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[Panando]

There is the age old debate of what is the best material for war hammers? Unfortunately, most tests have far too few samples to be able to have any confidence that the ranking is anything more than luck. Though there has been some good and recent mechanical analysis which indicates density should matter only a tiny bit.

So I decided to design a new test:

Test Design:

• An Arena with 100 cells, in each cell is a 1v1 between a Dwarf and a Goblin
• The Dwarf is armed with a War Hammer made of one of the following materials: Copper, Silver, Steel, Platinum or Lead. I tried to select materials with a broad range of properties. In total there are 20 dwarves with each kind of war hammer.
• The Goblin has full iron coverage: breast plate, mail shirt, helmet, 2x gauntlets, 2x high boots, greaves, plus a leather cloak. The Goblin has no shield or weapon, and has been given a failed mood to make it a "target dummy". This is to reduce noise and make the tests much quicker to run, if two combatants disable each other it can make it takes dozens of times longer to conclude the test.
• The Dwarf and Goblins are all completely standardized using DFHack, with all size differences, personality, preferences, traits etc eliminated. This is important, because with only 20 dwarves per weapon, if some of them were larger on average this would definitely skew the results and we would just end up measuring which group had the largest dwarves relative to the goblins: seriously, we would.
• The Dwarf is given 75% of maximum physical stats, making it "very strong and very agile", it is also a proficient hammer user.
• The game is saved, and the test is re-run 25 times. All combat reports are logged by DFHack, and the logs are analyzed by a python script.
• In order to compare the weapons, we count the number of hammer bashes required to strike down the goblin. This is not intended to be representative of the number of hammer bashes to strike down a goblin in a real game, but is a useful metric to compare the performance of different materials.
• I can only see one limitation of measuring number of hammer bashes: it is possible that a heavier hammer might cause the dwarf swinging it to tire out and become exhausted faster, by measuring actions rather than time (which is difficult to measure with logs) time spent exhausted is "invisible". The main test didn't take long enough for any dwarf to become exhausted so the data isn't useful for measuring exhaustion rate but I do look at this briefly in one of the short tests.

Results

500 samples. Number of hammer bashes required to strike down the ironclad Goblin:
(The lower bound and upper bound are for the 95% confidence interval for the mean)

Code: [Select]

| weapon              | mean  | stdev | confidence_level | margin_of_error | lower_bound | upper_bound |
|---------------------|-------|-------|------------------|-----------------|-------------|-------------|
| platinum war hammer | 16.80 | 9.81  | 0.95             | 0.86            | 15.94       | 17.66       |
| steel war hammer    | 17.19 | 9.53  | 0.95             | 0.84            | 16.35       | 18.02       |
| copper war hammer   | 18.14 | 10.18 | 0.95             | 0.89            | 17.25       | 19.03       |
| lead war hammer     | 18.37 | 9.90  | 0.95             | 0.87            | 17.50       | 19.24       |
| silver war hammer   | 18.39 | 9.53  | 0.95             | 0.84            | 17.55       | 19.22       |
The performance of all the different materials was extremely close, with the worst performer, the Silver War Hammer, requiring on average only 9% more bashes to destroy the Goblin than the best performer, the Platinum War Hammer.

Looking at the 95% confidence intervals we really can't conclude whether Copper or Silver performs better because of the near total overlap of the confidence intervals, nor whether Steel or Platinum performs better, however there is a reasonable possibility that Steel and Platinum outperform Silver.

One reason I chose to add lead (instead of iron) is because the material properties of lead are truly abysmal for weapons, being far worse than weapon grade materials. This did not seem to matter in the slightest.

This test helps to demonstrate, yet again, just how close the performance of different kinds of dense metal is for war hammers.

Quick Tests

I'm also going to add some quick tests, involving only 100 fights per weapon per test instead of 500. A small number of samples can help to identify trends if they are very strong. Also it will help to demonstrate my point about the importance of large sample sizes.

