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Category: Hunting and Combat
Topic: DF Redux
Message #: 1778
Author: HOFMANNM1
Date: 7/26/2008 1:52:58 PM
Subject: Redux, and Things

Comrades,

I am leaving GemStone. I simply do not have time to play any longer. Before I leave, I want to put in one document everything I've figured out about redux.

Even the most basic understanding of Damage Reduction (redux) has prerequisites. Redux applies to AS/DS resolutions, which look like this:

Anathemus swings a broadsword at you!
  AS: +130 vs DS: +55 with AvD: +36 + d100 roll: +48 = +159
  ... and hits for 37 points of damage!
  Deep, bloody slash to your right thigh!
  You are knocked to the ground!
  You are stunned for 3 rounds!

For any given hit, one can obtain a value for raw damage and crit damage.

Raw damage is that damage that is solely a result of the endroll (marked above in bold) and the Damage Factor (DF), which itself depends only on weapon type, torso worn armor, and various multipliers such as CMAN Mighty Blow.

Crit damage is significantly more complicated; the game takes the sum of raw damage and crit padding or weighting and divides by the crit divisor, which depends on location hit, torso worn armor, and relevant armor accessories worn. The truncation of this quotient is the crit rank, which cannot exceed a value of 9. The actual crit rank for any given hit can range from this maximum to one half of it, rounded up. Once obtained, the actual crit rank is checked against a crit table specific to the damage type (e.g. slash, puncture) and body part (e.g. left eye, abdomen) and a crit message is selected that corresponds to a specific amount of crit damage.

Note: Crit padding cannot reduce what would have been a crit rank 1 or higher to a crit rank 0, and crit weighting cannot increase what would have been a crit rank 0 to a crit rank 1 or higher.

The sum of raw damage and crit damage, plus damage weighting or padding, is referred to as total damage. It is generally accepted that redux does not apply to damage weighting or padding, making hits involving either quantity unacceptable for redux calculations. [Incidentally, this is probably worth testing by someone at some point.]

When the defender has redux, the amount of total damage taken is reduced. This is a fairly recent modification to redux, taking place sometime around or after the switch from GemStone 3 to GemStone 4. In GemStone 3, redux applied only to raw damage (hence the archaic names ?Damage Factor Reduction? and ?DFRedux?). As such, calculators or methodologies using this approach are no longer accurate and will provide wildly divergent measurements. Unfortunately, the full interactions of redux are not yet known. To first order, it is permissible to define a Redux Factor (RF) as follows:

RF = 1 ? reduced total damage / unreduced total damage

Thus, a character that experienced no reduction would have an RF of .000. Let us return to the example given previously.

Anathemus swings a broadsword at you!
  AS: +130 vs DS: +55 with AvD: +36 + d100 roll: +48 = +159
  ... and hits for 37 points of damage!
  Deep, bloody slash to your right thigh!
  You are knocked to the ground!
  You are stunned for 3 rounds!

Reduced total damage refers to the ??and hits for? message. In GemStone, damage is rounded to the nearest whole integer or one if it would be rounded to zero. This uncertainty is negligible in almost every case. To obtain unreduced total damage, one requires a DF table, the endroll, and a table of crit messages. The crit message is that marked above in bold. It is not necessary to know how much crit padding or crit weighting occurred in any given hit, which is good because such information is impossible to obtain in the overwhelming majority of cases.

Unreduced raw damage is obtained by subtracting 100 from the endroll and multiplying by the Damage Factor, which is itself obtained by matching the weapon type (falchion, handaxe, etc.) to the armor group (Clothing, Soft Leather, Rigid Leather, Chain, Plate).

Unreduced crit damage is obtained by matching the crit message to the table. In very few cases, the same crit message can be used in more than one crit rank for more than one value of crit damage: it is best to discard these hits.

It is also best to discard any hit that has an especially low amount of damage relative to the granularity of GemStone rounding, for example a hit that only does 3 or 4 damage.

.

For this hit, we first find a reduced total damage of 37. Consulting a table, we find that a broadsword vs. clothing has a Damage Factor of .450, giving us a value for unreduced raw damage of:

URD = (159 - 100) * .450 = 26.55 = 27

Next, we obtain a value for unreduced crit damage of 17 for the rank 4 puncture crit to the left arm. Finally, we find a Redux Factor value of:

RF = 1 - 37/(27 + 17) = 1 - 37/44 = .159

Second Order

It has been shown that the ratio of crit to total damage (CDR) has a significant effect on the redux factor demonstrated for that hit. For the purposes of this section, it is useful to propose a baseline or average RF from which actual or observed values deviate, and the same for CDR. More specifically, the deviation of any given hit's CDR from the baseline value in hundredths will cause a deviation of 2.5 thousandths in the opposite direction from the baseline RF. The baseline RF for a character is determined by level, redux skills trained, and spells known. The baseline CDR is somewhat more difficult to define, but in the interests of universality the author has proposed a baseline value of .24 for all characters and hits. This is not to say that the average hit for the average character has such a CDR, but that it is roughly representative of the mean for all usual hits. Returning to the previous example:

Anathemus swings a broadsword at you!
  AS: +130 vs DS: +55 with AvD: +36 + d100 roll: +48 = +159
  ... and hits for 37 points of damage!
  Deep, bloody slash to your right thigh!
  You are knocked to the ground!
  You are stunned for 3 rounds!

