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Howdy, ya'll. I made another big mathy blog post. This time I dived into how most of the major damage-oriented combat feats work in terms of the EDV a typical full-martial can expect. Some of my results surprised me, they might surprise you too.
LINK Feats of Fury
Just a nit, but a magus can take weapon spec once he picks up fighter training at 10th level.
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Some great analysis. Two thoughts:
1. If you can find a way to illustrate the conclusions in graphs, that would make it much better.
2. Something I've been realizing a bit recently is the value of peak damage potential. I think this is one reason why Power Attack is more valuable than EDV figures suggest (and also a reason why Holy Weapons are better than static "I could just get a +3 weapon and power attack and end up with more damage" analysis would indicate). Later in the analysis, you mention making friends with the bard, buying a green prism ioun stone, etc which I would think are all standard tactics. You could add, "get the cleric/wizard/arcanist to cast greater magic weapon on your sword, eat a hero's feast, maximize your belt of strength, get the cleric to take the heroism subdomain for the aura of heroism power, make friends with a paladin high enough level to share his smites, flank whenever you can, smile when the hunter's wolf companion knocks the enemy prone, etc."
As an example of how quickly things can add up, I played a PFS scenario the other day and in the first fight, by round 2, our bloodrager had the following bonuses: Aura of heroism from the cleric (+2 morale), haste from the arcanist (+1 haste), flank from the hunter's wolf (+4 due to a menacing amulet of mighty fists), prone enemy from the hunter's wolf (+4), and a -2 to penalty to the enemies' AC from my cleric's aura of menace. Total effective bonus to his attacks (including the AC penalty as an attack bonus): +13. When you're sitting at +13 higher than your normal baseline, you're not terribly concerned that you are taking penalties to hit. You just want to maximize your peak damage potential. Power Attack has a bigger effect on the peak damage total than, say, weapon specialization, so if you have to choose between the two, you choose Power Attack. Likewise, the analysis of the +1 Holy Weapon as, "just buy a +3 weapon and power attack" is misleading because you're going to be power attacking with the +1 Holy weapon as well and still hitting every time. The Holy Weapon is better in that situation because it increase peak damage by 2d6 rather +2.
A frostbite magus will see similar results on a normal basis. After the first hit, a foe will often (typically) be -2 dex from fatigue, -2 AC from entanglement for a typical total of -3 AC. (Possibly more if strength loss from fatigue results in medium encumbrance and limits a dex bonus). Toss in a flank and some very mild buffing (bless or prayer), and the character will fly one or two steps up your attack bonus color chart--if they were already good in that department, they probably end up in "don't roll a 1" or "how much damage can I stack on this thing anyway?" territory.
Just a nit, but a magus can take weapon spec once he picks up fighter training at 10th level.I thought about that, but decided the caveat wasn't worth the page space.
Well, except that you specifically state they can't take it, which is inorrect. It's not a caveat, it's a class feature.
Edit: whether or not it's worth a full analysis is a different point that I was not making.
Besides the fact that the Magus can take Weapon Specialization I’ve actually seen Arcane Strike mostly on Bards. I'd imagine that an Arcane Duelist with TWF who uses Arcane Strike with Inspire Courage and Dance of a Hundred Cuts could be pretty effective though I haven't seen such a PC in play yet. Perhaps I'll build an NPC like that for use as a monster.
Interesting in the abstract, though I find that depending on the class and situation, abstractions to this degree tend to fall apart. When I've run 2-hand vs. TWF comparisons on specific build concepts, the question of whether TWF is 'worth it' (even without considering resources) entirely depends on the ways in which the build can add damage - having Haste or a similar effect available also makes a huge difference in favor of two-handing, and a Haste effect is typically available one way or another.
Ranger/Slayer aside, strength-based TWF isn't all that difficult to do; you only need 17 DEX to get Improved Two-Weapon Fighting and Two-Weapon Rend, while Greater Two-Weapon Fighting for a -10 offhand is arguably not even worth the feat anyways. Again though, strength-based TWF on a Barbarian is probably going to come out fairly lousy, while on a Double Bane Inquisitor it's nuclear.
So just a tip. You spend a large amount of text to describe why your baseline is basically just bab and no class features and whatnot.
It'd convey everything you want by saying you're using the warrior NPC class. It's a generic full bab nothing else but the gear you listed guy.
Something else I just noticed and am unsure of. The Unchained monk can only use an IUS to make it's extra ki attack. So in the weapon calculations the KI increase is smaller than getting an extra attack with your weapon. Not sure if you already factored that in or not.