Dwarves with max physical stats, legendary combat skills:

Code: [Select]

| weapon              | mean  | stdev | confidence_level | margin_of_error | lower_bound | upper_bound |
|---------------------|-------|-------|------------------|-----------------|-------------|-------------|
| steel war hammer    | 12.66 | 7.64  | 0.95             | 1.50            | 11.16       | 14.16       |
| platinum war hammer | 13.13 | 8.16  | 0.95             | 1.61            | 11.52       | 14.74       |
| lead war hammer     | 13.76 | 7.43  | 0.95             | 1.46            | 12.30       | 15.22       |
| copper war hammer   | 14.58 | 8.04  | 0.95             | 1.58            | 13.00       | 16.16       |
| silver war hammer   | 15.53 | 7.18  | 0.95             | 1.41            | 14.12       | 16.94       |

Dwarves with max physical stats, legendary combat skills, both Dwarves and Goblins 25% bigger than average

Code: [Select]

| weapon              | mean  | stdev | confidence_level | margin_of_error | lower_bound | upper_bound |
|---------------------|-------|-------|------------------|-----------------|-------------|-------------|
| silver war hammer   | 13.97 | 7.75  | 0.95             | 1.39            | 12.58       | 15.35       |
| platinum war hammer | 14.76 | 8.35  | 0.95             | 1.49            | 13.26       | 16.25       |
| copper war hammer   | 15.07 | 8.49  | 0.95             | 1.52            | 13.55       | 16.59       |
| lead war hammer     | 15.13 | 8.11  | 0.95             | 1.45            | 13.67       | 16.58       |
| steel war hammer    | 16.07 | 7.78  | 0.95             | 1.39            | 14.67       | 17.46       |

Dwarves with feeble (35% of max) physical stats, lvl1 skills:

Code: [Select]

| weapon              | mean  | stdev | confidence_level | margin_of_error | lower_bound | upper_bound |
|---------------------|-------|-------|------------------|-----------------|-------------|-------------|
| steel war hammer    | 84.52 | 45.58 | 0.95             | 8.93            | 75.59       | 93.45       |
| silver war hammer   | 91.08 | 48.84 | 0.95             | 9.57            | 81.51       | 100.65      |
| platinum war hammer | 92.22 | 51.91 | 0.95             | 10.17           | 82.05       | 102.39      |
| lead war hammer     | 93.33 | 44.34 | 0.95             | 8.69            | 84.64       | 102.02      |
| copper war hammer   | 97.26 | 42.78 | 0.95             | 8.38            | 88.88       | 105.64      |

Compare with the 100% physical high skill dwarves: these dwarves took 6.7x longer to kill the Goblin. (Note: the same weak dwarves armed with Steel Picks would have no trouble striking down the ironclad goblins in about 15 hits)
In this test the weak dwarves had trouble killing the Goblin before passing out from exhaustion, some would pass out from exhaustion multiple times, this made the tests take *much* longer to run to conclusion.

Number of times passed out from exhaustion:

Code: [Select]

| Weapon   | mean | stdev | 95% CI      |
|----------|------|-------|-------------|
| Steel    | 1.05 | 0.95  | [0.63,1.47] |
| Lead     | 1.25 | 1.08  | [0.78,1.72] |
| Silver   | 1.37 | 1.26  | [0.82,1.92] |
| Copper   | 1.4  | 1.35  | [0.81,1.99] |
| Platinum | 1.56 | 1.27  | [1.00,2.12] |

While the platinum warhammer users did pass out from exhaustion the most, there is extreme overlap within the confidence intervals, and the platinum war hammer is roughly twice as heavy, if there was a dramatic effect it should be more obvious.

Summary of quick tests

You may have noticed the rankings jumped around wildly, like Silver and Steel totally swapped places between the two "peak physical" tests where the only thing changed was making everyone 25% bigger. This is very likely not bceause Silver performs better against larger targets, but because the sample size is much too small to draw conclusions on which material is better, the only thing being tested is who got luckiest. However the point of these tests was mainly to root out if there's any really strong effect, like weak dwarves totally sucking with platinum warhammers or large beastly strong dwarves being murder machines with platinum warhammers. No statistically significant effect was detected.

Conclusion

The Null Hypothesis that "It doesn't matter what dense metal war hammers is made from" holds up pretty well in this testing. There is no strong statistical evidence for any dense metal being better than another for striking down ironclad goblins.

However there is statistically weak evidence for Platinum and Steel being superior, a conclusion that would be supported by prior, albeit weaker, testing and some theoretical analysis based on accepted combat formulas.

As a note: in 50.07 bludgeoning weapons perform abysmally compared with steel edged weapons unless you are fighting fully steel clad dwarves from a rival dwarven civilization. If you are trying to optimize artifact weapon creation for effectiveness (rather than value), you should ALWAYS try to have the dwarf use steel rather than platinum, if the outcome is an edged weapon the result will be an extremely good weapon, but if the result is a bludgeoning weapon it won't be measurably worse as steel than if it had been made of platinum.

