I had taken a few cracks at making weapon lists before, each with varying degrees of success. My most current model as them organized categorically with the idea that weapons created in a similar way, with similar heft and balance, as well as mode of damage should be grouped together. This way someone using a longsword should have no problem picking up a short sword and someone used to using a mace should be able to freely swap it out with a morning star. It's simplistic and sensible (on the surface at least) and that's what I'm all about.
As it stands there's about a half dozen categories for melee weapons only. Of course one thing that I carried over from the 3.x days were damage types, specifically Slashing, Piercing and Bludgeoning. I liked the idea behind it, that weapons had differing ways of dealing damage and that enemies and certain armors (given the right splat-tastic book) would treat some damage types as ineffective and others as effective. This was predicated on the somewhat bizarre system of 'I have damage reduction against everything but this'. So for example a skeleton may have DR 5/Bludgeoning. Now we can all agree that an arrow or the thrust of a dagger should have little effect on a walking, talking (well maybe not talking) skeleton. A sword slash would also be inefficient since a slash is geared towards soft targets but not to the same degree as a stab would be. In this respect you would think that the piercing type weapon would be ineffectual, the slashing weapon would have reduced effectiveness and the bludgeoning weapon would reign supreme. However, in this odd DR/"My One Weakness!" system all damage types save the magic bullet are penalized. So to remedy this you could adapt the system to be more flexible or build something from the ground up.
Then I read this interesting post over at Delta's D&D Hotspot and the subsequent discussion in the comment section and I was very impressed. So much so that I spent some time skimming over the exhaustive work of Matthew James Stanham of Silver Blade Adventures fame in this post on Dragon's Foot. Matthew's post takes a look at how the interactions between specific weapons and armor class evolved organically between the edition's of D&D and it's precursor Chainmail. If you're interested in mechanics changes over the ages it's some very interesting stuff so take a look.
In the meantime I'd like to take a look at the categories of damage types outlined in the comments section of Delta's post. To summarize the contents of the posts and citations; the basic principle is that the more concentrated the force of impact the more likely the user was to damage the target. Conversely, the more surface area (and I'd wager thickness although it's not clearly stated) of the armor that catches the impact the more the force of the blow can be spread out and absorbed by the armor rather than it's occupant. A fairly straightforward principle grounded in basic physics. It reminds of me of a weapons and armor lecture I had in school where one of the topics we discussed was laminated armor and how a single uniform sheet of material could better absorb an impact rather than multiple plates riveted together. Of course, like all armor there is no one size fits all approach and there are very likely times when piecemeal construction would be more suitable, ablative and reactionary armor immediately come to mind but I digress.
Now that we have the guiding principle down let's look at the construction and intended use of different categories of weapons. I will be quoting Matthew who is quoting Catherine Hanley author of War and Combat who appears to be quoting Gamble. My aren't citations an tangled web of confusion?
The axe was a powerful weapon, as Gamble explains: 'By combining a relatively smaller curved edge with a heavy head, all of the striking force was combined to hit in a small area, which is opposed to a sword in which the force is distributed evenly along the entire length of the blade.'
"The axe, with its greater weight concentrated behind a smaller cutting edge, had the potential to inflict terrible wounds if used to its maximum effect, as did the mace, whose heavy head was capable of smashing bones even through layers of armour."
Now if we look at this we see that the Axe is almost guaranteed at inflicting damage against an armored opponent due to the force being confined to not only a small area (the axe head) but an even smaller area on the edge. Compare this with a hammer which has a similar principle of confining the force to the head but the flat blunt edge causes the force to be spread out. I think the sword comparison is especially apt since the Axe and Mace are making full use of the wielder's moment, err sorry torque, much like how it is easier to use a wrench or open a door the further your arm (and the force you exert) is from the pivot point. Contrast this with a sword whose impact can be anywhere from the tip (maximum torque) to the cross guard. While this makes for a versatile weapon allowing two forms of damage, cutting and impact as Matthew later explains, it does however limit it's effectiveness at penetrating armor.
Now then, since we've looked at the basic physics on how the weapon deals damage let's think on how to translate this to game mechanics. If we define damage, or perhaps more specifically damage dice, as a reflection of how much harm the weapon deals to the users body there are two ways to look at the Axe. First off, it's construction makes it very likely to penetrate armor and thus chop into the target's body. However, it's small area of impact also means that only a small portion of the users body will be hit. Of course if the axe embeds itself deep enough this could lead to a very severe injury. Looking at it this way we see that the axe has a good chance of causing moderate wounds, however due to the nature of it's construction if it hits the right place and makes a deep enough wound it could be very fatal.
Putting this into game terms I would give the axe a small damage die (d4 or d6) and a large critical, whether it be critical modifier and/or critical range depends on your interpretation. If it's a system where armor is used as a target number to hit then the axe would receive a bonus to hit for armor. Comparatively the simple sword whose damage, if using a cutting motion, depends on the amount of area the blade is able to slice leads to a highly variable damage. Let's say damage dice of d10 or d12 with a bonus to hit against lightly or unarmored targets. Lastly, we have the mace which relies on similar principles of operating as the axe. It does not however have the Axes simultaneous strong and weak point of minimal area/focused impact making the mace the least variable in terms of damage, let's say 2d4 for the good average. This is just a shot in the dark here but I'd wager that mace can more easily transfer it's force through the rigid metal of plate than it could the soft and flexible material of leather or hide. Similarly, if the plates in platemail are non-overlapping the mace would have an even easier time of transmitting force than it would moving through the non-uniform interconnected layers of chain or scale mail. For this reason I would give the mace a bonus to hit versus banded and plate mail, a penalty to hit vs chain/ring or scale mail and no modifier versus light armor of leather or hide (although I'd have to reconsider for brigadine).
To quickly summarize we have
Weapon Damage Critical vs Armor
Axe d6 18-20/x3 +1 hit any armor
Sword d10 19-20/x2 +1 vs light, -1 vs heavy
Mace 2d4 20/x2 +2 vs plate/banded, -2 vs mail
Note: These values are for the most part created in a system vacuum.
This was whipped up on a bout of inspiration so I'm sure there are a few flaws in the logic and reasoning here and there. I'd like to take a look at the methods of damage dealing Matthew describes, cutting, thrusting, and impact, but my creative urges have already expired so I'll leave them for a later post. That being said if you have any thoughts you'd like to share on the matter I'd very much welcome them.