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I'm not sure you're rating the Improved Critical/Critical Focus feats high enough. I think they need to be weighed for the case when you have a large static bonus to damage. In particular, a smiting paladin.
Imagine the paladin smiting with a nodachi and adding 2H Strength, Power Attack, Bonded Weapon and Smite damage. Expanding the crit range to 15-20/x2 or increasing the likelihood of confirming a hit on an iterative attack with Critical Focus becomes more attractive. Given that you can make the BAB +9 prerequisites, you're getting at least a +9 damage from both Power Attack and Smite. If you're threatening a crit on the first Smite-hit against an undead, fiend or dragon, your Smite bonus damage is already doubled and confirming that crit becomes really interesting. Given that it's your first hit, it's also likely that you won't be wasting the damage on overkill.
Also, I think Staggering Critical shouldn't be underrated; even on a succesful save the enemy is staggered for a round, and therefore can't full attack back. That gives you great odds to win out an HP race.
On vital strike: you choose a Large impact +2 greatsword as weapon to test the feat. Problem is, barring a few very niche archetypes you can't wield that. Better do this with a Large impact +2 bastard sword held 2 handed (but still a one handed weapon, note you need exotic weapon proficency to wield it). It's a 3d8 dmg weapon becoming 4d8 if your character somehow grows to large size so vital striking with it would cause you to roll 8d8/12d8/16d8 while large. The main concern here is you can't charge and vital strike UNLESS you are a CN barbarian or fighter worshipping Gorum AND wielding a greatsword (Gorum's Swordsmanship).
Edit: also consider how power attack and furious focus interact with each others and vital strike.
I'm not sure you're rating the Improved Critical/Critical Focus feats high enough. I think they need to be weighed for the case when you have a large static bonus to damage. In particular, a smiting paladin.
Imagine the paladin smiting with a nodachi and adding 2H Strength, Power Attack, Bonded Weapon and Smite damage. Expanding the crit range to 15-20/x2 or increasing the likelihood of confirming a hit on an iterative attack with Critical Focus becomes more attractive. Given that you can make the BAB +9 prerequisites, you're getting at least a +9 damage from both Power Attack and Smite. If you're threatening a crit on the first Smite-hit against an undead, fiend or dragon, your Smite bonus damage is already doubled and confirming that crit becomes really interesting. Given that it's your first hit, it's also likely that you won't be wasting the damage on overkill.
Also, I think Staggering Critical shouldn't be underrated; even on a succesful save the enemy is staggered for a round, and therefore can't full attack back. That gives you great odds to win out an HP race.
The numbers would be the same wouldn't they? You'd still be doing X% more damage on a crit, regardless of if the base is 10 or 50. It's up to the user to see the X% and realize that it does more the more damage base you have.
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I'm not sure you're rating the Improved Critical/Critical Focus feats high enough. I think they need to be weighed for the case when you have a large static bonus to damage. In particular, a smiting paladin.
Imagine the paladin smiting with a nodachi and adding 2H Strength, Power Attack, Bonded Weapon and Smite damage. Expanding the crit range to 15-20/x2 or increasing the likelihood of confirming a hit on an iterative attack with Critical Focus becomes more attractive. Given that you can make the BAB +9 prerequisites, you're getting at least a +9 damage from both Power Attack and Smite. If you're threatening a crit on the first Smite-hit against an undead, fiend or dragon, your Smite bonus damage is already doubled and confirming that crit becomes really interesting. Given that it's your first hit, it's also likely that you won't be wasting the damage on overkill.
Also, I think Staggering Critical shouldn't be underrated; even on a succesful save the enemy is staggered for a round, and therefore can't full attack back. That gives you great odds to win out an HP race.
Critical focus is rated exactly correctly. It's a feat tax that provides a gateway to the status effect on critical feats. Staggering critical et al look like great feats, but in many cases they will suffer from the same thing my frostbite magus does--the dead condition overriding all the others. "I hit for 15 points of damage, 12 points of non-lethal (low level magus) and the target is fatigued, entangled, and does a 22 succeed in intimidating him?" "There's nothing left to intimidate." If the smiting paladin in your scenario lands his 95 damage crit, there's a very good chance the target will be dead rather than staggered. In theory, critical rider feats should be at their best on characters with high crit chance but relatively low damage crits such as a twin kukri ranger or slayer rather than a smiting paladin with a nodachi or greatsword.
