As a result of the conversation about split-special-damage weapons, I've been taking a closer look at how much of a bonus/penalty damage types get vs. the different monsters. My first look at it is at http://forums.spiralknights.com/en/node/34185?page=5

I have been using the weapon damage values from here: http://forums.spiralknights.com/en/node/7447

Since then, I've come up with a pretty good idea of how much damage weapons do to things they're strong/weak against in a general sense. Against resistant enemies, special damage seems to do the following, where A and B are parameters determined in some fashion by the depth and possibly the weapon's * rating:

Adjusted damage = (base - A) * B + A

So the first A damage is unaffected by the resistance, and the rest is reduced linearly by it.

For depth 28 and 5* weapons, it looks like A = 20, B = 0.15 gives good results.

For vulnerable enemies, the picture is a little more complicated. It looks like this: Below a certain threshold, the amount of bonus damage added looks like a parabola that opens downwards. Above that threshold, the amount of bonus damage added is constant. So with four parameters C, D, E, and F we can match the damage to the following function:

Adjusted damage = base + MAX(C * H(base - D), E - (base - D)^2 / F)

(where H is the unit step function)

C is the constant bonus added after the base damage reaches a certain value, D is the base damage at which the maximum damage bonus is added, E is the maximum damage bonus, and F is a conversion value. For depth 28 and 5* weapons, it looks like C = 81 (or 82), D = 125, E = 95, F = 95 gives good results.

The damage values used came from the Venom Veiler, Callahan, Polaris, Acheron, Barbarous Thorn Blade, Divine Avenger, Fang of Vog, Fearless Rigadoon, and Hail Driver. Every other 5* weapon either did not have a complete set of damage listings available at depth 28 or duplicated the numbers provided by one of those weapons (for example, Gran Faust duplicated the damage numbers of the Divine Avenger). The damage values for all available attacks were used (all swing damages for swords, charged attacks, expanded+non-expanded Polaris shots, etc.) but not for status damage. For split normal/special weapons, it was assumed that half the base damage was normal, and the normal and special damages were calculated independently of each other. That means that for a split normal/special weapon the adjusted damage is assumed to be calculated as follows:

Adjusted damage = base / 2 + f(base / 2)

where f() is the appropriate function from above.

Edit - I took these formulas and used them to graph the different combinations of damage types, to get an idea of how they compared. The general results: at very low base damages, split normal/special weapons are terrible, doing far less damage to vulnerable enemies, and split special/special weapons are worse, also doing less damage to neutral enemies. As base damage increases, this situation improves. You reach a threshold where split special/special weapons do better than base damage to neutral enemies (this threshold looks to be a little above the base damage of AP or Sentenza).

Split damage weapons also start to catch up to full-special weapons in damage to vulnerable enemies, and after a while you reach another threshold (somewhere around twice the base damage of the first one) where split damage weapons surpass full-special weapons in damage to vulnerable enemies. At this point, split special/special damage would be king, doing more damage to both vulnerable and resistant enemies than full-special weapons, and also doing more damage to neutral enemies than either full-special or normal/special weapons. There aren't any split special/special weapons in this base damage range, though. A lot of 5* sword attacks do fall into this range, however; the Divine Avenger's first swing, for example, would do slightly **less** damage to constructs/undead (at least at depth 28) if the DA became pure elemental.

As base damage increases further, these advantages fade. Next you reach a point where split special/special's damage to neutral enemies drops back below the base damage, leaving split normal/special at the top of the heap for damage output. Then comes the point where the damage vs. vulnerable enemies equalizes. After this, the only difference between full-special and normal/special weapons is that normal/special weapons do better damage to resistant enemies, and the only difference between normal/special and special/special is that special/special weapons do less damage to neutral enemies.

Chronovore, this is interesting and valuable; thank you.

In the part about vulnerable enemies, you are using a somewhat complicated function (piecewise linear/quadratic) to fit the data. When figuring out weapons for myself and advising others, I will have difficulty conveying such a function in a few pithy words. So I'm wondering whether such a complicated function is required. How closely do the data fall on this parabola? Is there a piecewise linear function that works almost as well?