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[Zivilin]

ABSTRACT
The aim of this study was to conclusively verify whether bolt weight (or, more specifically, the density of the material from which the bolt was produced) has significant effect on crossbow performance. Rigorous scientific methodology was employed in order to improve on current experimental setups and design such a one which would deliver the most objective results possible. The study concluded that heavier bolts have higher penetration, making them more useful against armored targets.
 
INTRODUCTION
A number of studies have been performed in order to verify whether the weight of a bolt has any influence on a Marksdwarfs destructive potential. Surprisingly, these studies seem to have achieved drastically differing results. Test on Bolts and Weights (July 2011), by IT 000, reported that heavier bolts did not produce a noticeable increase in crossbow firepower - squads equipped with heavy and light bolts did perform differently, but this was attributed to other, unspecified factors. A more recent study, Crossbow Ammunition Testing (July 2012) by Wrex, reported that heavier bolts caused more damage as compared to lighter bolts.

In this study, an appropriate experimental setup was designed in order to resolve this issue conclusively.

METHODOLOGY
The experiment was based on the setup used in Test on Bolts and Weights: a 10 by 10 matrix of 3-tile cells, each containing two dwarfs separated by a fortification tile.

Spoiler (click to show/hide)

Yes, the art of creating different-looking dwarfs eludes me

This elegant setup enables the performance of 100 separate and isolated experiments, and obtain 100 samples for analysis. However, after testing this setup a problem related to the sequence in which the dwarfs attack was identified. This is presented in the following figure, which shows 8 ticks into the experiment.

Spoiler (click to show/hide)

As it can be seen, all dwarfs do not fire simultaneously, but they fire in groups of 20 per tick. This means that some dwarfs achieve First Strike over others. First Strike can create serious imbalance in a comparative experiment of this kind, since the First Strike bolt can instantly incapacitate the opponent in a number of ways:

• Head shot (Instant Kill)
• Arm Shot (Crossbow/Ammo dropped)
• Shots causing Extreme Pain and leading to Unconsciousness (allows the opponent a few more potshots)

The operation of the attacking algorithm is an interesting discussion in itself, but it is not the subject of this article and thus will not be further discussed.

Even if the First Strike advantage was not as advantageous as suspected, another problem is the (relatively) large deviation in results obtained from such a (relatively) small number of samples. When performing experiments on a control group i.e. each cell containing a pair of identically equipped and skilled dwarfs, the results often yielded 40:60 or 60:40. This is relatively far from the predicted 50:50 scenario and means that if a 40:60 result is achieved in an experiment, then no reliable conclusion can be made due to it being within range of statistical error.

The final form of the experimental setup was decided to be as follows:

Team A Weapon: Cedar crossbows Ammo: 100 iron bolts Armor: None Skills: Proficient Archer Proficient Marksdwarf

| Team B | Weapon: Cedar crossbows | Ammo: 100 light iron bolts | Armor: None | Skills: Proficient Archer | Proficient Marksdwarf

| Team V | Weapon: None | Ammo: None | Armor: Varies | Skills: None |

Spoiler (click to show/hide)

Light iron is a modified version of iron, differing only in density: The density of iron is 7850, whilst the density of light iron was set to 200, the same as adamantium. If the wiki weight formulas are true, an iron bolt weighs around 1.17 urist, whilst a light iron bolt weighs 0.03 urist.

One experiment 10 by 10 matrix is filled with Team A vs Team V, whilst the other is filled with Team B vs Team V. Since Team V members are unarmed, they were inevitably slaughtered with no losses to the opposing team. The criterion used to evaluate the effectiveness of both teams (A and B) was the average number of bolts used to obliterate a single member of Team V. This value was obtained by checking the remaining bolts of each dwarf on teams A and B and subtracting it from the initial 100. The higher the average value of bolts needed to kill a team V dwarf, the less effective that bolt type is.

RESULTS

4 Tests were performed, each with Team V differently armored:

Test 1 Team V unarmored

| Test 2 | Team V equipped with shields | iron shield | | | | | |

| Test 3 | Team V equipped with armor | iron breastplate | iron chain mail | iron greaves | iron helm | 2x iron gauntlet | 2x iron high boot |

| Test 4 | Team V equipped with armor and shields | iron breastplate | iron chain mail | iron greaves | iron helm | 2x iron gauntlet | 2x iron high boot | iron shield

The results obtained are presented in the Table below:

Test No.	| Test 1	| Test 2	| Test 3	| Test 4
Team A avg. no. of bolts	| 12.14	| 14.07	| 18.79	| 17.71
Team B avg. no. of bolts	| 14.09	| 14.37	| 35.29	| 43.10

Also, here is some fun statistical data in the form of histograms:

Spoiler (click to show/hide)

CONCLUSIONS
There seemed to be little to no difference in effect of bolt weight on damage caused against unarmored opponents, or opponents equipped with shields. Any differences observed are most probably statistically insignificant.

