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[Zivilin]

INTRODUCTION
The effectiveness of bolts made out of various materials is a common topic of discussion among the DF population [1] [2]. There are a some sources which already address the effects of forging weapons and armor out of the different materials [3], as well as mention the effectiveness of various types of bolts [4]. However, up till now no definitive comparison study was performed to obtain and organize a large amount of empirical data. The aim of this study is to rectify this gap by:

• Designing an objective (insofar as that is possible) experimental setup
• Obtaining a large amount of experimental results
• Analyzing the obtained data using suitable criteria and basic statistical analysis

METHODOLOGY
The core of the experiment was based on the setup used in this Author's previous study [5]. However, the number of single experimental cells was expanded from a 10 by 10 matrix (100 cells) to a 50 by 20 matrix (1000 cells). Increasing the amount of experimental data by an order of magnitude will improve the accuracy of the obtained results.

Each cell consists of two arena dwarfs separated by a fortification tile. One arena dwarf is the assailant (team A) whilst the other is the defender (team D). Arena dwarfs are a modified version of common dwarfs, differing from their brethren in two aspects:

• Arena dwarfs exhibit no size variations
• Arena dwarfs exhibit 100 times slower skill growth

Arena dwarf modifications code

Spoiler (click to show/hide)

Average size enforcement:

Code: [Select]

[BODY_APPEARANCE_MODIFIER:HEIGHT:100:100:100:100:100:100:100]
[APP_MOD_IMPORTANCE:500]
[BODY_APPEARANCE_MODIFIER:BROADNESS:100:100:100:100:100:100:100]
[APP_MOD_IMPORTANCE:500]
Stunted skill rate:

Code: [Select]

[SKILL_RATES:1:8:8:16]

This naturally eliminates dwarf size and skill gain as factors affecting the results of the study. The parameters of both team A and team D are shown in the table below.

	| Team A	| Team D
Weapon:	| Cedar crossbow	| None
Ammo:	| 100 [varies] bolts	| None
Armor:	| None	| Varies
Skills:	| Archer: Proficient | Marksdwarf: Proficient	| None |

Two parameters were varied during the course of the study: the material of the bolts fired by Team A and the material of the armor donned by Team D. All major materials were tested for both these items. The complete list is given below

Bolts: Candy, Steel, Iron, Bronze, Copper, Silver, Fake bone, Wood (birch).
Armor: Candy, Steel, Iron, Bronze, Copper, Leather, None

Note: Bone bolts could not be generated in the Arena using standard setting, so a fake bone inorganic material based on the bone tissue template was created as a substitute. It is uncertain how closely fake bone bolts resemble in-game ones. The code for fake bone is provided below.

Spoiler (click to show/hide)

Code: [Select]

[INORGANIC:FAKE_BONE]
[USE_MATERIAL_TEMPLATE:METAL_TEMPLATE]
[STATE_NAME_ADJ:ALL_SOLID:fake bone]
[STATE_NAME_ADJ:LIQUID:molten fake bone]
[STATE_NAME_ADJ:GAS:boiling kafe bone]
[DISPLAY_COLOR:7:0:1]
[BUILD_COLOR:7:0:1]
[MATERIAL_VALUE:1]
[SPEC_HEAT:1000]
[ITEMS_WEAPON][ITEMS_WEAPON_RANGED][ITEMS_AMMO][ITEMS_DIGGER][ITEMS_ARMOR][ITEMS_ANVIL]
[ITEMS_HARD]
[ITEMS_METAL]
[ITEMS_BARRED]
[ITEMS_SCALED]
[SOLID_DENSITY:500]
[IMPACT_YIELD:200000]
[IMPACT_FRACTURE:200000]
[IMPACT_STRAIN_AT_YIELD:100]
[COMPRESSIVE_YIELD:200000] cortical bone
[COMPRESSIVE_FRACTURE:200000]
[COMPRESSIVE_STRAIN_AT_YIELD:100]
[TENSILE_YIELD:115000]
[TENSILE_FRACTURE:130000]
[TENSILE_STRAIN_AT_YIELD:100]
[TORSION_YIELD:115000]
[TORSION_FRACTURE:130000]
[TORSION_STRAIN_AT_YIELD:100]
[SHEAR_YIELD:115000] used 'bone (limb)' from wikipedia tensile strength
[SHEAR_FRACTURE:130000]
[SHEAR_STRAIN_AT_YIELD:100]
[BENDING_YIELD:115000]
[BENDING_FRACTURE:130000]
[BENDING_STRAIN_AT_YIELD:100]
[MAX_EDGE:1000]
[STATE_COLOR:ALL_SOLID:WHITE]

Note 2: Team D dwarfs armored in metal were equipped with breastplate, chain mail shirt, greaves, helm, a pair of gauntlets and pair of high boots, all made from the metal being tested. Team D dwarfs armored in leather were equipped with armor, leggings, helm, a pair of gloves and pair of high boots, all made from cow leather. Unarmored Team D arena dwarfs were left naked (no clothes as well).

