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PostPosted: Mon Feb 02, 2015 9:32 pm 
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Joined: Tue May 08, 2012 11:08 am
Posts: 49
How Strength Affects Damage


Introduction
For years people have offered various conflicting opinions on the answer to a simple question: does Strength affect melee damage? This study, while still in its beginning stages, can at least offer an answer to this. YES, Strength does increase melee damage.

Current work has been limited to merely providing a yes/no answer. Future work will attempt to quantify the relationship between Damage and Strength. In addition, the effects of Honing (and possibly Hardening) of weapons, various Class and/or Racial damage bonuses, and any other potential modifiers, such as Level, prac%, etc will (hopefully) eventually be investigated.


Method
Procedure
A previous study, which I may repost at a later date, was able to show the relationship between hit damage and experience as a function of a mob's Level, such that Exp = Floor(3 x Damage x Mob_Lvl / 5). Using this, it can be shown that for each Hit Point of damage inflicted on a Level 10 mob (in this case 'a stout young sapling'), 6 Experience Points are given.
Sapling mobs happen to also have the useful property of not fighting back, meaning that it is possible to disengage from battle. This allows a simple script to be made which disengages and mends the weapon after every hit, to ensure that no potential damage loss is incurred through weapon degradation. Concurrent with this, the Score is checked, a short calculation converts the Exp gain to Damage, and the results are written to a text file.

Test characters
Saplings are a Tree-type mob, against which Hunters have a damage bonus of approximately 50%, though the exact amount and method has not yet been studied. For this reason, two Warriors were used, the first of 19 18 18 stats, the second of 15 18 18 stats. Both characters were of Level 33 (characters over lvl 30 get no Kill Hit Damage, simplifying testing), on foot, wimpy mood, 99% Axes practiced. To remove any potential OB effects, the 19 Str character received additional inventory weight so that both chars had the same OB.
To simplify analysis, I chose the lowest-damage weapon I could find, in this case 'a sharp pickaxe' which seems to have a base damage roll of 1d2. The statistics of dice rolling makes statistical analysis of high-damage weapons much more difficult, so this choice allows qualitative (and later, potentially, quantitative) results to be had.

Controls
In addition to things mentioned above, all other potential effects were controlled for. The same room was used to conduct the test, a lantern was held in both light and dark hours, the characters were regularly given food and water to prevent hunger/thirst.


Results
For each character, 500 hits vs the target mob were recorded. The results are immediately obvious and compelling. For both 15 and 19 Str, the majority of hits dealt 1-2 damage, split approximately equally between the two numbers. For 15 Str, an additional small amount of hits dealt 3-4 damage, while for 19 Str, not only were hits of 3-12 damage observed, they also constituted a larger proportion of overall hits.

15 Str Damage

19 Str Damage


Conclusion
While further work needs to be done to quantify the effect, there seems little doubt that Strength directly impacts melee damage dealt. Further testing will be undertaken at other Str levels, different classes, etc. In addition, higher-damage weapons will later be tested, to check if the Str effect may be masked by higher dice rolls or not.


Comments, questions, and suggestions are welcomed.


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PostPosted: Fri Jun 17, 2016 1:06 pm 
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Joined: Wed Feb 24, 2016 10:39 am
Posts: 21
Thank you Thuvia, your post is excellent!
And your post caused me to test strength bonus damage and to decide what formula str bonus have.