There is a clear difference in the performance of heavy and light bolts when used against an armored opponents. Dwarfs equipped with light iron bolts required on average twice as many shots in order to take down an armored, unshielded opponent as there iron bolt using brethren, 2.5 times more shots to bring down an armored and shielded opponent. Interestingly, at he the end of Test 4, 5 Team V dwarfs were left standing completely unwounded on the Team B side, the opposing Team B dwarfs having used up fruitlessly all of their light iron bolts.

Thus it can be concluded that ammo weight is indeed used in some manner in ranged crossbow attacks, adding to armor penetration. This effect is practically unnoticeable on unarmored opponents, possibly due to the powerful parameters of the vanilla crossbow. If these parameters were weakened more data could be gathered. Other future works include testing the effects of sharpness, both sharpness and weight, testing default materials (instead of modified as opposed to modified ones), testing the effect of Marksdwarf, Archer, Shield skills, etc. etc.

[JTTCOTE1]

* Slow Clap *
This is amazing. First of all, it's written like a lab report, secondly, you fixed all the major problems with the previous tests.

* Fast Clap *
I will definitely be using iron/steel bolts from now on

* Standing Ovation *

[parlor_tricks]

*Ovates Standingly*


Great presentation of the experiment!

[Thatdude]

Well done, very good tests.

So to conclude, from now on we know it's alright to arm our hunters with bone/wood/whatever bolts but it's very important that our military gets the fancy copper/silver/bronze ones. Very good work, you have furthered the cause of dwarfdom!

[AutomataKittay]

Weight's just one of many factors of bolt efficiency, but this' very good to know. Props to you for collecting all those data!

[parlor_tricks]

Adding to this, you want to have multiple squads of marks dwarves by the looks of it.

First strike is extremely important from a military perspective, so perhaps over compensating on the marksdwarf side is the best way to achieve force superiority against attackers.

The thread where someone made everyone in his fort carry cross bows starts  may become the optimal self defence mechanism for forts.

[Zivilin]

Thank you, thank you, I am very gratified by your warm reception of this research paper.

However, I must caution against drawing conclusions which reach beyond the scope of this study. The sole conclusion which can be safely made is that ammo weight IS a factor in crossbow performance, and that heavier ammo is better than lighter ammo, all other things being equal. As AutomataKittay has observed, weight is hardly the only performance parameter. There seemed to be a bit of confusion as to whether the weight of a bolt contributed in any way to a ranged attacks destructive power, so I set out to confirm this hypothesis, and (hopefully) did. However, the test was made between two types of bolts which differed only in weight/density. I can make no assumptions on the superiority of one default metal over another, since they differ in more ways than weight/density.

I found it interesting that all wood types do not have their three shear parameters (yield, fracture and impact) specifically defined, only their density. I assume this means they all have the default values given in the material_template_default.txt file under [WOOD]? I know only the bare basics of modding, so I would appreciate if someone with more knowledge confirmed. If so, the damage potential of wooden bolts is defined solely by the density of the particular tree type, unless there are other factors than weight and the three shear parameters (and quality of craftdwarfship of the bolts, of course)?

[AutomataKittay]

Thank you, thank you, I am very gratified by your warm reception of this research paper.

However, I must caution against drawing conclusions which reach beyond the scope of this study. The sole conclusion which can be safely made is that ammo weight IS a factor in crossbow performance, and that heavier ammo is better than lighter ammo, all other things being equal. As AutomataKittay has observed, weight is hardly the only performance parameter. There seemed to be a bit of confusion as to whether the weight of a bolt contributed in any way to a ranged attacks destructive power, so I set out to confirm this hypothesis, and (hopefully) did. However, the test was made between two types of bolts which differed only in weight/density. I can make no assumptions on the superiority of one default metal over another, since they differ in more ways than weight/density.