Criteria
There is no generally accepted, clear criterion for judging a weapons/armors effectiveness in the DF community. The Author took the liberty of defining his own criteria, defined below:

Average of bolts fired - this criterion is based on the average number of bolts fired in order to kill a dwarf. This is a fairly unambiguous criterion ans can be easily obtained by dividing the number of bolts fired over the course of a single experiment by the number of dwarfs participating (under the tacit assumption that all dwarfs were killed). Example: if 12123 bolts were fired in a standard-sized experiment, killing all 1000 Team D dwarfs, than the Average of bolts fired is 12.12 (rounded to the second decimal)

The average of bolts fired,  while a simple and convenient general criterion, does not fully express the effectiveness of the crossbow used in a combat situation. The modus operandi of dwarven tacticians is to utilize the crossbows cover fire in order to incapacitate the enemy, and then move in with a melee unit in order to deliver an elegant coup de grace to those left unconscious and/or writhing in pain. Thus, in many cases the Marksdwarfs will not have the chance to empty their quivers and a criterion based on such an assumption is effectively useless. To remedy this, two other criteria were formed:

Lethality-N - probability that a dwarf is killed after the Nth volley. This experiment is more ambiguous. in fact, for it to be properly executed it would be required all Team A members should be given no more than N-bolts. However, due to the massive amount of time and effort required to set up even a single 1000-sample experiment, it was decided that the results from the 100 bolt tests would be used, introducing slight inaccuracy. Head shots have a more prominent effect on this criterion (because they are instantaneous) than Spine shots and Throat/Heart shots (because they are time-delayed). Example: if after 3 volleys fired in a standard-sized experiment, 100 of the 1000 dwarfs are
killed, then the 3-Lethality of Team A's weapon against team D's Armor is 10%.

Suppression-N - probability that a dwarf is incapacitated (either killed or left unconscious) after the Nth volley. One more, this is a fairly ambiguous criterion - partly because it inherits the ambiguity of lethality-N, and partly because the term "incapacitation" can be differently defined. For example, a dwarf who loses his weapon can also be called incapacitated, since his offensive power is greatly reduced. A retching and vomiting dwarf is also said to have reduced combat capability. However, it was decided that only death and unconsciousness would be included as they are the most powerful indicators of the ability of crossbow fire to suppress an attacking force. Example: if after 3 volleys fired in a standard-sized experiment, 100 dwarfs are dead and 500 dwarfs are unconscious out of the initial 1000, then the 3-Suppression of Team A's weapon against team D's Armor is 60%.

The results were gathered by running amateurish scripts of the Author's design on the gamelog files. Certain inaccuracies might have emerged due to poor programming design. If such inaccuracies are found, they will be edited and rectified at a later date. Data pertaining to other interesting criteria (wound types) were gathered, but they will not be considered in the study proper. Interesting additional data will be added as an addendum.

RESULTS
When discussing particular experiments, the phrase "Material A vs Material B" will imply "Bolts vs Armor" e.g.: "Steel vs Bronze" refers to the "Steel Bolts vs Bronze Armor" experiment.

The figure below presents the Average of Bolts Fired for various bolts and armors:

Average of Bolts Fired (per dwarf killed)

Spoiler (click to show/hide)

Note: Lack of a bar means that all participants of the experiment survived, resulting in an very unhelpful average of 100. These bars were removed from the figure to better see the remaining results

A number of interesting facts can be drawn from these results:

• The majority of the average number of bolts fired form two levels: When used against armor made out of a material "worse" than the bolt itself, the average number is around 12-14. When used against armor made out of a material equal to or "better" than the bolt itself, the average number of bolts is around 16-19.
  
