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Building Blocks #5: Weapon Comparisons #4

Calculating Weapon Damage pt 4: Weapon Effects

To recap we have so far learned how to calculate a generic weapon’s damage by adding base weapon damage, the damage modifier [D], and the seeker bonus [S].  Now let’s add in some specific weapon effects.

Let’s start with effects that simply add 1d6.  This would include the elemental effects (frost, flaming, shocking, acid), and pure good.  Some weapons add a similar bonus of +2d6, 4d6, or even in rare cases 6d6. Let’s look at those numbers while we are at it.

  1 2-20 Sum Avg
+1d6 0 3.5 66.5 3.325
+2d6 0 7 133 6.65
+4d6 0 14 266 13.3
+6d6 0 21 399 19.95

Any such effect we can simply add this average to our total damage regardless of the weapon type.  Now let’s get a little more complicated, starting with the weapon ability righteousness.  This ability adds +2 damage against evil creatures (remember that for now we are using a generic monster so we’ll treat it as whatever alignment gets us more damage). This damage should be applied to our damage modifier [D]. To see how this changes damage lets plug 2 into our damage variable in the chart we used earlier. 

Weapon 1 2 – 17 18 19 20 Sum Avg
Club 0 2 2 2 4 40 2
Rapier 0 2 4 4 4 44 2.2
Kopesh 0 2 2 6 6 46 2.3
Greataxe 0 2 2 2 6 42 2.1

We can see clearly here that such bonuses scale better with certain weapons.  Other effects that are similar to these are weapons that increase strength (or whichever stat is used for damage). Anything that increases the damage modifier can be calculated this way regardless of how the increase is achieved. This includes the enhancement bonus of a weapon, which shall hence forth be known as [E].  Heres the damage for a generic +1 bonus.

Weapon 1 2 – 17 18 19 20 Sum Avg
Club 0 1 1 1 2 20 1
Rapier 0 1 2 2 2 22 1.1
Kopesh 0 1 1 3 3 23 1.15
Greataxe 0 1 1 1 3 21 1.05

 To calculate for a higher bonus simply multiply these numbers by that bonus.  If you have a known strength/damage modifier you can add in this damage in the same manner.

Now let’s put these 2 principles together with bane weapons.  A bane weapon adds not only a #d6 damage against certain monster types based on its strength (lesser, standard, and greater = 1d6, 2d6, and 3d6) but it increases the enhancement bonus of a weapon against these monsters (the number is 1, 2, & 4). So against the appropriate monster type a standard bane kopesh would do an additional 6.65 + 2.3 = 8.95 damage.   A greater bane greataxe would do an additional 9.975 + 4*1.05 = 9.975 + 4.2 =  14.175 damage.

Let’s next consider the vorpal effect. On a natural 20* this ability will kill most creatures unless they have more than 1000 hps or they are red or purple named.  Let’s assume for our purposes that one of these cases is true (let’s be honest, generally people only get really serious about weapon damage comparisons when looking at a raid boss).  If the vorpal strike doesn’t automatically kill the creature it will instead do 100 damage.  To get our average damage per swing we do some simple math 100/20 (the minimum number of swings to guarantee a natural 20). This tells us that we get an additional 5 damage per swing regardless of the type of weapon (each weapon has an equal chance to roll a natural 20.)

Now let’s look at smiting, banishing, disruption, and greater disruption.  Like the vorpal effect these either kill a monster outright on a natural 20* or do 100 damage.  However, smiting, banishing, and disruption do an additional 4d6 damage per strike. This gives us 13.3 + 5 = 18.3 damage per swing. Greater disruption adds 6d6 damage per strike which is 19.95 + 5 = 24.95 damage per swing.

Next we will look at bursting and blast effects.  Bursting effects (typically these are elemental) usually do their standard 1d6 damage on normal hits, but then they do additional bursting damage on a critical hit and this additional damage is dependent on the critical multiplier.  Blast effects (also typically elemental) do an additional 4d6 damage on a natural 20. This is easy to calculate and isn’t weapon dependent so let’s calculate that first: 4*(d6)/20 (again the minimum die rolls to ensure a 20) = 4*(3.5)/20 = 14/20 = .7 damage per swing.

Burst effects are a little trickier, lets pull out our 4 weapons again.  We don’t need to consider the standard damage, we’ve already calculated that at the beginning of this segment. So let’s just look at the bursting piece and then add in the standard damage in the last column.  Bursting adds 1d10 damage per multiplier (1 for x2, 2 for x3, 3 for x4, etc).

Weapon 1 2 – 17 18 19 20 Sum Avg Total
Club 0 0 0 0 5.5 5.5 0.275 3.6
Rapier 0 0 5.5 5.5 5.5 16.5 0.825 4.15
Kopesh 0 0 0 11 11 22 1.1 4.425
Greataxe 0 0 0 0 11 11 0.55 3.875

Again notice how the kopesh is consistently better than the rapier which is consistently better than the great axe (or if you prefer to think of it this way, 19-20/x3 is consistently  better than 18-20/x2, which is consistently better than 20/x3, which is better than 20/x2).

Finally let’s consider the crazy weapon abilities.  Some of these can be very difficult to calculate because the numbers simply aren’t known.  Things like incineration, lightning strike, cacophony, and similar effects have unknown attributes, particularly with proc rates.  We recently learned that lightning strike has a 1.5% proc rate and does 20d20+400 damage per strike from Eladrin.  Since we have so far calculated damage per swing let’s convert this information to that.  While tests have been done on other abilities, we generally don’t have official numbers. The one thing that is particularly difficult to calculate is the radiance weapon’s ability to blind thereby allowing sneak attacks and increasing dps of rogues  in an unconventional manner.  However, since we typically do these calculations for end bosses that are immune to blindness effects I’m going to conveniently ignore this ability!   Now let’s end this segment with the lightning strike calculation.  This will serve as an example of how to calculate these abilities.

First the damage.  The average roll of a d20 is 10.5 (remember that for a die that includes all numbers between 1 and it’s highest number is half the highest number + .5).  This means the damage can be expressed as 20*10.5 + 400 = 610 damage.

Now let’s convert that into damage per swing.  If this procs on 1.5% of hits that means in  100 hits we will get 1.5 lightning strikes.  However, this does not include misses which we need to factor in.  We get 19 hits every 20 swings so how many swings does it take to get 100 hits?  Using ratios we can set up the equation 19/20 = 100/x where x equals the number of swings it takes to get 100 hits.  Let’s break out the algebra.

19/20 = 100/x >>> 19x = 100*20 >>> 19x = 2000 >>> x = 2000/19 >>> x = 105.26 swings

Now if we get 1.5 lightning strikes in 100 hits which is the same as 105.26 swings we need to know how much damage that is.  1.5 strikes * 610 damage = 915 damage.  That gives us 915 damage per 105.26 swings or 915/105.26 damage per swing = 8.69 damage per swing.  Note here that this calculation must be redone if the chance to hit changes.  Let’s redo the calculation assuming that we only hit on a roll of 6 or better.  This would mean we get 15 hits in 20 swings.

15/20 = 100/x >>> 15x = 100*20 >>> 15x = 2000 >>> x = 2000/15 >>> x = 133.33 swings

915/133.33 damage per swing = 6.86 damage per swing.

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).

*actually this is a natural 20 that is confirmed as a critical hit.  This is commonly referred to as a vorpal strike.  Remember though that we are assuming that all critical hits are confirmed.

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