[Blue_Dwarf]

You are truly a scholar of dwarven science.

These posts should be bound in a quire and copied, so that we can read them and ponder.

[dikbutdagrate]

Thanks Panando!

I found it a little surprising that copper did as well as it did.

Divine metal could also be tested, but it probably comes out being the same as any other metal.

Honestly, bothering to test adamantine again for some hard numbers, likely wouldn't be a bad idea either. You know, just to verify theres at least one metal you shouldn't want to forge your warhammers out of.

[Panando]

Thanks Panando!

I found it a little surprising that copper did as well as it did.

I'm not surprised that copper did as well as it did. For the most part the momentum is the same (a heavier weapon hits with less velocity) and it's the momentum that for the most part does the damage. This is also seen with morningstars often performing very similar to maces (excluding some special cases) because the morningstar only has a low amount of pierce, so for the most part it's just dumping a pile of momentum onto a body part and twisting spines and stuff.

Honestly, bothering to test adamantine again for some hard numbers, likely wouldn't be a bad idea either. You know, just to verify theres at least one metal you shouldn't want to forge your warhammers out of.

Worth testing. I just did a quick test (96 samples) with various materials, peak physical highly skilled dwarves:

Code: [Select]

| weapon                   | mean  | stdev | confidence_level | margin_of_error | lower_bound | upper_bound |
|--------------------------|-------|-------|------------------|-----------------|-------------|-------------|
| silver war hammer        | 14.07 | 8.57  | 0.95             | 1.72            | 12.36       | 15.79       |
| shining metal war hammer | 16.29 | 8.17  | 0.95             | 1.64            | 14.66       | 17.93       |
| wagon wooden war hammer  | 21.92 | 9.57  | 0.95             | 1.91            | 20.00       | 23.83       |
| adamantine war hammer    | 38.94 | 14.90 | 0.95             | 2.98            | 35.96       | 41.92       |

Due to the low number of samples I wouldn't put too much weight on silver out-performing "shining metal" (but it most likely does), but it's certainly safe to assume divine metal war hammers are not amazing and may well be worse than common metal war hammers.

As expected adamantine does badly. TBH the wood war hammer (also representing bone) did better than I would have expected, you still wouldn't want to issue a military dwarf a bone artifact war hammer but I was expecting it to do worse.

[Putnam]

Divine metal's significantly worse than normal metal, in the sense that it has difficulty doing anything but bruising vs armor.

[Asdfe]

Another excellent thread. It's funny how many truisms over the years that have been build around DF are dubious at best, if not flat out wrong.

[Panando]

Another excellent thread. It's funny how many truisms over the years that have been build around DF are dubious at best, if not flat out wrong.

Generally popular wisdom is broadly correct. Like while you get some people who will insist that silver is the best material for war hammers, you also get the prevailing viewpoint that material doesn't really matter.

There's only one very wrong truism I've uncovered: and that is the best weapon vs undead. Masterwork steel edged weapons (pick, battle axe and short sword - not the spear) strike down and mangle undead dramatically faster than blunt weapons, and although they produce more parts that get renaimated, those parts are trivial to strike down (basically if the limb could be slashed off, it can also be mangled in one hit, since the requirement for both is basically "do catastrophic damage to every layer"). Striking down a zombie in 5 hits, then striking down the 3 appendages which got cut off in 1 hit per piece, is much faster than taking 30 hits with a war hammer to mangle the zombie in one piece. So blunt weapons theorycraft well vs undead, but their performance is just so abysmal that the theorycrafting doesn't stand up to testing.

The belief in blunt weapons being best vs undead probably came from early versions of undead which were extremely particular about under which conditions they would sit down and shut up and IIRC small severed parts could be extremely hard to strike down, unlike now when they get easily struck down in one slash.

[Bumber]

Another excellent thread. It's funny how many truisms over the years that have been build around DF are dubious at best, if not flat out wrong.

Or just outdated.

[ldog]

I gotta say I've been very disappointed with platinum warhammers.
They especially underperform for weak dwarfs and against unarmored targets. Although I haven't done any !science!
I have been using them extensively since I figured out you can make them consistently via work order.
I was making platinum crossbows as well for that extra bit of oomph (because we all know crossbows are melee weapons in DF) but again see no real benefit, especially for the extra weight.
Interesting that the conventional wisdom on silver is wrong, and I've never really seen any benefit to it in practice.
Back to good old steel it is.

