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Building Blocks 14: Weapon Comparisons 13

Calculating Weapon Damage pt 13: Damage Reduction

Most raid bosses have some sort of damage reduction. Damage reduction is a defense mechanic that represents how well a monster resists physical damage.  Most often damage reduction is able to be bypassed by using a specific weapon type.  We express damage reduction as a DR #/condition.  Unless the condition is met by the weapon, all physical weapon damage (base damage + [E] + [D] + [S]: this sum is the first of the floaty numbers) is reduced by the # (to a minimum of 0).  You can see why kind of damage a specific weapon deals by looking in its examine window.  Damage reductions typically fall into 1 of 4 categories: general, weapon type, alignment, and material.

General damage reductions include magic (armor effect invulnerability), epic (level 20 monks), and /- (this damage reduction is not able to be bypassed, big elementals are a common example).  These damage reductions have less to do with what kind of damage weapons do and whether or not they are magical or epic – but both of these are more problems for monsters than players.

All weapons have 1 of 3 weapon types: slashing, bludgeoning, and piercing.  Some monsters have damage reduction that requires one of these types (some respective examples are zombies, skeletons, and rakshasa – though they often also require good

in addition to piercing). Some rare weapons are able to deal 2 damage types, but otherwise the only option to bypass this type of damage reduction is to get an appropriate base weapon.  This is why most players carry a few weapons (particularly bludgeon weapons) that aren’t their preferred type.

Some monsters require a weapon that deals alignment based damage: good/evil or lawful/chaotic.  Of all damage reductions players will have to deal with, good is the most common and can be commonly bypassed by holy, pure good, flame touched, and righteousness.  Many raid bosses require good as at least part of their damage reduction such as devils and demons.  Evil damage reduction is very rare, the most prominent example being Eladrin.  The unholy attribute for weapons is rare, but green steel weapons also bypass evil DR. Lawful DR is bypassed by axiomatic and true law weapons and tharaak hounds are a prominent example.  Chaotic DR likewise is bypassed by anarchic and true chaos weapons and is a feature of maruts.  The common theme typical with this type of damage reduction is aligned outsiders that require weapons of the opposite alignment.  A few weapons have attributes that bypass any aligned damage.

Material damage reduction is based on what a weapon is made of.  These include silver (vampires and devils), cold iron (demons and fey), adamantine (constructs and warforged), mithral (stormreaver), and crystalline (crystals).  Outside of good damage reduction, material DR is the most common and are generally again determined by creature types.  The weapon ability “metalline” bypasses most material DR.

Sometimes the condition is expressed as “[condition 1] OR [condition 2]” and in this case damage reduction is bypassed so long as at least 1 of the conditions is met.  Typically this is “good OR [material type].  Lesser devils typically have “good OR silver” while lesser demons have “good OR cold iron.”

More powerful monsters (often raid bosses) have damage reduction expressed as “[condition 1] AND [condition 2].” In these cases BOTH conditions must be met for damage reduction to be bypassed.  Typically this also involves “good AND [material type].  Powerful devils have good AND silver, powerful demons have good AND cold iron, and both Cannith raids feature bosses with good AND adamantine DR.  The prevalence of these combinations is why metal line of pure good weapons are sought after weapons (although less so with the new crafting system).  Another variation is liches which typically have good AND bludgeoning DR.

Although it is exceptionally rare for monsters, players sometimes have multiple layers of damage reduction.  For example, a monk might have the following damage reductions: 10/epic, 10/slashing OR bludgeoning, 5/evil, and 3/-.  Damage reduction does not stack, rather the highest applicable DR applies.  If this monk was attacked with an epic piercing weapon they would be benefit from DR 10.  If attacked by an evil slashing weapon this monk would still benefit from DR 10 because the weapon is not epic.  On the off chance that this monk was hit with an epic, evil, slashing weapon, the DR 3/- would still apply.

So let’s calculate some damage reduction.  Here’s the problem.  DR is not subtracted until several of our weapon components are added together, including [D] and [S].  This means that reducing the base weapon damage to a minimum of 0 is incorrect, any remaining DR not applied to base weapon damage is further taken from [D] and [S].  In math terms this means that [weapon] + D + S – DR = damage.  I will express weapon damage as a negative number with the understanding that in such cases if [weapon] + D + S < 1 then damage = 0.  We CANNOT subtract this damage from our other weapon attributes (unless the increase [D] or [E] like righteousness or bane weapons) because extra damage dice are not affected by damage reduction.