Improved critical is one of those feats that really benefits from a chart to see how it compares, however, I don't think that the average damage boost from Improved Critical is as valuable as damage boosts that apply on every attack like Power Attack, Deadly Aim, and Weapon Specialization because it is unpredictable and has a tendency to be a "win more" ability. It alway feels good to land a 150 damage crit, but when the dice are rolling your way, there is a good chance that you are going to win anyway. Feats and abilities that still help even when the dice are against you are IMO more valuable than the averages indicate.
Improved critical is one of those feats that really benefits from a chart to see how it compares, however, I don't think that the average damage boost from Improved Critical is as valuable as damage boosts that apply on every attack like Power Attack, Deadly Aim, and Weapon Specialization because it is unpredictable and has a tendency to be a "win more" ability. It alway feels good to land a 150 damage crit, but when the dice are rolling your way, there is a good chance that you are going to win anyway. Feats and abilities that still help even when the dice are against you are IMO more valuable than the averages indicate.
If you wield a high-crit weapon and have a 75% chance to confirm critical hits, crits add 11.25% to your average damage. Improved Critical will add another 11.25% average damage on top of that. So if you deal at least 20 damage with an attack, Improved Critical brings in more average damage than Weapon Specialization.
Sure, there are situations where you don't need to score a critical. There are also situations where scoring a critical is a huge advantage, like one-shotting on an AoO or scoring a crit after blowing your first attack. Statistically, anything that's "win more" is also potentially "lose less", or sometimes "didn't lose after all".
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Improved critical is one of those feats that really benefits from a chart to see how it compares, however, I don't think that the average damage boost from Improved Critical is as valuable as damage boosts that apply on every attack like Power Attack, Deadly Aim, and Weapon Specialization because it is unpredictable and has a tendency to be a "win more" ability. It alway feels good to land a 150 damage crit, but when the dice are rolling your way, there is a good chance that you are going to win anyway. Feats and abilities that still help even when the dice are against you are IMO more valuable than the averages indicate.If you wield a high-crit weapon and have a 75% chance to confirm critical hits, crits add 11.25% to your average damage. Improved Critical will add another 11.25% average damage on top of that. So if you deal at least 20 damage with an attack, Improved Critical brings in more average damage than Weapon Specialization.
Sure, there are situations where you don't need to score a critical. There are also situations where scoring a critical is a huge advantage, like one-shotting on an AoO or scoring a crit after blowing your first attack. Statistically, anything that's "win more" is also potentially "lose less", or sometimes "didn't lose after all".
Not at all. Some abilities that are win more can have no impact at all on lose less or didn't lose at all. For example, imagine a feat that only worked on x4 crit weapons and increased the crit multiplier to x7. It would improve your average damage but in nearly all situations, a X4 crit from an effective character is going to kill the target just as dead as a x7 crit. Sure, having that x7 crit will improve average damage calculations but it will not make a significant improvement on the character's combat effectiveness. Such an ability would manage to be "win more" without being "lose less" or "didn't lose at all."
Average damage is a convenient statistic that is relatively easy to calculate and often (but not always) correlates with a character's combat effectiveness. However, average damage and combat effectiveness are not the same thing and critical damage is one of those situations where it is possible that the increase in average damage is not an accurate measurement of the increase in combat effectiveness. Use of Power Attack is another such situation. There are a number of situations where using Power Attack will increase average damage but decrease combat effectiveness and also situations where using Power Attack will decrease average damage but increase combat effectiveness.
Now if you want a mathematical demonstration, you will have to dig into discrete probabilities in specific scenarios which is a pain. There is a good reason that most comparisons use average damage: it's easier and more universal. But it can be misleading as the following example demonstrates:
A. Orcs per round. Attacker has a 75% chance to hit an orc (who has 25 hp) and does either (1) 1d12+18 (20/x3) or (2) 1d12+16 (19-20/x3).
(1) drops an orc 50% of the time on the 1st non-critical hit and 100% of the time on the second. A confirmed critical (3.75% chance) drops an orc 100% of the time. Total chance of dropping a fresh orc 39.375% Average damage: 20.2125
(2) drops an orc 33% of the time on the 1st non-critical hit and 100% of the time on the second. A confirmed critical (7.5% chance) drops an orc 100% of the time. Total chance of dropping a fresh orc: 33.075% Average Damage: 20.25
In this scenario, attacker (2) with Improved Critical but not weapon specialization has a very minor advantage in average damage per attack due to Improved Critical but is actually going to kill the orcs noticeably more slowly than attacker (1) with Weapon Specialization.