I used shiny copper dagger to test damage bonus. This dagger has 2d4 damage right after mend.
Why just after mend? It is cause every weapon after 1-2 hits starts scratching and this gives weapon -1 dmg.
Here is the proof, sharp pointed dart hits with mend after different hits:
Code:
---------------------------------------------------------------------------------
   WEAPON            |   MOB                    |STR |DIFF |  N  | PROBABILITY
---------------------------------------------------------------------------------
sharp pointed dart   |a stout young sapling     |14  |2    |26   |25.49 %
sharp pointed dart   |a stout young sapling     |14  |3    |51   |50.00 %
sharp pointed dart   |a stout young sapling     |14  |4    |25   |24.51 %
---------------------------------------------------------------------------------
Xavg = 2.9902, Variance = 0.7070, N = 102
---------------------------------------------------------------------------------
sharp pointed dart(4 mend)|a stout young sapling     |14  |1    |95   |19.00 %
sharp pointed dart(4 mend)|a stout young sapling     |14  |2    |210  |42.00 %
sharp pointed dart(4 mend)|a stout young sapling     |14  |3    |160  |32.00 %
sharp pointed dart(4 mend)|a stout young sapling     |14  |4    |35   |7.00 %
---------------------------------------------------------------------------------
Xavg = 2.2700, Variance = 0.8468, N = 500
---------------------------------------------------------------------------------
sharp pointed dart(40 mend)|a stout young sapling     |14  |1    |111  |22.20 %
sharp pointed dart(40 mend)|a stout young sapling     |14  |2    |253  |50.60 %
sharp pointed dart(40 mend)|a stout young sapling     |14  |3    |130  |26.00 %
sharp pointed dart(40 mend)|a stout young sapling     |14  |4    |6    |1.20 %
---------------------------------------------------------------------------------
Xavg = 2.0620, Variance = 0.7254, N = 500
---------------------------------------------------------------------------------
sharp pointed dart(100 mend)|a stout young sapling     |14  |1    |141  |28.20 %
sharp pointed dart(100 mend)|a stout young sapling     |14  |2    |240  |48.00 %
sharp pointed dart(100 mend)|a stout young sapling     |14  |3    |118  |23.60 %
sharp pointed dart(100 mend)|a stout young sapling     |14  |4    |1    |0.20 %
---------------------------------------------------------------------------------
Xavg = 1.9580, Variance = 0.7240, N = 500
---------------------------------------------------------------------------------


So:
a) nonscratched dart has 2d2 damage
b) with mend after 4 hits average damage had droped by 0.7 damage so its nearly 1-2 hits unscratched and 2-3 hits scratched
c) with mend after 40 hits formula close to 2d2-1
d) with mend after 100 hits damage malus of scratching goes more than 1

Also i used http://anydice.com to get what probabily standard XdY dices has Avg and Variance and Distribution

So i chose to mend shiny dagger after 50 hits to fasten my tests (so base dagger damage is like 2d4-1)
Let see what damage shiny copper dagger have:
Code:
---------------------------------------------------------------------------------
   WEAPON            |   MOB                    |STR |DIFF |  N  | PROBABILITY
---------------------------------------------------------------------------------
shiny copper dagger  |a stout young sapling     |14  |1    |57   |5.70 %
shiny copper dagger  |a stout young sapling     |14  |2    |126  |12.60 %
shiny copper dagger  |a stout young sapling     |14  |3    |186  |18.60 %
shiny copper dagger  |a stout young sapling     |14  |4    |236  |23.60 %
shiny copper dagger  |a stout young sapling     |14  |5    |190  |19.00 %
shiny copper dagger  |a stout young sapling     |14  |6    |141  |14.10 %
shiny copper dagger  |a stout young sapling     |14  |7    |63   |6.30 %
shiny copper dagger  |a stout young sapling     |14  |8    |1    |0.10 %
---------------------------------------------------------------------------------
Xavg = 4.0560, Variance = 1.5928, N = 1000
---------------------------------------------------------------------------------
shiny copper dagger  |a stout young sapling     |9   |1    |24   |4.80 %
shiny copper dagger  |a stout young sapling     |9   |2    |60   |12.00 %
shiny copper dagger  |a stout young sapling     |9   |3    |89   |17.80 %
shiny copper dagger  |a stout young sapling     |9   |4    |113  |22.60 %
shiny copper dagger  |a stout young sapling     |9   |5    |108  |21.60 %
shiny copper dagger  |a stout young sapling     |9   |6    |72   |14.40 %
shiny copper dagger  |a stout young sapling     |9   |7    |32   |6.40 %
shiny copper dagger  |a stout young sapling     |9   |8    |2    |0.40 %
---------------------------------------------------------------------------------
Xavg = 4.1500, Variance = 1.5810, N = 500
---------------------------------------------------------------------------------

And only 2d4-1 formula is very close to my results (again you can check theoretical dices at http://anydice.com)
And with 9 str tests you can see that str below 14 str has no dmg malus.

