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Building Blocks 15: Weapon Comparisons 14

Calculating Weapon Damage pt 14: Fortification

Fortification is hopefully a concept most players will be aware of.  Simply put, fortification is a defense that represents the ability to resist critical hit (and sneak attack) damage.  As we have seen throughout these segments critical hits not only add a significant amount of damage but do so in a way that creates a damage spike.  For a player, fortification is not just important because of the basic increase in damage, but because of these damage spikes which are sometimes, particularly for new players more damage than a player has hit points.  Even if this is not the case these spikes can be significant.

Fortification is expressed as a percentile which represents how often any critical hit will be negated.  Players typically opt for 100% fortification and warforged characters get a stacking base fortification of +25%.  Monsters have slightly more varied fortification values.  Some creature types (undead, constructs, and elementals being the most prominent) are more or less immune to critical hits and have higher fortification values usually exceeding 100%.  Most other basic monsters do not have any fortification, but most raid bosses (especially epic versions) have some amount of fortification, though even epic raid bosses typically do not exceed 80% fortification.

There are several ways to reduce a monsters fortification.  The feats improved sunder and opportunist (rogue only) as well as weapon magical abilities destruction and improved destruction reduce fortification to any target.  Some other magical weapon properties also reduce fortification, but can be creature type specific.

It’s also worth noting that weapon burst, blast and vorpal effects do still go off even if the target negates the critical hit through fortification.  It is the first floaty number (weapon damage+xE+xD+yS) that is affected.  None of these values is multiplied on a critical hit.

So how do we calculate fortification?  The short version is that we need to have a sample size that includes 100 hits that are critical threats.  Then we would turn a percentage of those threats into normal hits and account for the change in damage.  The problem here is that we need to also maintain our critical threat ranges and how often critical hits occur.  Now we need a ratio of swings per critical hits and things will start getting messy.

Let’s start by calculating weapon damage for 0% and 100% fortification.  This is easy, all critical hits are either successful (0%) or negated (100%).  If all critical hits are successful, well that’s what we’ve already been assuming so our weapon calculations are the same as before.  So let’s calculate weapon damage without critical hits.

Min 2 Falchion 100% 0%
2d6+5 11.4 15
[D] 0.95 1.25
[S] 0 0.6
Holy 6.65 6.65
Acid burst 4.975 4.975
Acid blast 2.35 2.35
Slicing 2.375 2.375
Totals (w/o [D] & [S]) 27.75 31.35
.
Epic Antique Greataxe 100% 0%
3d10+6 21.375 25.875
[D] 0.95 1.15
[S] 0 0.3
Righteousness 1.9 2.3
Force burst 4.425 4.425
Totals (w/o [D] & [S]) 27.7 32.6
.
+5 Holy burst Gbane 100% 0%
2d4+5 9.5 12.5
[D] 0.95 1.25
[S] 0 0.6
Holy burst 9.8 9.8
Greater bane 12.825 13.725
Totals (w/o [D] & [S]) 32.125 36.025
.
Lit 2 Falchion 100% 0%
2d6+5 11.4 15
[D] 0.95 1.25
[S] 0 0.6
Holy 6.65 6.65
Electric burst 4.975 4.975
Electric blast 2.35 2.35
Lightning strike 8.6925 8.6925
Totals (w/o [D] & [S]) 34.0675 37.6675
.
+5 Holy burst (vorpal) 100% 0%
2d4+5 9.5 12.5
[D] 0.95 1.25
[S] 0 0.6
Holy burst 9.8 9.8
Vorpal bane 18.3 18.3
Totals (w/o [D] & [S]) 37.6 40.6
.
Epic Sword of Shadows 100% 0%
5d6+10 26.125 42.625
[D] 0.95 1.55
[S] 0 0.9

Notice that for 100% fortification that the eSoS is now the worst weapon to use because all of its damage is affected by the fortification.  Also, at 100% fortification each weapon has the same values for D and S.

Now we need to consider the in between values of fortification.  As I said before, a straight forward calculation could be messy, so we aren’t going to do that.

Instead we are going to use the values for 100% and 0% fortification and use these as a ratio. To do this we will drastically increase our sample size, in fact, our samples will be the total damage for either 0% or 100% and we will use 100 samples.  That is to say that for every 1% of fortification we will use 1 sample of 100% fortification and for the rest of the samples (100-% fortification) we will use the 0% fortification value.  Add these 100 values together and divide by 100 for an average.  To simplify, literally, we can also reduce the sample size according to fractions.  20% for instance is 20/100 or 1/5.  That would mean we take (1*100% + 4*0%)/5 for our value.  To make my calculations easy, I will calculate 20%, 40%, 60%, and 80% for each weapon.  These are also fairly common raid boss fortifications and we can say that other fortification values will naturally be between these values giving us a decent idea of the gamut of values.

Min 2 Falchion 20% 40% 60% 80%
2d6+5 14.28 13.56 12.84 12.12
[D] 1.19 1.13 1.07 1.01
[S] 0.48 0.36 0.24 0.12
Holy 6.65 6.65 6.65 6.65
Acid burst 4.975 4.975 4.975 4.975
Acid blast 2.35 2.35 2.35 2.35
Slicing 2.375 2.375 2.375 2.375
Totals (w/o [D] & [S]) 30.63 29.91 29.19 28.47
.
Epic Antique Greataxe 20% 40% 60% 80%
3d10+6 24.975 24.075 23.175 22.275
[D] 1.11 1.07 1.03 0.99
[S] 0.24 0.18 0.12 0.06
Righteousness 2.22 2.14 2.06 1.98
Force burst 4.425 4.425 4.425 4.425
Totals (w/o [D] & [S]) 31.62 30.64 29.66 28.68
.
+5 Holy burst Gbane 20% 40% 60% 80%
2d4+5 11.9 11.3 10.7 10.1
[D] 1.19 1.13 1.07 1.01
[S] 0.48 0.36 0.24 0.12
Holy burst 9.8 9.8 9.8 9.8
Greater bane 13.545 13.365 13.185 13.005
Totals (w/o [D] & [S]) 35.245 34.465 33.685 32.905
.
Lit 2 Falchion 20% 40% 60% 80%
2d6+5 14.28 13.56 12.84 12.12
[D] 1.19 1.13 1.07 1.01
[S] 0.48 0.36 0.24 0.12
Holy 6.65 6.65 6.65 6.65
Electric burst 4.975 4.975 4.975 4.975
Electric blast 2.35 2.35 2.35 2.35
Lightning strike 8.6925 8.6925 8.6925 8.6925
Totals (w/o [D] & [S]) 36.9475 36.2275 35.5075 34.7875
.
+5 Holy burst (vorpal) 20% 40% 60% 80%
2d4+5 11.9 11.3 10.7 10.1
[D] 1.19 1.13 1.07 1.01
[S] 0.48 0.36 0.24 0.12
Holy burst 9.8 9.8 9.8 9.8
Vorpal bane 18.3 18.3 18.3 18.3
Totals (w/o [D] & [S]) 40 39.4 38.8 38.2
.
Epic Sword of Shadows 20% 40% 60% 80%
5d6+10 39.325 36.025 32.725 29.425
[D] 1.43 1.31 1.19 1.07
[S] 0.72 0.54 0.36 0.18

As we should expect each weapon’s D value closes in on the 100% value of 0.95 and S approaches 0 in the same manner.  You may also notice that they do so in a linear fashion, that is to say the reduction is spread out evenly.

We can look at this and see how fortification affects weapons with a higher crit value (or if you prefer to think of it this way weapons with a higher value of D) much more than weapons with lower values.

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).