B. Death or Glory! Attacker still has a 75% chance to hit, but this time it's a dragon who has 20 hp remaining. For the purpose of this scenario, the dragon is guaranteed to kill the attacker if the attacker misses or does hits but does not kill the dragon. Since it's a dragon and they rely on lots of mediocre hits to do big damage, we'll assume that staggering the dragon (at 0 exactly) is also a win. The dragon probably drops the attacker to negatives but doesn't kill him and the attacker whether (1) or (2) is stabilized by his companions.
(1) has a 83% chance to kill the dragon on a normal hit and a guaranteed kill if he crits. He has an 8.3% chance to stagger the dragon on a hit. That's about a 69% chance of survival/victory if he stays to slug it out with the dragon.
(2) has a 67% chance to kill the dragon on a normal hit and a guaranteed kill if he crits. He has an 8.5% chance to stagger the dragon on a hit. That's about a 56% chance of survival/victory if he stays to slug it out with the dragon.
Again, (2) has a higher average damage per attack but has a lower chance of defeating the dragon.
More to the point, when the fighter/barbarian/whatever is making his decision to stick around and slug it out or withdraw, is he going to figure on hit crit damage or his base damage? If he needs a crit to take out the dragon, he needs to withdraw whether he threatens on 15-20, 17-20, 18-20, or 19-20. It is the character's base damage and chance to hit that drive the tactical decision and crits shouldn't come into it. Crits can make a big difference in a fight, but they don't come when you plan them (unless you have an ability that makes it happen--then it's a whole different kettle of fish), so they are not able to drive tactical decision-making in the same way that predictable abilities do. That is a disadvantage of critical based damage that is not captured in average damage calculations but needs to figure in your mind when you weigh how valuable crit increasing abilities are.
I'll certainly grant that with something like a scythe critical hits tend to draw unnecessary overkill, though even then the corollary is that one has the capability of one-shotting even extremely tough targets.
Generally though, for every scenario that can be posted about the uselessness of overkill, one could be posted about the problems with underkill. Particularly for a high-threat, x2 weapon, the variability really isn't as wild as it may seem. 'Gambling' on a 30% threat weapon scoring a crit over three attacks isn't really different from 'gambling' that those iterative attacks will land in the first place.
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Let's have a look at the probabilities:
Let's run with the 75% hit rate and assume the third attack is a haste attack, so the probability for hits runs 75%/75%/50%.
At least one crit is 1-((.7+.25*.3)^2*(.7+.5*.3))= 48.95% (up from 27.14% if you don't have improved crit)
All three hits is .75*.75*.5=28.125%
At least two hits is pretty likely .75*.75*.5 (hit hit hit)+.75*.25*.5 (hit miss hit)+.25*.75*.5 (miss hit, hit)+.75*.75*.5 (hit hit miss) = 75%.
and I think the expected number of hits (counting a crit as two hits) is probably somewhere around 2 and a half but I'm not inclined to try to figure out the exact math right now.
If you're talking full iteratives, it's 75%/50%/25% and the odds of at least one confirmed critical with 15-20 range are 26.3% while the odds of at least two hits over a full attack are 50%.
Obviously, it's going to be better to have improved critical than to not have improved critical, but you usually have to take Improved Critical or something else and if you're in a situation where a little more base damage improves your expected hits to kill figure from two to one or from three to two, I expect that makes more of a difference to your decision tree than improved critical. If you need one hit, it's almost guaranteed. Two hits is likely but a gamble. Three hits (including crits) is not terribly likely but you could get lucky. Improving your odds of getting three (effective) hits does not impact the tactical situation as much as changing the math so that you only need two hits instead of three.
This is the same reason that Power Attack may be more or less combat effective than average damage numbers indicate.
Either way, my main point is that it is important to realize the limitations of average damage calculations: they are indicators of combat effectiveness, but can be misleading in certain comparisons--especially when comparing the most advantageous ratio of attack bonus to damage or the value of extended critical ranges and multipliers.
--EDIT--
I figured out that it's not actually that hard to calculate the odds of getting one or fewer hits and no crits on the full iterative 75/50/25 attack with a 15-20 or 18-20 crit range.
It's 42.8% if you do not have improved crit and goes 36.8% if you do have the expanded crit range. So the odds getting two hits worth of damage on a full iterative attack are about 57% without improved crit and 63% with improved crit.
Again, it's obviously better to have improved crit than not to have it, but anything that changes the math so that you need one hit rather than two is likely a much bigger deal since you have a 90.6% chance of scoring at least one hit's worth of damage over those three attacks. If you can get there with -3 to hit from Power Attack, that gives you a 76.6% chance of getting the damage you need.