• Candy bolts have a fairly stable effectiveness against all types of armor (an average of around 14), except for candy armor itself, against which they are completely useless
• Wood and bone is better against candy armor than candy bolts
• Wood has no effect on steel, iron, bronze or copper armor
• Candy armor fairs worse against silver bolts, but only by a small margin
• Fake bone bolts are generally worse than all metal bolts, but still deal lethal damage (eventually) against all armor types, unlike wood

Next, Supression-1  is presented (lethality-1 had too few samples to obtain obtain results)

Probability that a dwarf is incapacitated after the first shot

Spoiler (click to show/hide)

Once more, observations are listed below:

• Bolts of all metals except for candy exhibit high suppressive ability (in the range of 30-35%) against all armor types. What is more, this value does not vary for leather-armored and unarmored arena dwarfs.
• The suppressive ability of candy bolts is significantly lower than other metals (in the 25% range)
• Wood and bone bolts have a suppressive ability of around 20-25% of unarmored and leather-armored targets
• Bone bolts provide significantly less suppression against steel-armored and candy-armored targets
• Wooden bolts offer little to no suppression against any metal armor (with the exception of candy, which is in the 2% range)
• Silver bolts have the highest suppressive abilities, reaching 35-38%. Note: They are also the heaviest

Finally, Lethality-3 and Suppression-3 are presented (3 is the assumed number of shots a Marksdwarf can launch before an enemy reaches him/her)

Probability that a dwarf is killed after the third shot

Spoiler (click to show/hide)

Probability that a dwarf is incapacitated after the third shot

Spoiler (click to show/hide)

Observations:

• Lethality is difficult to estimate due to large variations of in values obscuring any patterns. Suppression also includes the number of unconscious dwarfs, giving a larger sample base. In general, lethality-3 for most bolts reached 10%
• The suppressive ability of most bolts ranges around 65% by the third volley. Variation is small among metal bolts and no type of bolt is clearly superior (silver and steel seem to be a few percent ahead of the rest)
• Bone bolts exhibit an expected drop off of suppressive ability against steel and candy armor
• Wooden bolts remain useless against metal armor. However, there suppressive ability against unarmored and leather-armored opponents are almost as good as that of metal bolts.

CONCLUSIONS

• Wooden bolts should generally be used only against unarmored or leather armored targets. Metal armor renders them useless, except for candy armor, against which they are merely bad.
• Bone bolts have the potential to kill any armored unit, however they become increasingly ineffective against "better" armors. Steel armor would be the cut off. However, against iron armor and lower they rival metal bolts in suppressive ability.
• Metal bolts (except for candy) are universally good against all types of armored and unarmored opponents. Although there are small scale differences between their performance (heavier bolts like those made of silver seem to have higher suppressive ability), these are not enough to strongly recommend one type over the other.
• Candy bolts are not amazingly better against armored opponents than other metal bolts. In fact, they can be described as "average" in most respects. They are also completely ineffective against candy armor.

[Sprin]

WOW...

[Zivilin]

This addendum was compiled from additional data gained during the course of the study, but not directly related to its subject. Since I think they are pretty interesting on their own, I thought I'd share them as well, in a separate, more casual post.

Values are normalized as "percentage of total hits" unless stated otherwise.

NON-WOUND EVENTS

This covers all bolt-dwarf interactions which did not result in the latter being wounded.

Deflections
Deflections occured exclusively for Candy vs Candy, Bone vs Candy, Bone vs Steel and Wood vs Any Metal. No other deflection occurred ANYWHERE. I hypothesize that deflection requires two conditions to be satisfied:

• The armor having a higher value of [SHEAR YIELD] than the bolt. Some information on shear yield is helpfully provided by Urist da Vinci here
• The bolt being very light OR the material of the bolt being far less dense than the material of the armor

It is certain for now that only light bolts (wood, bone, candy) appear to deflect at all. An interesting question is whether a heavy metal (e.g. iron) bolt could be made to deflect of armor without modifying the bolts weight, only, say, the armors density, or some other parameter.

Glance Offs
A bolt was reported to "glance off" a body part exactly 54 times, and each time it was off of an eyelid or eyeball. I do wonder how that works, exactly.

Misses
There were exactly 84 misses during the whole experiment, and how they happened is anybodies guess. Theoretically, the dwarfs have no maneuverability, so they can't jump away from attacks. Alas, no setup is perfect.

