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[Pirate Bob]

Sort of, see here:
http://www.bay12forums.com/smf/index.php?topic=117284.0
...
EDIT2: Here's a flowchart image for tldr folks:

Spoiler (click to show/hide)

(1) Maybe we could ask Zivilin to repeat his dodging study using a few different values of the dodge skill.  If not, I can try to replicate it.

(2) I think the flowchart looks very nice.  One issue - the damage that occurs when a projectile dents plate armor is very different than the protection offered by chain mail.  Chain mail appears to just convert edged damage to blunt, meaning that (serious) fractures, chips, bruises and jams can occur.  When plate armor is dented but not fractured, ONLY bruises can occur, and a quick scan of the logs suggests these bruises are never serious (not brains hearts etc) but only to outer layers (muscle, skin, fat).  I think I need to rewrite my analysis to only call hits "nonserious" if they cause "bruising the skin", "bruising the fat" and/or "bruising the muscle", but no other damage to make this clearer.  Hits through chainmail can definitely result in only bruising, but still damage internal organs (bruising guts, speen, etc), so long as there is no bone in the way.  Damage to organs covered by bone (heart, brain, lungs) seems to require that the bone be broken first.

I'm not totally sure if I understand which situations you are referring to when you say armor is "dented" or "fractured" so maybe I don't have this straight, but you definitely need to consider what I call "nonserious" wounds separately from wounds through chain mail. 

[Urist Da Vinci]

OK, updated flowchart:

Spoiler (click to show/hide)

http://www.graphviz.org/ is nice because you don't have to mess around with drawing shapes and arrows, you just have to feed instructions to the image generator.

[Pirate Bob]

I took a look at the material page of the wiki, and I agree that this seems like a good place to put our analysis.  I also agree that it makes sense to put everything (or almost everything) on one page.  However, I think it might be nice to include some parts (or at least links to them) on other pages as well.  For example, I think it makes sense to mention the formula you worked out for projectile velocity on the crossbow and bow pages, and to give results for how armor performs with 34.11 values on the armor page. 

Putting the results on the material page would be especially nice if we could verify that the behavior for melee weapons is the same or similar.  I quickly tested copper spears (with the bash attack removed) against adamantine uniarmor, but I seem to have messed this up.  I set the "velocity multiplier" for spears to 62, hoping that this would just set the velocity of the blow.  Copper spears have a mass of 3.572, so this would give momentum = 221, and also a contact area of 20.  The momentum for 50% penetration of thickness=20 zero quality adamantine armor with zero armor user is (50000000-5000000/2)*(20*20)/2400000=417.   Last night when I calculated this I somehow got that the momentum for 50% penetration would be 222 - maybe I forgot to adjust the contact area?  Anyway, no surprise that I got 100% deflections from this test.  I hope to try again with higher velocity multipliers (specifically 117 to start) to see if deflection behaves as expected. 

I also need to reanalyze my results for chain mail using the criteria that nonserious hits should only include bruising of skin, fat, and muscle.  I have a script which calculates this from logs written, so now I just need to run it on my existing logs for chain mail.  I expect that, with this criteria, protection from mail will fall smoothly to almost zero, without the plateau I previously saw at ~30%, but we'll see.

Edit:  It occured to me that the Casual Reader may be able to tell us if melee weapons follow the same rules as projectiles without any significant testing.  I have posted a spreadsheet of the predictions of applying projectile behavior to melee weapons, assuming that melee weapon momentum is determined by mass*velocity mulitplier, to DFFD.  No need to worry about the numbers - if a cell is colored red, then that means the armor should be penetrated 100% of the time, and if it's green then there should be 100% protection (either deflection or hit reduced to bruising skin, fat or muscle).  These numbers are for layer thickness=20, so that means breastplates and helms, although I'm not sure how many cases are close enough that the lower thickness of greaves, gauntlets and boots matters.

