, it is increasing with level, no matter what the scale factor is.

By the way, I misunderstood how you defined sRF before. When I did the fit assuming sRF=1-(1-pRF)^2, the average error pretty much vanished if I sacrificed absolute error. I accepted a deviation of up to 3 points of damage after rounding.

A vanishing average error doesn't necessarily mean things are good. If a uniform random variable happens to have the redux as its mean, then if you take a lot of samples and take the average it'll look like it's a good approximation to the redux.

However, the number of samples we have is very few compared to what usually makes an average vanish...by vanish, we're talking 14 zeros after the decimal point.

This vanishing average happens with a scale factor of 0.5300bunchofnumbers. If I round that to 0.53, we only get three zeros after the decimal point, but the absolute error is about the same. It's better than 0.535, certainly, and it's the best fit I've gotten.

If we pin the redux down at 0.221 and solve for the threshold, we get about 122.52. This seems a bit too high to me, but I haven't measured it so I can't say for sure.

I think it would be helpful if you explained how you ensured that the error in your measurement is less than 0.001 in magnitude.