[Ulfarr]

Spoiler: Slightly off topic: (click to show/hide)

Silver being the "best" could come from a logistics standpoint. As these tests prove, silver warhammers don't perform significatly worse and it allows one to conserve better metals for edged weapons and/or amor.

On topic:
Looking at the results of the quick tests, there seem to be a drop in warhammer effectiveness against bigger targets. Would it be possible to test:

1) Whether that is true or just a result of a small sample size

2) If it is true, how does the effectiveness change in relation to target's size. Idealy target size should range from smaller than a dwarf (say a kobold) to way larger (forgotten beast/titan).

3) If target size affect warhammer effectiveness, does it also affect other weapons' effectiveness?

[duckman]

Spoiler: Slightly off topic: (click to show/hide)

Silver being the "best" could come from a logistics standpoint. As these tests prove, silver warhammers don't perform significatly worse and it allows one to conserve better metals for edged weapons and/or amor.

On topic:
Looking at the results of the quick tests, there seem to be a drop in warhammer effectiveness against bigger targets. Would it be possible to test:

1) Whether that is true or just a result of a small sample size

2) If it is true, how does the effectiveness change in relation to target's size. Idealy target size should range from smaller than a dwarf (say a kobold) to way larger (forgotten beast/titan).

3) If target size affect warhammer effectiveness, does it also affect other weapons' effectiveness?

There was a significant boost to larger creatures' ability to absorb blunt force relatively early on in 4X.XX. I don't remember which specific update that was, but it was in the notes somewhere.

Edit: Wait, it might have been their resistance to force transmission that got a boost. So giants wouldn't get shattered shoulders from being punched in the upper arm anymore.

[muldrake]

Thanks Panando!

I found it a little surprising that copper did as well as it did.

Divine metal could also be tested, but it probably comes out being the same as any other metal.

Honestly, bothering to test adamantine again for some hard numbers, likely wouldn't be a bad idea either. You know, just to verify theres at least one metal you shouldn't want to forge your warhammers out of.

Could a dwarf even pick up one made of slade?  I'm pretty sure short of modding that this would have to be an artifact.

Honestly, the only real surprise here (although it is great to have actual objective data now) is they run pretty close to each other in quality and (surprisingly) silver is the worst.  I've always made my earliest hammers out of silver because I like imagining dwarves bashing people's brains out with Maxwell's Silver Hammer.  Apparently I should have been using copper (or my usual early game standard bronze).  ETA:  I just noticed you said the overlapping confidence intervals mean they're basically a wash, with one of them possibly being nearly microscopically better.  So I can stick with silver for cheap hammers I suppose.

I sometimes use bismuth bronze, too, no real reason why, I just like it.  And what else are you going to do with bismuthinite?  I'm pretty sure they'd be nearly identical other than dwarf preferences for weapon purposes.

Without going to any more effort, what is your opinion on bronze?  I usually use it for (at least mediocre) early game furniture, weapons, and mostly picks and axes, reserving the dross metals for blunt force weapons like hammers (which appears to have marginal advantages to using more valuable metals in as I suspected).  I make exceptions for reanimating/thralling biomes where you really don't want to cut undead into multiple pieces if you can avoid that.

Considering how dangerous those critters are, it's probably worth the added investment in better materials for even a slight advantage.

Generally popular wisdom is broadly correct. Like while you get some people who will insist that silver is the best material for war hammers, you also get the prevailing viewpoint that material doesn't really matter.

There's only one very wrong truism I've uncovered: and that is the best weapon vs undead. Masterwork steel edged weapons (pick, battle axe and short sword - not the spear) strike down and mangle undead dramatically faster than blunt weapons, and although they produce more parts that get renaimated, those parts are trivial to strike down (basically if the limb could be slashed off, it can also be mangled in one hit, since the requirement for both is basically "do catastrophic damage to every layer"). Striking down a zombie in 5 hits, then striking down the 3 appendages which got cut off in 1 hit per piece, is much faster than taking 30 hits with a war hammer to mangle the zombie in one piece. So blunt weapons theorycraft well vs undead, but their performance is just so abysmal that the theorycrafting doesn't stand up to testing.

"Best" is pretty situational.  Except in the most terrifying of biomes you are rarely showing up immediately facing an existential threat.  So "best" may just mean you have nothing but silver.  Generally even the resource-sparse embarks have stuff like tetrahedrite lying around.