In particular, all types of swords and daggers (except those made of adamantine) are predicted to always penetrate with stabbing or pommel strike attacks, but not to penetrate with slashes so long as the armor material is equal or better than the sword (addy>steel>iron=bronze>copper).  I think I remember having stabs be deflected in adventure mode, but it's been a while since I actually played dwarf fortress, so I'm not sure  .  Can anyone confirm that this or other predictions of my table are untrue?  Logs would be ideal, but "I'm sure I remember X" would be helpful too.  Any deflection of any attacks other than sword slash/slap or axe hack would disprove my wild speculations.

Writing this also made me realize that we never did get around to testing whether our results for dwarven targets hold for other races.  However, I can't imagine that humans or elves have enough size difference to change things much. 

[Urist Da Vinci]

...
  Can anyone confirm that this or other predictions of my table are untrue?  Logs would be ideal, but "I'm sure I remember X" would be helpful too.  Any deflection of any attacks other than sword slash/slap or axe hack would disprove my wild speculations.

Writing this also made me realize that we never did get around to testing whether our results for dwarven targets hold for other races.  However, I can't imagine that humans or elves have enough size difference to change things much. 

1. Using this thing:

Code: [Select]

[ITEM_WEAPON:ITEM_WEAPON_SPEAR_VARIABLE]
[NAME:variable spear:variable spear]
[SIZE:300]
[SKILL:SPEAR]
[TWO_HANDED:37500]
[MINIMUM_SIZE:32500]
[MATERIAL_SIZE:3]
The format is ATTACK:EDGE/BLUNT:contact area:penetration size:verb2nd:verb3rd:noun:velocity multiplier
[ATTACK:EDGE:2:10000:100:100:NO_SUB:100]
[ATTACK:EDGE:2:10000:200:200:NO_SUB:200]
[ATTACK:EDGE:2:10000:300:300:NO_SUB:300]
[ATTACK:EDGE:2:10000:400:400:NO_SUB:400]
[ATTACK:EDGE:2:10000:500:500:NO_SUB:500]
[ATTACK:EDGE:2:10000:600:600:NO_SUB:600]I find that iron variable spear vs steel uniarmor, and iron variable spear vs adamantine uniarmor, both transition from deflection to tearing somewhere between 300 and 400. So your table predictions are untrue.

Considering the bucketload of variables that affect melee combat, I'd just wrap up the ranged results and do melee in its own thread another time.

2. Humans don't appear to get different results, and very large creatures like giants get bugged armor that is thicker than the penetration depth of arrows.

[Pirate Bob]

1. Using this thing:

Code: [Select]

[ITEM_WEAPON:ITEM_WEAPON_SPEAR_VARIABLE]
[NAME:variable spear:variable spear]
[SIZE:300]
[SKILL:SPEAR]
[TWO_HANDED:37500]
[MINIMUM_SIZE:32500]
[MATERIAL_SIZE:3]
The format is ATTACK:EDGE/BLUNT:contact area:penetration size:verb2nd:verb3rd:noun:velocity multiplier
[ATTACK:EDGE:2:10000:100:100:NO_SUB:100]
[ATTACK:EDGE:2:10000:200:200:NO_SUB:200]
[ATTACK:EDGE:2:10000:300:300:NO_SUB:300]
[ATTACK:EDGE:2:10000:400:400:NO_SUB:400]
[ATTACK:EDGE:2:10000:500:500:NO_SUB:500]
[ATTACK:EDGE:2:10000:600:600:NO_SUB:600]I find that iron variable spear vs steel uniarmor, and iron variable spear vs adamantine uniarmor, both transition from deflection to tearing somewhere between 300 and 400. So your table predictions are untrue.

Considering the bucketload of variables that affect melee combat, I'd just wrap up the ranged results and do melee in its own thread another time.

2. Humans don't appear to get different results, and very large creatures like giants get bugged armor that is thicker than the penetration depth of arrows.