WOUND TYPES

This covers a part of the wound type analysis. For each direct hit (not a deflection, glance off or miss) a single, most critical wound caused by this hit was chosen. Since the process was automated, there might be some inaccuracies present in the data. The script qualified wound types in the following order of superiority:

Brain tear > Heart tear > Throat tear > Up/Mid Spine Tear > Up/Mid Spine Bruise > Low Spine Tear > Low Spine Bruise > Severe > Shatter > Fracture > Jam > Tear > Chip > Bruise

Absolute priority was given to lethal injuries (from Brain Tear to Up/Mid Spine bruise), then Lower spine injuries, and then the rest. In a majority of cases Edge and Blunt injuries rarely occur together, and the cases they do are accounted for already (e.g. A head shot causes muscle tearing, skull shattering and brain tearing, but only brain tearing is registered). Some interesting results are given:

Bruises/Tears and Chips/Jams
For each bolt type (except candy bolts) their existed a clear transition between the dominance of bruising wounds and tearing wounds. This of course is due to the armor type changing from equal to or "better" than the bolt to "worse" than the bolt. The point of transition is marked by the sudden appearance of jams, which appear to be a form of chipping damage.

Tears and bruises

Spoiler (click to show/hide)

Chips and jams

Spoiler (click to show/hide)

Misc

• Around 60% of shots to the head cause brain tears (i.e. instant death)
• Around 80-90% of the cases of body parts being severed concern fingers, the rest noses. There were single incidents of severing lower legs and guts (?)

Hit zones
Finally, I compiled and calculated the percentages of a particular body part being hit. Reminder: this data is true for Proficient Archers and Marksdwarfs shooting from two tiles away through a fortification at enemies who can;t dodge:

Hit zones

Spoiler (click to show/hide)

The Vitruvian dwarf.
(Urist da Vinci I am not)

Results based on 1333889 bolts fired during the course of the experiment

Acknowledgments
I would like to thank the 56000 dwarfs which lent their crossbows to the cause of science.
I would like to double thank the 50960 dwarfs who sacrificed their lives for that very same cause.
I'd like to congratulate the surviving 5040 dwarfs and invite them to my future fortresses, since they appear to be professional survivors.

[Sprin]

WOW...

[Darnis]

This was a triumph; Bone bolts might vary from creature to creature? This would be pretty amazing as then Forgotten beast bone bolts might be superior to Puppy Bone bolts

Great read, well organized and presented information.

[GreatWyrmGold]

This was a triumph.
I'm making a note here: HUGE SUCCESS.
It's hard to overstate my satisfaction.

[Zivilin]

Did You mean that, or was it simply that You could not resist filling in the lyrics?
But look at me still talking when there's Science to do.
I've experiments to run,
There is research to be done,
On the dwarfs who are still alive.

[GreatWyrmGold]

Darnis put the song into my head.

Go ahead and leave me. I think I prefer to stay inside.

[Kofthefens]

This is phenomenal. Well done.

[Viking]

What you have done here is a thing of beauty and should be consulted for a long time.  Were you a dwarf, you'd have earned a royal bedroom with some gem encrusted candy furniture and such at least.

[Sprin]

WOW...

[Wrex]

A severed gut can occur if their innards are sliced open by a projectile, then one hits the exposed intestines.

[misko27]

WOW..

This is a very impressive test. It reiforces my belief that silver is good. I'm a little surprised that bronze performs better then iron in several cases.

[GreatWyrmGold]

In reality, iron replaced bronze due to price. Tin was rare.

[Urist Da Vinci]

.... An interesting question is whether a heavy metal (e.g. iron) bolt could be made to deflect of armor without modifying the bolts weight, only, say, the armors density, or some other parameter.
...

...
Hit zones
Finally, I compiled and calculated the percentages of a particular body part being hit. Reminder: this data is true for Proficient Archers and Marksdwarfs shooting from two tiles away through a fortification at enemies who can;t dodge:

Hit zones

Spoiler (click to show/hide)

The Vitruvian dwarf.
(Urist da Vinci I am not)

Results based on 1333889 bolts fired during the course of the experiment

...

a) I'll see if I can make unedited iron bolts deflect off edited armor.

b) I looked at [BODY_DETAIL_PLAN:HUMANOID_RELSIZES] in b_detail_plan_default.txt.
Each body part has a relative size. If you divide the body part's size by the sum of sizes for all external body parts, you get percentages that are very similar to the Vitruvian dwarf (1-5% error for most main body parts, so I get 18.12% for the upper body etc.). This doesn't hold for heads, hands, and feet, but I probably made a calculation mistake when including the fingers, toes, nose, etc.

I would conclude that the chance of a body part being hit is proportional to the size of the body part relative to the sum of all body part sizes.

This also implies that dwarves don't deliberately aim for headshots when using crossbows.
A quick test in arena mode reveals that dwarves don't get free headshots when firing a crossbow at an adjacent unconscious enemy, instead using the typical random shots.