I found it interesting that all wood types do not have their three shear parameters (yield, fracture and impact) specifically defined, only their density. I assume this means they all have the default values given in the material_template_default.txt file under [WOOD]? I know only the bare basics of modding, so I would appreciate if someone with more knowledge confirmed. If so, the damage potential of wooden bolts is defined solely by the density of the particular tree type, unless there are other factors than weight and the three shear parameters (and quality of craftdwarfship of the bolts, of course)?

http://dwarffortresswiki.org/index.php/DF2012:Material_definition_token I think this cover what you're missing, I see a lot of notes about default parameter if not set

My first thought was to ask about MAX_EDGE, but I suspect other factors affect it more than the edge from what I'm aware of with bluemetal vs steel weapon researches

[Zivilin]

http://dwarffortresswiki.org/index.php/DF2012:Material_definition_token I think this cover what you're missing, I see a lot of notes about default parameter if not set

My first thought was to ask about MAX_EDGE, but I suspect other factors affect it more than the edge from what I'm aware of with bluemetal vs steel weapon researches

Thanks, this will definitely help.

In the unforseen future I'll try to single out some probable factors and see if they have a significant effect on crossbow performance like weight had.

[Rallan]

However, I must caution against drawing conclusions which reach beyond the scope of this study. The sole conclusion which can be safely made is that ammo weight IS a factor in crossbow performance, and that heavier ammo is better than lighter ammo, all other things being equal. As AutomataKittay has observed, weight is hardly the only performance parameter. There seemed to be a bit of confusion as to whether the weight of a bolt contributed in any way to a ranged attacks destructive power, so I set out to confirm this hypothesis, and (hopefully) did. However, the test was made between two types of bolts which differed only in weight/density. I can make no assumptions on the superiority of one default metal over another, since they differ in more ways than weight/density.

Now I'm no dwarven physicist, but I can see ways to get a rough guesstimate on the importance of weight. You could take normal-weight iron and see how much you have to nerf its properties before it performs as poorly as light iron. Or you could take a material with crappier properties (like copper or silver) and see how dense you have to make it to get similar results to normal iron.

[Quantumtroll]

This is a seminal piece of research! I think the methodology presented here should be a model for future investigations, where possible.  This work and its method:

1. Allows for a control group, which can be used to determine the significance of the results.
2. Avoids feedback problems inherent in having experimental groups with different equipment fighting each other. 
3. Gathered fine-grained data (# bolts used) rather than less precise binary data (dead/alive), providing superior statistics.
4. Was transparent and easy to understand, so the results were clear.
5. Discusses its weaknesses and limitations.

What I've learned:

1. Run a few controls to determine variance.
2. Each experimental group should perform identical tasks, i.e. face identical enemies.
3. Consider the type and quality of data gathered. Perhaps time to kill, or number of dead enemies after a given amount of time, etc.
4. Presentation is important.

I'd love to use this setup to find out whether the silver bolts that I favor are any good.  And how bad is wood vs bone vs copper against a typical goblin ambush?

[rhesusmacabre]

Excellent first post Zivilin!

Another thing maybe worth investigating is how important bolt density is against creatures of different sizes and skintypes.

I'd love to use this setup to find out whether the silver bolts that I favor are any good.  And how bad is wood vs bone vs copper against a typical goblin ambush?

Wood and bone can quickly incapacitate goblins but usually take an age to kill, so they're best used in conjunction will melee troops. It's all good target practice in any case.

[Rallan]

So to conclude, from now on we know it's alright to arm our hunters with bone/wood/whatever bolts but it's very important that our military gets the fancy copper/silver/bronze ones. Very good work, you have furthered the cause of dwarfdom!

Bolts in general are stupidly good, so I dunno if I'd worry much about making sure squads have the best bolts unless you're planning on doing something particularly hard like storming the Clown Car. Just having your marksdorfs fire from positions that enemies can't reach should be more than enough in most situations, and when you're up against goblin marksmen I wouldn't be at all surprised if armor is a bigger factor than bolt material.

[Noodz]

This paper is ☼science☼. Well done Zivilin!

I will stick to copper bolts from now on.

[AutomataKittay]

http://dwarffortresswiki.org/index.php/DF2012:Material_definition_token I think this cover what you're missing, I see a lot of notes about default parameter if not set

My first thought was to ask about MAX_EDGE, but I suspect other factors affect it more than the edge from what I'm aware of with bluemetal vs steel weapon researches

Thanks, this will definitely help.

In the unforseen future I'll try to single out some probable factors and see if they have a significant effect on crossbow performance like weight had.

I would enjoy seeing a report of experimenting with wooden bolts' density since featherwood trees are lighter than even bluemetal by half, and they're relatively poor in performance.