1.  Clearly the table is wrong, as you say.  However, given that my rough predictions say that an iron spear should penetrate steel at momentum 295 and adamantium at 416, this suggests that the velocity multiplier may just act as a "momentum" like SHOOT_FORCE.  As you say, there are almost certainly other factors which impact melee combat (attacker stregth, weapon skill, etc), but I still suspect that these go into determining the momentum of the weapon, and that once the weapons hits it might follow the same behavior as projectiles.  I tried testing this with a similarly modified long sword, and originally found that the transition for slashing (contact area 60000) occurred around velocity 800000 against steel armor, which is consistent, but then I also got deflections at 1500000 against the same target later.  It seems likely that random variables or combat conditions (like directness of the hit) also figure into determining deflection in melee, either directly or through determining the weapon momentum.

In any case, I agree that due to the many variables in melee, this will be very hard to test and we/someone else should do it at a later time.  I still think there is decent support for the hypothesis that, once the momentum is determined, melee weapons will behave the same as projectiles, but proving this seems beyond the current scope.  I think we have enough information to say "this is what happens for projectiles, and we suspect something similar for melee..."

2.  Glad to hear that things do not vary much between human sized targets.

I have been running calculations of deflection off standard dwarf fortress armor over the past few days, as I would like to be able to include protection vs. momentum curves in the final write-up.  These are largely complete, but in the process I discovered that armor penetration occurs at lower momentum/more often if the target has fallen over.  I think the most appropriate thing to report is results for standing targets, as once you fall over you're pretty much dead anyway.  I'm working on that, and also will try to start adding things to the wiki if I get a chance (maybe this weekend).

We also should probably try to put a summary of our findings in bug 5516.  HiEv already posted a link to this thread there, but I think it would be nice to add a clear statement that plate armor does nothing, and one or more ways the raws can be adjusted to cause some plate armors to deflect bolts.  Maybe also a link to whatever final write-up(s) we do on the wiki or elsewhere.

Edit:  I have started adding our results to the wiki.  So far just text, but I'd like to have some plots (especially Urist's flowchart).  It also need some expanding, and some details checked/filled in.  Constructive editing would be most welcome...

[Pirate Bob]

I've finished my testing of copper bolts vs. standard dwarf fortress armor (breastplate, helm, greaves, 2 gauntlets, and two low boots, with and without 2 chain mail shirts).  The statistics aren't great, as I only ran with 72 dwarves at each force point.  I more wanted to get a general shape for all curves rather than exact numbers, and I will do larger runs at a few points of interest.  Furthermore, I found that, once dwarves have fallen over, there is a significantly larger chance that armor will be penetrated.  I therefore only included on each dwarf before it had first fallen over, but this further reduced my sample size.  I therefore expect errors of up to 10% (which is most noticeable in the values for iron armor at momentum >100, which can fluctuate between 0 and 10%.  It is not clear that these differences are significant for iron armor at high momentum.)

EDIT:  THIS IS ALL WITH CONACT_AREA=10.  Sorry I forgot to mention that initially.  Contact area=2 (standard) produces much less interesting results as all plate armor effectively has the same thickness (as contact_area * layer_size gets rounded up to 100).

Spoiler (click to show/hide)

Armor User 0, Armor Quality 0, no chain mail


Armor User 15 (grand master), Armor Quality 0, no chain mail


Armor User 0, Armor Quality 0, 2 chain mail shirts


Armor User 15 (grand master), Armor Quality 0, 2 chain mail shirts


Armor User 15 (grand master), Armor Quality 5 (masterwork), 2 chain mail shirts

Here is a spreadsheet with all the raw data on DFFD.

Now for the (for me) exciting part.  If you look at momentum between 70-75, you will see that all armors provide some level of protection, with <10% protection for bronze/copper, ~20-40% protection for iron, 80-90% protection for steel, and >90% protection for adamantine.  This seems like a decently realistic result, but I am no expert on medieval armor.  In any case, it should hopefully be easy enough for anyone to look over these curves and pick a bolt momentum which gives the level of armor protection they think is most appropriate.

