Keen & Improved Critical, Part 2



There has been some discussion of my numbers and analysis in my original rant on this subject. Let's take an absolutely basic approach and just compare the longsword to the rapier. This table shows all of the math involved for Strength values between 10 and 30.





" 1x Str Bonus " is just the normal Strength bonus to damage for that Strength.

" is just the normal Strength bonus to damage for that Strength. " Crit Rate " is the rate of crits for that weapon (longsword = 19-20 = 10%, rapier = 18-20 = 15%)

" is the rate of crits for that weapon (longsword = 19-20 = 10%, rapier = 18-20 = 15%) " Ave Die Damage " is the average damage of the base die (longsword = 1d8 = 4.5, rapier = 1d6 = 3.5).

" is the average damage of the base die (longsword = 1d8 = 4.5, rapier = 1d6 = 3.5). " Die Damage +1x Str " is Ave Die Damage + 1x Str Bonus

" is Ave Die Damage + 1x Str Bonus " Crit Bonus Damage (100% confirmed) " is the average crit damage (which = "Die Damage +1x Str") times the Crit Rate of the weapon. In other words, if your crit rate is 10% (one in ten hits is a crit) and the average crit damage is 10 points, those 10 points averaged over all 10 hits equals +1 point per hit. This assumes you always confirm your critical hits ; in other words, it's the ideal situation for the critseeking player. In situations where you're not always able to crit, your Crit Bonus Damage will reflect that (the next three columns -- 75%, 50%, and 25% -- represent that).

" is the average crit damage (which = "Die Damage +1x Str") times the Crit Rate of the weapon. In other words, if your crit rate is 10% (one in ten hits is a crit) and the average crit damage is 10 points, those 10 points averaged over all 10 hits equals +1 point per hit. ; in other words, it's the ideal situation for the critseeking player. In situations where you're not always able to crit, your Crit Bonus Damage will reflect that (the next three columns -- 75%, 50%, and 25% -- represent that). Note that because your iterative attacks are each 5 points worse than the previous attack (+10/+5/+0, for example), the 75%, 50%, and 25% columns reflect that reduced chance of confirming exactly, assuming that your primary attack has a 100% chance of confirming the crit.



Note that you can't really be in a situation where you have a 100% chance to crit because a roll of 1 on a d20 always misses, but in an idealized example we can ignore that small chance of failure to make our tables cleaner.

The columns then repeat similar data except that it's based on using the weapon two-handed, and thus getting x1.5 Str Bonus.

Table 1: Comparative Possible Damage Modifiers for Crits in Longswords and Rapiers

Weapon Str 1x Str Bonus Crit Rate Ave Die Damage Die Damage + 1x Str Crit Bonus Damage (100% confirmed) Crit Bonus Damage (75% confirmed) Crit Bonus Damage (50% confirmed) Crit Bonus Damage (25% confirmed) 1.5x Str Bonus Die Damage + 1.5x Str Crit Bonus Damage (100% confirmed) Crit Bonus Damage (75% confirmed) Crit Bonus Damage (50% confirmed) Crit Bonus Damage (25% confirmed) Longsword 10 0 10% 4.5 4.5 0.45 0.3375 0.225 0.1125 0 4.5 0.45 0.3375 0.225 0.1125 Rapier 10 0 15% 3.5 3.5 0.525 0.39375 0.2625 0.13125 0 3.5 0.525 0.39375 0.2625 0.13125 Longsword 12 1 10% 4.5 5.5 0.55 0.4125 0.275 0.1375 1 5.5 0.55 0.4125 0.275 0.1375 Rapier 12 1 15% 3.5 4.5 0.675 0.50625 0.3375 0.16875 1 4.5 0.675 0.50625 0.3375 0.16875 Longsword 14 2 10% 4.5 6.5 0.65 0.4875 0.325 0.1625 3 7.5 0.75 0.5625 0.375 0.1875 Rapier 14 2 15% 3.5 5.5 0.825 0.61875 0.4125 0.20625 3 6.5 0.975 0.73125 0.4875 0.24375 Longsword 16 3 10% 4.5 7.5 0.75 0.5625 0.375 0.1875 4 8.5 0.85 0.6375 0.425 0.2125 Rapier 16 3 15% 3.5 6.5 0.975 0.73125 0.4875 0.24375 4 7.5 1.125 0.84375 0.5625 0.28125 Longsword 18 4 10% 4.5 8.5 0.85 0.6375 0.425 0.2125 6 10.5 1.05 0.7875 0.525 0.2625 Rapier 18 4 15% 3.5 7.5 1.125 0.84375 0.5625 0.28125 6 9.5 1.425 1.06875 0.7125 0.35625 Longsword 20 5 10% 4.5 9.5 0.95 0.7125 0.475 0.2375 7 11.5 1.15 0.8625 0.575 0.2875 Rapier 20 5 15% 3.5 8.5 1.275 0.95625 0.6375 0.31875 7 10.5 1.575 1.18125 0.7875 0.39375 Longsword 22 6 10% 4.5 10.5 1.05 0.7875 0.525 0.2625 9 13.5 1.35 1.0125 0.675 0.3375 Rapier 22 6 15% 3.5 9.5 1.425 1.06875 0.7125 0.35625 9 12.5 1.875 1.40625 0.9375 0.46875 Longsword 24 7 10% 4.5 11.5 1.15 0.8625 0.575 0.2875 10 14.5 1.45 1.0875 0.725 0.3625 Rapier 24 7 15% 3.5 10.5 1.575 1.18125 0.7875 0.39375 10 13.5 2.025 1.51875 1.0125 0.50625 Longsword 26 8 10% 4.5 12.5 1.25 0.9375 0.625 0.3125 12 16.5 1.65 1.2375 0.825 0.4125 Rapier 26 8 15% 3.5 11.5 1.725 1.29375 0.8625 0.43125 12 15.5 2.325 1.74375 1.1625 0.58125 Longsword 28 9 10% 4.5 13.5 1.35 1.0125 0.675 0.3375 13 17.5 1.75 1.3125 0.875 0.4375 Rapier 28 9 15% 3.5 12.5 1.875 1.40625 0.9375 0.46875 13 16.5 2.475 1.85625 1.2375 0.61875 Longsword 30 10 10% 4.5 14.5 1.45 1.0875 0.725 0.3625 15 19.5 1.95 1.4625 0.975 0.4875 Rapier 30 10 15% 3.5 13.5 2.025 1.51875 1.0125 0.50625 15 18.5 2.775 2.08125 1.3875 0.69375

