## Building Blocks 12: Weapon Damage 11

Calculating Weapon Damage pt 11: Resistances, Immunities, and Vulnerabilities

Many monsters have resistances or even immunities to certain types of elemental damage.  We can see this in the floaty numbers when we hit a monster.  A yellow number means that some of the damage was resisted, a white 0 indicates that all of the damage has been resisted, and in some cases instead of a number we simply get an immune message.  In most cases even the lowest level of resistance of 10 will essentially negate an elemental weapon property.

To calculate resistance we can’t just subtract from our end total.  First off, an enemy can’t take negative damage, in such cases damage is reduced to 0. (Note that in some rare cases elemental damage can heal a monster – golems are a common example).  More importantly we need to take into account that many elemental weapon properties do extra damage on a critical hit and sometimes even more on a vorpal strike – though each of these extra damages is a separate item that can get hit with resistance.  Let’s consider our lightning 2 falchion for an extended example.  As a reminder here’s it’s damage profile.

 Lit 2 Falchion 2 – 14 15-16 17-18 19 20 Avg 2d6+5 12 24 24 24 24 15 [D] 1 2 2 2 2 1.25 [S] 0 2 2 2 2 0.6 Holy 7 7 7 7 7 6.65 Electric burst 3.5 9 9 9 9 4.975 Electric blast 0 5.5 5.5 5.5 19.5 2.35 Lightning strike 0 0 0 0 0 8.6925 Totals (w/o [D] & [S]) 22.5 45.5 45.5 45.5 59.5 37.6675

Let’s say that a monster has resistance of electricity 10.  Our way of displaying damage as component parts has another key function here.  We can’t just add in all the electric damage together and then apply the resistances.   It is instead applied to each component separately (you can see this displayed in the floaty numbers).  So for our electric burst and electric blast properties we need to subtract 10 damage from each hit with a minimum damage of 0.

 Lit 2 Falchion 2 – 14 15-16 17-18 19 20 Avg Electric burst 0 0 0 0 0 0 Electric blast 0 0 0 0 9.5 0.475

We can see that even a minimal 10 resistance to electricity almost completely negates these properties.  Now it’s true that this is not an entirely clear picture.*  It does not accurately reflect the probability that these abilities can do more than 10 damage per hit, particularly on weapons that have higher crit multipliers.  However, we are primarily concerned with raid bosses and typically they will have resistances higher than 10.  These numbers give us a pretty clear idea that basic weapon properties do not penetrate resistances well and will largely be negated by even the smallest resistance.  Even on a x4 weapon the most elemental damage it can do in a 1 shot elemental burst is 6+30=36.

But what about lightning strike?  This ability only procs 1.5 times in 100 hits but it does a much larger amount of damage, much higher than any resistance save complete immunity can bring.  Lets consider a resistance of 30 and see how that changes the average damage.  Remember that it takes 105.26 swings to get 100 hits and that lightning strike does an average of 610 damage per strike (20d20+400).

1.5*(610-30)/105.26 = 870/105.26 = 8.265

That compares to our old value of 8.6925.  This relatively minimal impact makes sense.  This is because the damage from lightning strike is a rare spike in damage and the resistance only applies on these rare occasions.  Similar abilities that are a spike in elemental damage are also less effected by resistances, but can still be negated by immunities.

So here’s our new table for a lightning 2 weapon against an enemy with 30 electrical resistance.

 Lit 2 Falchion Avg Old 2d6+5 15 15 [D] 1.25 1.25 [S] 0.6 0.6 Holy 6.65 6.65 Electric burst 0 4.975 Electric blast 0 2.35 Lightning strike 8.265 8.6925 Totals (w/o [D] & [S]) 29.915 37.6675

Conversely some monsters are vulnerable to certain elemental damage and take an extra 50% damage.  Unlike resistances this is far easier to calculate, just multiply any applicable damage by 1.5 (150%).  Under these circumstances the lit 2 falchion does more dps than the eSoS (45.67 and 42.625 respectively).  Extra damage is indicated by purple numbers and some class abilities can also increase a monster’s vulnerability slightly (elemental savants being the most prevalent).

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).

*If you wanted to get a very accurate idea of how resistance is affecting a weapon’s damage profile you would need to go back into the process of looking at damage dice.  To do this we would need to calculate each possible combination of die rolls, subtract the resistance from each of these numbers (minimum value of 0) and then average the resulting numbers.  This gets more complicated with more dice as the combinations exponentially increase.  I will give an example of 2d10 with a resistance of 10, but I hope that you can already see that when we are calculating damage against a monster with resistance 30 basic weapon elemental damage is more or less completely negated.  The first number is the roll of the first die, the numbers after represent the first roll added to each of the possible rolls of the second (1-10).  The third set of numbers is the second set reduced by 10 for the resistance.

1: 2 3 4 5 6 7 8 9 10 11: 0.0.0.0.0.0.0.0.0.0.1

2: 3 4 5 6 7 8 9 10 11 12: 0.0.0.0.0.0.0.0.1.2

3: 4 5 6 7 8 9 10 11 12 13: 0.0.0.0.0.0.0.1.2.3

4: 5 6 7 8 9 10 11 12 13 14: 0.0.0.0.0.0.1.2.3.4

5: 6 7 8 9 10 11 12 13 14 15: 0.0.0.0.0.1.2.3.4.5

6: 7 8 9 10 11 12 13 14 15 16: 0.0.0.0.1.2.3.4.5.6

7: 8 9 10 11 12 13 14 15 16 17: 0.0.0.1.2.3.4.5.6.7

8: 9 10 11 12 13 14 15 16 17 18: 0.0.1.2.3.4.5.6.7.8

9: 10 11 12 13 14 15 16 17 18 19: 0.1.2.3.4.5.6.7.8.9

10: 11 12 13 14 15 16 17 18 19 20: 1.2.3.4.5.6.7.8.9.10

This gives us a total of 100 values with a sum value of 212 which gives us an average of 212/100=2.12 with a 10 resistance.  If we just looked at pure averages we would have 11-10=1.

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