In game, there is still the issue that bolt masses get rounded when determining bolt velocites, which results in silver bolts having significantly higher momenta than iron/steel ones for the same crossbow parameters.  I think I may have a (slightly messy) fix for this as well.  Create duplicates of all bolt materials, but change their density to 600 (equal to wood, but you can use whatever you like so long as they're the same).  Then remove [ITEM_AMMO] from all standard materials, and give the bolt materials [ITEM_AMMO] and no other item tags.  Then you also need to remove whatever tag makes the material show up as ore that can be mined (not sure about this - will add when I figure it out) and add reactions to create bolts out of each bolt material from each corresponding normal material (which I was told is possible, but haven't tried).  Have to go now - will update if and when I get this to work.

[Sutremaine]

Then you also need to remove whatever tag makes the material show up as ore that can be mined (not sure about this - will add when I figure it out) and add reactions to create bolts out of each bolt material from each corresponding normal material (which I was told is possible, but haven't tried).

That tag isn't on the metal itself, it's on the stone that you smelt to produce the metal. For example, tetrahedrite has [METAL_ORE:COPPER:100] and [METAL_ORE:SILVER:20].

[Pirate Bob]

Then you also need to remove whatever tag makes the material show up as ore that can be mined (not sure about this - will add when I figure it out) and add reactions to create bolts out of each bolt material from each corresponding normal material (which I was told is possible, but haven't tried).

That tag isn't on the metal itself, it's on the stone that you smelt to produce the metal. For example, tetrahedrite has [METAL_ORE:COPPER:100] and [METAL_ORE:SILVER:20].

Oh excellent!  So all I have to do to prevent the bolt materials from showing up as ores is not specifically create ores for those metals.  I now realize I should have known that, because as you point out tetrahedrite produces multiple metals, and copper, iron etc can be produced from several ores.  Thanks!

Edit: One other thing - we should try to create bug reports for the new issues we've discovered in this study (in addition to of course adding to 5516).  In particular, I think the crazy way in which bolt velocities are created deserves it's own report.  I'd be willing to bet this is just a case of Toady using integers for everything, without noticing the strangeness that happens when calculating bolt velocities.  It (probably) should be relatively easy for him to fix if he wants to, and even easier just to close the report if he doesn't.  In any case, it can't hurt to alert him to it.  I am pretty sure there was lease one more thing we found, but I can't remember what it was.

Edit #2: I remembered another potential bug - bolt quality does not seem to do anything.  The wiki claims that quality determines damage, but I've seen no evidence to support this.  If it does turn out that bolt quality is not used after exhaustive testing, I think that might be worth reporting.  I suspect that bolt quality changes MAX_EDGE, per Quietust's statement, but that MAX_EDGE simply does not matter in any of the calculations involving bolts.  It certainly doesn't matter for vanilla bolts  .

[Pirate Bob]

I tried to use Zilivin's Vitruvian Dwarf to calculate probabilities of armor deflecting at different momenta based on the armor covering body parts hit and make sure it agrees with my data.  I think that the thick parts (>=20) of standard armor should be the breastplate, covering the upper body, and the helm covering the head, making up 23% coverage, with armor less than 20 thickness covering another 67% of the body.  I did not worry about chain mail for now, just plate mail.  My data for protection vs. momentum shows a first plateau at ~90% for very low force which corresponds nicely to the total coverage.  However, after the initial force drop, the second plateau is at about 55% protection, which is no where near the amount covered by thicker armor.

Careful inspection of the log (posted on DFFD) for copper bolts vs. adamantine armor at momentum 171 (force 128), armor user 15, quality 0, shows that
1) The breastplate appears to cover both the upper and lower body.
2) Any hits to the gauntlets or low boots are deflected (while the dwarves are still standing).
3) Hits to the greaves (only) or the (unarmored) upper arms are not protected.
4) Once the dwarves fall over, all hits penetrate.
I did not run a computerized analysis of the file - I just looked at it by eye, so it's quite possible I missed something.  However, the above all occurred many times each.