keen

Table 2: Comparative Stacking Damage For Longsword and Rapier

Weapon Str Str 1x, With keen and

Improved Crit stacking Str 1.5x, With keen and

Improved Crit

stacking Longsword 10 5.9 5.85 Rapier 10 5.1 5.08 Longsword 12 7.2 7.15 Rapier 12 6.5 6.53 Longsword 14 8.5 9.75 Rapier 14 8.0 9.43 Longsword 16 9.8 11.05 Rapier 16 9.4 10.88 Longsword 18 11.1 13.65 Rapier 18 10.9 13.78 Longsword 20 12.4 14.95 Rapier 20 12.3 15.23 Longsword 22 13.7 17.55 Rapier 22 13.8 18.13 Longsword 24 15.0 18.85 Rapier 24 15.2 19.58 Longsword 26 16.3 21.45 Rapier 26 16.7 22.48 Longsword 28 17.6 22.75 Rapier 28 18.1 23.93 Longsword 30 18.9 25.35 Rapier 30 19.6 26.83

From Table 2 you can see that even if you let keen and Improved Crit stack, the one-handed longsword is still better than the one-handed rapier until you reach Str 24, and the two-handed longsword is still better than the two-handed rapier until you reach Str 18 (the points where the rapier starts to do better are marked in red). In other words, the rapier needs these two abilities to stack just to maintain parity (i.e., "keep up") with the longsword; both are martial weapons of the same size, and should therefore be about equal. Otherwise the longsword's +1 damage relative to the rapier means it's consistently doing more damage, and is therefore a better weapon.



Now back to Table 1.



Just by looking at the numbers, you can see that the Crit Bonus Damage (100%) doesn't average out to much ... in most cases, it's less than 2 points, and in all cases presented here it's less than 3 points. You have to think of it in these terms:



If I add keen to my weapon, I'm adding the Crit Bonus Damage (100%) to every primary attack I make with that weapon. If I take Improved Critical with that weapon, adding the Crit Bonus Damage (100%) to every primary attack I make with that weapon. If I add an energy property ( flaming , frost , shock , etc.) to my weapon, I'm adding and average 3.5 damage to every primary attack I make with that weapon. If I take Weapon Specialization with that weapon, I'm adding 2 damage to every primary attack I make with that weapon.

the energy property is better than

keen

Weapon Specialization is better than Improved Critical

And remember that we're just looking at the primary attack, where you have an optimal, 100% confirmation of crits scenario. The energy property and Weapon Specialization add the same value to every single iterative attack that hits, while it becomes harder and harder to confirm threats with your iterative attacks and therefore your added average crit damage goes down with every iterative attack.



keen

always

any

best

optimal

keen

keen

with

keen