OK, now are test results with different strength (mend after 50 hits)
Code:
---------------------------------------------------------------------------------
   WEAPON            |   MOB                    |STR |DIFF |  N  | PROBABILITY
---------------------------------------------------------------------------------
shiny copper dagger  |a stout young sapling     |15  |1    |52   |5.20 %
shiny copper dagger  |a stout young sapling     |15  |2    |137  |13.70 %
shiny copper dagger  |a stout young sapling     |15  |3    |166  |16.60 %
shiny copper dagger  |a stout young sapling     |15  |4    |229  |22.90 %
shiny copper dagger  |a stout young sapling     |15  |5    |197  |19.70 %
shiny copper dagger  |a stout young sapling     |15  |6    |134  |13.40 %
shiny copper dagger  |a stout young sapling     |15  |7    |73   |7.30 %
shiny copper dagger  |a stout young sapling     |15  |8    |8    |0.80 %
shiny copper dagger  |a stout young sapling     |15  |9    |4    |0.40 %
---------------------------------------------------------------------------------
Xavg = 4.1400, Variance = 1.6675, N = 1000
---------------------------------------------------------------------------------
shiny copper dagger  |a stout young sapling     |16  |1    |37   |3.70 %
shiny copper dagger  |a stout young sapling     |16  |2    |109  |10.90 %
shiny copper dagger  |a stout young sapling     |16  |3    |169  |16.90 %
shiny copper dagger  |a stout young sapling     |16  |4    |231  |23.10 %
shiny copper dagger  |a stout young sapling     |16  |5    |180  |18.00 %
shiny copper dagger  |a stout young sapling     |16  |6    |130  |13.00 %
shiny copper dagger  |a stout young sapling     |16  |7    |82   |8.20 %
shiny copper dagger  |a stout young sapling     |16  |8    |34   |3.40 %
shiny copper dagger  |a stout young sapling     |16  |9    |17   |1.70 %
shiny copper dagger  |a stout young sapling     |16  |10   |6    |0.60 %
shiny copper dagger  |a stout young sapling     |16  |11   |5    |0.50 %
---------------------------------------------------------------------------------
Xavg = 4.4800, Variance = 1.8909, N = 1000
---------------------------------------------------------------------------------
shiny copper dagger  |a stout young sapling     |17  |1    |44   |4.40 %
shiny copper dagger  |a stout young sapling     |17  |2    |91   |9.10 %
shiny copper dagger  |a stout young sapling     |17  |3    |138  |13.80 %
shiny copper dagger  |a stout young sapling     |17  |4    |200  |20.00 %
shiny copper dagger  |a stout young sapling     |17  |5    |175  |17.50 %
shiny copper dagger  |a stout young sapling     |17  |6    |131  |13.10 %
shiny copper dagger  |a stout young sapling     |17  |7    |98   |9.80 %
shiny copper dagger  |a stout young sapling     |17  |8    |43   |4.30 %
shiny copper dagger  |a stout young sapling     |17  |9    |30   |3.00 %
shiny copper dagger  |a stout young sapling     |17  |10   |26   |2.60 %
shiny copper dagger  |a stout young sapling     |17  |11   |14   |1.40 %
shiny copper dagger  |a stout young sapling     |17  |12   |6    |0.60 %
shiny copper dagger  |a stout young sapling     |17  |13   |4    |0.40 %
---------------------------------------------------------------------------------
Xavg = 4.9390, Variance = 2.3163, N = 1000
---------------------------------------------------------------------------------
shiny copper dagger  |a stout young sapling     |18  |1    |37   |3.70 %
shiny copper dagger  |a stout young sapling     |18  |2    |65   |6.50 %
shiny copper dagger  |a stout young sapling     |18  |3    |130  |13.00 %
shiny copper dagger  |a stout young sapling     |18  |4    |187  |18.70 %
shiny copper dagger  |a stout young sapling     |18  |5    |168  |16.80 %
shiny copper dagger  |a stout young sapling     |18  |6    |122  |12.20 %
shiny copper dagger  |a stout young sapling     |18  |7    |91   |9.10 %
shiny copper dagger  |a stout young sapling     |18  |8    |55   |5.50 %
shiny copper dagger  |a stout young sapling     |18  |9    |51   |5.10 %
shiny copper dagger  |a stout young sapling     |18  |10   |35   |3.50 %
shiny copper dagger  |a stout young sapling     |18  |11   |23   |2.30 %
shiny copper dagger  |a stout young sapling     |18  |12   |16   |1.60 %
shiny copper dagger  |a stout young sapling     |18  |13   |13   |1.30 %
shiny copper dagger  |a stout young sapling     |18  |14   |5    |0.50 %
shiny copper dagger  |a stout young sapling     |18  |15   |2    |0.20 %
---------------------------------------------------------------------------------
Xavg = 5.4770, Variance = 2.7162, N = 1000
---------------------------------------------------------------------------------
shiny copper dagger  |a stout young sapling     |19  |1    |28   |2.80 %