Assuming that armor covering the head, upper and lower body, hands, lower arms, and feet is "thick" (total 57.5% coverage) does explain the result.  However, I am completely at a loss as to why the gauntlets and low boots are acting like thicker armor, as they have LAYER_SIZE:15, the same as greaves (which are penetrated).  I am using vanilla raws for all armor, and bolt contact area 10.  I also don't know why the breastplate covers the lower body, but I probably just don't understand all the armor tags for that.

[Urist Da Vinci]

...
Assuming that armor covering the head, upper and lower body, hands, lower arms, and feet is "thick" (total 57.5% coverage) does explain the result.  However, I am completely at a loss as to why the gauntlets and low boots are acting like thicker armor, as they have LAYER_SIZE:15, the same as greaves (which are penetrated).  I am using vanilla raws for all armor, and bolt contact area 10.  I also don't know why the breastplate covers the lower body, but I probably just don't understand all the armor tags for that.

The hands and feet have a smaller size and smaller natural contact area than the legs or torso?

Average dwarf hand has a contact area of 19, so perhaps you get different results if you hit more than 50% or 25% of the hand at once? 10/19=0.526. With contact area 2 bolts, this "wierdness" would only apply to the rare finger/toe hits. I do vaguely recall seeing bolts glance off fingers and eyes in our earlier tests. I haven't kept any of the combat logs.

[Pirate Bob]

I have created a little mod based on our research here.  It decreases the density of bolts to be 600 (equal to wood).  It also decreases [SHOOT_MAXVEL] to 833, for a momentum of 75.  This should deflect most of the time off of steel and addy, about 30% of the time off iron, and hardly at all off other metals.  It should also do about the same amount of damage to unarmored/less than iron armored targets as vanilla bolts.

I did this by creating custom metals with the density=600, and removing [ITEM_AMMO] from all normal metals and adding it to the custom metals (except steel and adamantine, as when I did this humans were showing up with steel ammo).  I then also added custom reactions to make light metal bolts from normal metal bars for dwarves.  I had to add these reactions to the craftsdwarf's workshop, as I don't know how to add them in the forge (or if that is even possible) - the wiki doesn't list the forge as a valid building for custom reactions.  Also, there are reactions which seem to be automatically generated at the forge for the light metals which have the [ITEM_AMMO] tag, but these don't work as you can't get bars of the light metal.  If anyone knows how to fix these things I can update it.  I also at one point saw light silver metal armor showing up in adventure mode, but I am pretty sure I fixed that.  If you see anything that is "metal tipped" other than bolts lying around, please let me know.

I'd very much appreciate any feedback anyone has about this in either adventure mode or dwarf mode.  I've tested it out a bit myself, but mostly just running around to make sure all the bolts/arrows are showing up where they should be, and not so much actual combat (although I did kill one kobald with light bolts).  I'll try to also run a large scale arena test of these bolts in the next few days.

[Pirate Bob]

I did a bunch of testing of the modded bolts over the weekend, and compiled the results into a spreadsheet which I added to the zip file containing the mod itself.  Bottom line - it works really well, actually better than I had expected.  It seems that bolts will never penetrate helms if (1) the target is still standing (2) the armor material is equal or better than the bolt, and not bronze.  Bronze helms only block bolts 50% of the time.  If the target falls over, then the helm can be penetrated.  This means no instead death from random kobold archers in adventure mode if you are wearing a good helm and standing.

I tried playing adventure mode quite a bit with this mod, and it was a lot of fun.  I created a demigod char, and with a full set of iron armor he was able to do extremely well if I used good tactics (such as killing archers first, avoiding their line-of-sight, taking on enemies one at a time).  I was even able to take down a overlord bandit camp (with 6 archers, about 8 melee bandits) without sneaking or using other exploits.  However, I also saved my game before attacking this camp, and when I tried just rushing in and attacking the melee guys first, one of them knocked me over and then the archers instantly turned me into a pincushion.  Note that, while I was standing, I only actually got hit by arrows a few times - most of the time I dodged/blocked them, but the 2-3 hits on me were deflected (probably somewhat lucky there, as deflection off iron should be <50%).

