## Building Blocks #3: Calculating Weapon Damage #2

Calculating Weapon Damage pt 2: Base Weapon Damage

Now that we know how to calculate dice averages we can calculate weapon damage which is primarily a function of dice rolling. Just like averaging dice we get a large sample size because of the number of swings. This will again simplify our calculations.

To start we need to determine how to express damage.  We have to be able to account for the critical hits because they are an important part of weapon damage.  Critical hits occur on specific rolls of our to-hit roll (which is a d20 roll) and these rolls are determined by the weapon.  Each weapon has what we call a critical profile.  The most common profile is 20/x2 (this is usually displayed as x2, the 20/ is usually not shown).  This means that when rolling to-hit if that roll is a natural 20 then the weapon will do twice it’s damage (x2).  This multiplied bonus also includes the damage bonus for a weapon which we will discuss later. Other common profiles are 19-20/x2, 18-20/x2, and 20/x3 (usually written x3). The number range before the ‘/’ tells you which natural rolls on your d20 to-hit roll qualify for the multiplier.  The second number is the multiplier used when you qualify for a critical hit. So an 18-20/x2 profile means that on a natural roll of 18, 19, or 20 the weapon damage is multiplied by 2*.

So clearly we need to factor in the to-hit roll in our equations to get a solid idea of how a weapon’s critical profile plays into weapon damage. To account for this we will calculate weapon damage as “damage per swing.” This will appropriately account for critical hits while also giving us a number that accurately averages these damage spikes.

As with averaging dice rolls we can simplify things because of our large sample size.  Weapons swing a lot so we can simply account for each possible permutation of the d20 as an equal chance.  This means we will calculate weapon damage for each of the 20 rolls of our to-hit dice, add them all together, and divide by 20 (the number of rolls). Before we start the math though we need to make some assumptions.  Because we are (at this point) calculating weapon damage generically we will assume a generic monster. This monster has no special defenses.  That means no damage reduction, no resistances, and a low armor class that we can hit no matter what the roll is. This will remove a huge variable from our calculations (for the time being).  Let’s also start simple and only calculate the base damage of a weapon.  We will add in other factors as we go.

So let’s pick a few weapons with different profiles and calculate weapon damage over 20 swings. Remember that a 1 always misses.  Let’s start with a basic weapon: the club (yes I know, nobody actually uses a club). The club does 1d6 damage and has a 20/x2 profile.

 Weapon 1 2 – 19 20 Sum Avg Club 0 3.5 7 70 3.5

On rolls between 2 and 19 the club does its normal damage and on 20 double damage.  Notice how a weapon with a 20/x2 critical profile in fact does its average damage.  This is because the double damage on a 20 in essence replaces the damage lost from a miss on a 1.  Let’s look at some other popular weapons.  For these examples I will choose the rapier (1d6 18-20/x2), kopesh (1d8 19-20/x3), and great axe (1d12 20/x3). These weapons give us not only a variety of base damages, but critical profiles.  Please keep in mind that these numbers are not a straight comparison. It may look like the great axe is the clear winner but that is a gross over simplification.

 Weapon 1 2 – 17 18 19 20 Sum Avg Crit+ Rapier 0 3.5 7 7 7 77 3.85 0.35 Kopesh 0 4.5 4.5 13.5 13.5 103.5 5.175 0.675 Greataxe 0 6.5 6.5 6.5 19.5 136.5 6.825 0.325

You may notice here that of the 3 weapons the kopesh critical profile in fact gives the greatest boost to damage compared to the average dice damage (this is what the last column is showing). Additionally, while most permutations of weapons use the base statistics, there are some special versions of weapons out there with better base die and better crit profiles.

If you have a topic or a build youd 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, tiem is unfortunately not an infinite resource of mine until I am high enough level to cast time stop).

*Actually what happens is a second to-hit roll is made.  If this roll scores a hit then the damage is multiplied, but if it misses then only normal damage is applied. For the sake of simplicity we are actually going to ignore this and assume a successful hit.  This will slightly inflate our numbers because at least 5% of potential critical hits cannot be confirmed (1 always misses).  Well explore this later…much later.

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