I also almost always embark with cassiterite and tetrahedrite to start up bronze production immediately (and if it is safe enough to take some extra time do it via bars instead of directly from ore in order to get some extra silver out of it).  I usually don't even bring a pick and the only high ticket item is the axe I need to cut down the first tree.

So almost all my early items are either wood or bronze.  I also start with clinodev's craftswarves embark, so while my original materials are pretty sub-optimal (but not by comparison to just crossing my fingers and hoping for a metals-rich embark), the quality of the craftsdwarfship somewhat mitigates this.

[Panando]

Without going to any more effort, what is your opinion on bronze?  I usually use it for (at least mediocre) early game furniture, weapons, and mostly picks and axes, reserving the dross metals for blunt force weapons like hammers (which appears to have marginal advantages to using more valuable metals in as I suspected).

Bronze is basically iron for most intents and purposes. It's perfectly effective for armor against goblin/human/elf weapons just as iron is, steel is slightly better but it's way more important to at least have iron/bronze armor and steel is just a slight upgrade except in the rare cases of steel weapons (some cavern dwellers, enemy dwarves). In contrast, just like iron, bronze is severely sub-optimal for any edged weapons precisely because edged weapons have trouble cutting through same material armor. It is highly optimal to make edged weapons out of steel, and basically to only use edged weapons made of steel since they severely outperform blunt weapons against nearly everything unless you have modded steel clad enemies.

Bronze is generally very cheap to embark with in ore form, at 1/4 the cost of iron, so can be good for making early armor.

[muldrake]

Bronze is basically iron for most intents and purposes. It's perfectly effective for armor against goblin/human/elf weapons just as iron is, steel is slightly better but it's way more important to at least have iron/bronze armor and steel is just a slight upgrade except in the rare cases of steel weapons (some cavern dwellers, enemy dwarves). In contrast, just like iron, bronze is severely sub-optimal for any edged weapons precisely because edged weapons have trouble cutting through same material armor. It is highly optimal to make edged weapons out of steel, and basically to only use edged weapons made of steel since they severely outperform blunt weapons against nearly everything unless you have modded steel clad enemies.

Good point and I do generally try to sell off the early bronze weapons (especially the seriously sub-optimal bronze edged weapons).  The absolute worst is when your starting military squads get attached to crappy weapons.  I try just not to have them on the map, or at the very least, not in military stockpiles.  About the only thing worse is if you aren't paying attention and they get attached to one of those miserable wooden training swords the elves always bring.

[ldog]

Bronze is basically iron for most intents and purposes. It's perfectly effective for armor against goblin/human/elf weapons just as iron is, steel is slightly better but it's way more important to at least have iron/bronze armor and steel is just a slight upgrade except in the rare cases of steel weapons (some cavern dwellers, enemy dwarves). In contrast, just like iron, bronze is severely sub-optimal for any edged weapons precisely because edged weapons have trouble cutting through same material armor. It is highly optimal to make edged weapons out of steel, and basically to only use edged weapons made of steel since they severely outperform blunt weapons against nearly everything unless you have modded steel clad enemies.

Good point and I do generally try to sell off the early bronze weapons (especially the seriously sub-optimal bronze edged weapons).  The absolute worst is when your starting military squads get attached to crappy weapons.  I try just not to have them on the map, or at the very least, not in military stockpiles.  About the only thing worse is if you aren't paying attention and they get attached to one of those miserable wooden training swords the elves always bring.

I used to let that bug the shit out of me too, but then life is full of disappointment, why should the dwarves be exempt. They can suck it up and deal with it when I take their crappy stuff away to give them masterwork steel. I haven't had a tantrum spiral from it or really anything other than bugs in many versions so as long as you go to reasonable lengths to keep order you should be good(other than what amounted to a civil war that I gave up trying to figure out WTF happened)

So considering the platinum is like twice the weight for little to no gain I'm going to consider it a bad choice and remove it from my work orders (probably not in DFHack just my own, I may suggest it to Myk, but I'll leave it up to him how he wants to handle it). The silver all things considered is still not an awful choice I guess. We're talking war hammers, maces and crossbows only of course. What do all y'all think? I mean you generally have steel or you don't have steel so it isn't like there's a need to conserve it usually. Maybe I will drop the silver down below steel, which the numbers above support (right now the upgrade path goes copper>bronze>bismuth bronze>iron>steel>silver>platinum and the work orders are chained to choose based on what you have to work with) So it'd still make sense to use silver if you don't have steel.