But here’s the cool thing.  Damage reduction is subtracted!  That’s like addition in reverse, which means that we can simply calculate damage reduction as a negative “bonus” to weapon damage.  However, damage reduction is an attribute of the monster, not the weapon, therefore we do not need to take into account the weapons critical profile.

So let’s look at a DR of 1/-.  Yeah I know, that’s really small, stay with me here.  We still miss on a 1, so there is no damage reduction applied.  On rolls of 2-20 we apply a -1 modifier for a total of -19 damage over 20 swings, or an average of -.095 damage.

By knowing DR 1/- we can now multiply this number by any number of DR we wish to calculate how much any DR subtracts from our weapon.  Here’s some common DR variations.

Damage Reduction 1 2-20 Sum Avg
DR 1 0 -1 -19 -0.95
DR 5 0 -5 -95 -4.75
DR 10 0 -10 -190 -9.5
DR 15 0 -15 -285 -14.25
DR 30 0 -30 -570 -28.5
DR 45 0 -45 -855 -42.75
DR 60 0 -60 -1140 -57

Remember, this cannot reduce [weapon] + D + S to less than 0.  Hopefully by looking at some of the higher values of damage reduction you can see why it is important to bypass damage reduction. -57 damage PER SWING is a major impact (assuming 100 swings per minute that’s 5700 damage per minute).

Let’s quickly look at our boss beaters against the very respectable DR 30/-.  That’s a -28.5 to damage.  Let’s create an equation to see for what value of [D] we break through DR 60/- and then apply this to our boss beaters in sequence to see what values are necessary for each.  To do this we need to determine what value of [D] gives us a result for weapon damage equal to the DR.  Then we can say for any value of [D] higher than this will overcome DR (though still heavily reduced in damage).  Here’s our equation (which you should recognize from before with the addition of DR): [weapon base] + x[E] + x[D] + y[S] = DRAvg.  As before x=[D] modifier and y=[S] modifier.  [E] is separate because some weapon attributes actually apply their bonus damage by adding to [E] (bane weapons).  Other weapon abilities will be ignored as they do not suffer the effects of damage reduction.

So, let’s assume a seeker bonus of 6 and crunch.  Let’s keep in mind here that like elemental resistances to get an accurate depiction of damage reduction we would in fact need to calculate each permutation of damage dice, but this will give us a general sense.  As usual, all damage applies.

Greensteel falchion: [2d6+5]+1.25D+.6(6) = 57 >>  15+3.6+1.25D = 57 >> 1.25D = 38.4 >> D = 30.72

Epic Antique Greataxe: [3d10+6]+1.15(2)+1.15D+.3(6)+2 = 57 >> 25.875+6.1+1.15D = 57 >> 1.15D = 25.025 >> D = 21.76

Normal falchion: [2d4+5]+1.25D+.6(6) = 57 >> 12.5+3.6+1.25D = 57 >> 1.25D = 43.4 >> D = 34.72

Greater bane falchion:  [2d4+5]+1.25D+.6(6)+3 = 57 >> 12.5+3.6+3+1.25D = 57 >> 1.25D = 40.4 >> D = 32.32

Epic SoS: [5d6+10]+1.55D+.9(6) = 57 >> 42.625+5.4+1.55D = 57 >> 1.55D = 8.975 >> D = 5.79

As we should expect the Epic SoS needs a far lower value of D as it does much more base weapon damage.  We should also expect the variations of falchion to have similar values for D since their base damage is similar.

Don’t think of this as the bar to use these weapons without breaking DR though.  These calculations are something of a mathematical exercise and don’t really help game play.  Even if you are breaking through DR of a monster and doing some damage, -57 damage per swing is significant.  Assuming 100 swings a minute, that’s -5700 damage a minute and that adds up.

If you have a topic or a build you’d like me to look at drop me an email (ddoepiceducation@gmail.com) or leave a comment.  I am in no way guaranteeing that I will consider, reply to, or let alone read comments in anything resembling a timely manner (sorry, time is unfortunately not an infinite resource of mine until I am high enough level to cast time stop).

Comment (1)

  1. Nuryam

    Another great post. 🙂

    You can buy blessed weapons in the ddostore, they count as goodaligned and can be cleansed for crafting while retaining that property.

    Paladins have a spell that gives a LG character DR 5/evil for a short period of time. I use it up to level 15 quite often.

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