shiny copper dagger  |a stout young sapling     |19  |2    |72   |7.20 %
shiny copper dagger  |a stout young sapling     |19  |3    |108  |10.80 %
shiny copper dagger  |a stout young sapling     |19  |4    |145  |14.50 %
shiny copper dagger  |a stout young sapling     |19  |5    |146  |14.60 %
shiny copper dagger  |a stout young sapling     |19  |6    |139  |13.90 %
shiny copper dagger  |a stout young sapling     |19  |7    |83   |8.30 %
shiny copper dagger  |a stout young sapling     |19  |8    |71   |7.10 %
shiny copper dagger  |a stout young sapling     |19  |9    |49   |4.90 %
shiny copper dagger  |a stout young sapling     |19  |10   |41   |4.10 %
shiny copper dagger  |a stout young sapling     |19  |11   |29   |2.90 %
shiny copper dagger  |a stout young sapling     |19  |12   |29   |2.90 %
shiny copper dagger  |a stout young sapling     |19  |13   |16   |1.60 %
shiny copper dagger  |a stout young sapling     |19  |14   |21   |2.10 %
shiny copper dagger  |a stout young sapling     |19  |15   |14   |1.40 %
shiny copper dagger  |a stout young sapling     |19  |16   |6    |0.60 %
shiny copper dagger  |a stout young sapling     |19  |17   |3    |0.30 %
---------------------------------------------------------------------------------
Xavg = 6.1660, Variance = 3.3137, N = 1000
---------------------------------------------------------------------------------
shiny copper dagger  |a stout young sapling     |20  |1    |20   |2.00 %
shiny copper dagger  |a stout young sapling     |20  |2    |49   |4.90 %
shiny copper dagger  |a stout young sapling     |20  |3    |91   |9.10 %
shiny copper dagger  |a stout young sapling     |20  |4    |96   |9.60 %
shiny copper dagger  |a stout young sapling     |20  |5    |126  |12.60 %
shiny copper dagger  |a stout young sapling     |20  |6    |128  |12.80 %
shiny copper dagger  |a stout young sapling     |20  |7    |97   |9.70 %
shiny copper dagger  |a stout young sapling     |20  |8    |57   |5.70 %
shiny copper dagger  |a stout young sapling     |20  |9    |67   |6.70 %
shiny copper dagger  |a stout young sapling     |20  |10   |73   |7.30 %
shiny copper dagger  |a stout young sapling     |20  |11   |41   |4.10 %
shiny copper dagger  |a stout young sapling     |20  |12   |30   |3.00 %
shiny copper dagger  |a stout young sapling     |20  |13   |30   |3.00 %
shiny copper dagger  |a stout young sapling     |20  |14   |26   |2.60 %
shiny copper dagger  |a stout young sapling     |20  |15   |17   |1.70 %
shiny copper dagger  |a stout young sapling     |20  |16   |28   |2.80 %
shiny copper dagger  |a stout young sapling     |20  |17   |13   |1.30 %
shiny copper dagger  |a stout young sapling     |20  |18   |7    |0.70 %
shiny copper dagger  |a stout young sapling     |20  |19   |4    |0.40 %
---------------------------------------------------------------------------------
Xavg = 7.3320, Variance = 3.9507, N = 1000
---------------------------------------------------------------------------------
shiny copper dagger  |a stout young sapling     |21  |1    |38   |1.90 %
shiny copper dagger  |a stout young sapling     |21  |2    |114  |5.70 %
shiny copper dagger  |a stout young sapling     |21  |3    |136  |6.80 %
shiny copper dagger  |a stout young sapling     |21  |4    |218  |10.90 %
shiny copper dagger  |a stout young sapling     |21  |5    |159  |7.95 %
shiny copper dagger  |a stout young sapling     |21  |6    |199  |9.95 %
shiny copper dagger  |a stout young sapling     |21  |7    |165  |8.25 %
shiny copper dagger  |a stout young sapling     |21  |8    |140  |7.00 %
shiny copper dagger  |a stout young sapling     |21  |9    |149  |7.45 %
shiny copper dagger  |a stout young sapling     |21  |10   |130  |6.50 %
shiny copper dagger  |a stout young sapling     |21  |11   |105  |5.25 %
shiny copper dagger  |a stout young sapling     |21  |12   |84   |4.20 %
shiny copper dagger  |a stout young sapling     |21  |13   |73   |3.65 %
shiny copper dagger  |a stout young sapling     |21  |14   |59   |2.95 %
shiny copper dagger  |a stout young sapling     |21  |15   |49   |2.45 %
shiny copper dagger  |a stout young sapling     |21  |16   |48   |2.40 %
shiny copper dagger  |a stout young sapling     |21  |17   |42   |2.10 %
shiny copper dagger  |a stout young sapling     |21  |18   |49   |2.45 %
shiny copper dagger  |a stout young sapling     |21  |19   |23   |1.15 %
shiny copper dagger  |a stout young sapling     |21  |20   |12   |0.60 %
shiny copper dagger  |a stout young sapling     |21  |21   |8    |0.40 %
---------------------------------------------------------------------------------
Xavg = 8.1665, Variance = 4.5681, N = 2000
---------------------------------------------------------------------------------