Anyway, I think this set of values is pretty nice, but I'd really appreciate other opinions.  If anything I think the arrows might be a little too weak against armor right now, but I'm not sure.  I may play around with slightly increasing bolt velocity and run some more tests.  Also, this might make fort mode too easy - dwarves in steel will be almost invulnerable to archers, while their steel arrows will go right through any lesser armor.  Then again, if you are able to make enough steel to fully arm and armor your military, then maybe you should be able to easily maul a few gobbos with inferior weapons and armor.  If you feel differently, you can easily turn up bolt velocity to whatever level of deadliness you think is appropriate (and please tell me how it works  ).

[Pirate Bob]

I added a bug report for the bolt velocity calculation (#6262).  I think I included all the important details, but please add comments/corrections if I left something out.

I also found that (now everyone try to act surprised  ) that there is at least one more layer of detail to bolt deflection that we don't understand.  In particular:
1) Deflection of bolts off human targets occurs slightly more often than off arena dwarves.  With iron armor, bolt mass 0.09, velocity 833, I found 42% deflection off humans and only 34% deflection off arena dwarves.  This could possibly be due to the lack of pain etc for arena dwarves, so I need to repeat the test with regular dwarves as well.  However, I think it is due to size because
2) The size of body parts clearly plays some role in deflection.  As described above, deflections occur more often than expected off hands/feet, and I have now also found that helms made of copper will deflect 100% of the time using the same mass=0.09 velocity=833 (copper) bolts.  I will try to tabulate results vs. various body parts and post here.  Does anyone know how to calculate the size of body parts?  I thought Urist posted it somewhere, but I'm not finding it.

That being said, I am unsure if I want to continue to pursue projectile research now, as I have spend an inordinate amount of time on this already.

Edit:
I forgot to mention that I've confirmed that in adventure mode all races seem to use the modified ammo materials I created without any issue.  At least, humans, goblins, and dwarves do.  Elves still use normal wooden bolts, which depending on the type of wood may be more or less dense than the modded bolts.  Wood will be deflected by all metal armors except adamantine due to its low IMPACT_YIELD causing the projectile to absorb the force of the blow, so this probably isn't a major issue.  Also, I did nothing about bone bolts, but they have density 500 and therefore should be somewhat less effective than the modded bolts. 

I'll repeat once again that if anyone else would like to work on this project, now or in the future, I will be more than happy to provide you with all my scripts, etc, and help you with getting them to run for you.  I hope to get most of them packaged up in some reasonable way in the next few weeks, but I'm having a hard time figuring out what I should include.  However, if someone tells me "I want to test X", I can probably provide them with a good start towards doing that.

Update #2:  I ran a test of my modded bolts vs. normal dwarves, and bolts only had a ~30% chance of deflecting off iron armor.  So there definitely is some kind of size issue.  The thing is, humans are larger than dwarves, and the data we had so far suggested that deflection is more likely off smaller body parts, so I have no idea what this is about.  Maybe humans have a larger percentage of their body in the torso and head (areas covered by thicker armor), and this skews the results?  I have no idea.

[MaximumZero]

I am utterly nonplussed, PirateBob. The work you do is amazing, and should seriously go in a scientific journal. Maybe you should submit it to MoMA as part of the DF exhibit?

[Urist Da Vinci]

I am utterly nonplussed, PirateBob. The work you do is amazing, and should seriously go in a scientific journal. Maybe you should submit it to MoMA as part of the DF exhibit?

That would only serve to confuse the general public (they would think Toady doesn't understand how his own program works) and draw undue attention to DF's violence. We would prefer that the spotlight stay on Toady, and not on the DF community. It would also never practically happen.