The CDR can be easily calculated as:

CDR = 17 / 44 = .386

Note that it is immaterial whether one uses both reduced or both unreduced values: it is fundamental to this understanding of redux that both crit damage and raw damage are reduced at the same rate, causing the redux factors to cancel out!

The deviation is thus:

delCDR = .386 - .240 = .146 = 14.6 hundredths

And one would expect a deviation in the RF of:

14.6 hundredths * -2.5 thousandths/hundredth = -36.5 thousandths = -.0365

Finally suggesting a baseline RF for this character of:

True RF = .159 + .0365 = .1955 = .196

Even with this correction, however, there is non-negligible randomization in the value obtained for RF. It is not within the purview of the author to decree what level of uncertainty is acceptable for any given player, but it is noted that after 10 to 15 hits further deviations of the averaged RF are quite small with this methodology.

It is extremely useful to have a single value with which one can usefully compare various training plans and situations.

Crit Divisors

Though this effect does not impact calculation of redux factors, it is worth noting that the crit divisor of a character with redux is measurably lower than that of a character without redux for equal armor conditions. This does not cause the character with redux to be at an overall defensive disadvantage to the character without. The quantitative effect is roughly:

1 ? RF/3

which is applied to the crit divisor in question. Thus, a character with no redux would have no crit divisor depression while a character with perfect (1) redux would experience a crit divisor of 6 in chain (2/3 * 9).

Order of Mark

It is also possible to formulate an entirely distinct theory of redux. Mark (who posts under SPYRIDONM on these boards) has proposed a two-RF theory that roughly speaking goes as follows: when the damage taken is under a certain threshold, a constant RF1 is applied only to raw damage; crit damage is not reduced. Once past this threshold, all damage is reduced more or less as stated above. There are several consequences to viewing redux through this lens, but it is the opinion of the author that both theories have their merits (indeed, for sufficiently large endrolls they become indistinguishable!).

Redux from Skills

It is somewhat more difficult to obtain a value for RF from skills alone. It has been shown by Porcell that the relative values of the redux skills are as follows:

Primary (physical fitness): 1
Secondary (armor, TWC, ambush, MOC, dodge, |CM, shield): .4
Tertiary (weapon): .3

It has further been shown that the threshold for obtaining redux is roughly 109 redux points, though this number increases for levels under ~21. For instance, the threshold for a level 16 character has been observed to be above 126 redux points. Level also has an impact on how much redux a character derives from a particular amount of redux points: a higher level character will experience a higher redux factor value than a lower level character. The amount of redux factor gained per redux point tapers off fairly rapidly around 400 redux points for a level 40 character. It should be noted that the concept of whether further training is ?worth it? for the purpose of higher redux is irreducibly subjective and cannot be answered in a universal fashion. The author?s intent is only to provide numbers from which an individual can draw a more informed conclusion. The most complete testing to date is available on Krakiipedia at the following location:

https://gswiki.play.net/mediawiki/index.php/Redux

The spell penalty is even less well understood, but preliminary findings indicate the following:

Foremost, that the penalty is multiplicative rather than subtractive. At each step of penalty, a modifier of 12/13 is applied to the base RF, where a step of penalty is defined by the character?s level divided by 20 and a seed of 2 as follows:

For a character at cap, up to 100/20 = 5 spells can be learned without penalty, and up to 5 + 5 + 2 = 12 spells can be learned without leaving the first level of penalty. For a level 100 warrior with a maximum of 100 spells, the penalty would be:

(0) 100 ? 5 = 95
(1) 95 ? 7 = 88
(2) 88 ? 9 = 79
(3) 79 ? 11 = 68
(4) 68 ? 13 = 55
(5) 55 ? 15 = 40
(6) 40 ? 17 = 23
(7) 23 ? 19 = 4
(8) 4 ? 21 < 0

(12/13)^8 = 52.7% modifier of the unpenalized RF.


It should be made clear that all statements made herein are made to the best of my empirical knowledge. I have no direct access to the code of the game itself, and as such it could work in an entirely different fashion from what I have proclaimed. The reason I endorse my findings is that they are to a large degree functionally equivalent with the workings of the game if not necessarily mechanically equivalent.


As a final note, I am pleased to be a part of this community. I hope that this information proves useful in the future.

-Anathemus' player