After i got results i had to play with http://anydice.com and thought some.
Clearly for me that str damage bonus result is based on 2dX formula dice with some -Y damage
Playing with http://anydice.com i got best describing result with next formula:

http://anydice.com formula
---------------------------
function: above NUMBER:n{
if NUMBER < 0 { result: 0 }
result: NUMBER
}

15 str: output 2d4-1 + [above 2d5-8]
16 str: output 2d4-1 + [above 2d6-8]
17 str: output 2d4-1 + [above 2d7-8]
18 str: output 2d4-1 + [above 2d8-8]
19 str: output 2d4-1 + [above 2d9-8]
20 str: output 2d4-1 + [above 2d10-8]
21 str: output 2d4-1 + [above 2d11-8]
---------------------------

And if we integrate results the formula will be next:
2d(Str-10) - 8 with zeroing negative results of dice

And next: the cherry on the cake!
Let see what master bonus is?
Code:
---------------------------------------------------------------------------------
   WEAPON            |   MOB                    |STR |DIFF |  N  | PROBABILITY
---------------------------------------------------------------------------------
shiny copper dagger(master)|a stout young sapling     |16  |3    |3    |0.30 %
shiny copper dagger(master)|a stout young sapling     |16  |4    |8    |0.80 %
shiny copper dagger(master)|a stout young sapling     |16  |5    |18   |1.80 %
shiny copper dagger(master)|a stout young sapling     |16  |6    |42   |4.20 %
shiny copper dagger(master)|a stout young sapling     |16  |7    |59   |5.90 %
shiny copper dagger(master)|a stout young sapling     |16  |8    |98   |9.80 %
shiny copper dagger(master)|a stout young sapling     |16  |9    |113  |11.30 %
shiny copper dagger(master)|a stout young sapling     |16  |10   |157  |15.70 %
shiny copper dagger(master)|a stout young sapling     |16  |11   |153  |15.30 %
shiny copper dagger(master)|a stout young sapling     |16  |12   |130  |13.00 %
shiny copper dagger(master)|a stout young sapling     |16  |13   |95   |9.50 %
shiny copper dagger(master)|a stout young sapling     |16  |14   |42   |4.20 %
shiny copper dagger(master)|a stout young sapling     |16  |15   |47   |4.70 %
shiny copper dagger(master)|a stout young sapling     |16  |16   |22   |2.20 %
shiny copper dagger(master)|a stout young sapling     |16  |17   |9    |0.90 %
shiny copper dagger(master)|a stout young sapling     |16  |18   |3    |0.30 %
shiny copper dagger(master)|a stout young sapling     |16  |19   |1    |0.10 %
---------------------------------------------------------------------------------
Xavg = 10.5160, Variance = 2.6847, N = 1000
---------------------------------------------------------------------------------

So from this test you can calculate that master have average +6 dmg and it ups Variance
I could not tell what formula is it cause it as strenth has not normal distibution like XdY formula
From my point of view master damage has close 2dX distibution with some cutting to high damage, and described with next values: Xmin = 2, Xmax=8, Xavg=6
I think formula close to 2d5 with 9 and 10 damage cutted to 8 dmg, but it just my decides.
[13.02.2017] Correction were made after projectiles tests: master damage is 2d5

http://anydice.com formula
---------------------------
function: above NUMBER:n{
if NUMBER < 0 { result: 0 }
result: NUMBER
}
output 2d4-1 + [above 2d6-8] + 2d5
---------------------------

And after zillion hits and test damage with different weapons i can conclude next:
weapon melee damage _does_ not depend on: char lvl/race/prof, skill %
weapon melee damage is always as it is

By the way weapon damage reveal thread will be soon ... When i'll win the fight vs my laziness to write post again :)


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