Yes and most of the time you can do better things than vital strike - even with standard actions.
I did some thinking on the math.
*Disclaimer":
1. All calculations are under the assumption that you can hit your full threat range. If you don't things change. This does matter at higher levels because you might not hit with a keen rapier on 14 using iterative attacks/power attack/combat expertise.
2. I'm really tired at the moment, I probably made some mistakes.
19-20/x2=20/x3 is true.
Reason:
19-20/x2 adds 2 events with a chance to confirm adding (base+bonus) damage while 20/x3 as one event with the same chance to confirm adding 2*(base+bonus) damage. For this type of random event it does not matter where the factor 2 shows up (because you multiply the occurences and chances, multiplication is commutative).
For the same reason: 15-20/x2=19-20/x4 power critical (critical focus) does not change this either (but you have to take into account that you may not hit on a 14 with iterative attacks at this stage of the game). The Feats that make a difference here are those that apply static crit effects.
On the Falcata: The calculation above shows that Falcata/Rapier damage ratio is only slightly better then Longsword/Bastardsword damage ratio (1.3 without feats 1.6 with improved crit, 1.84 if you add power crit on top). The rapier has a better range to apply static crit effects. On the other hand (again) you might not hit on 14.
Now for the Falchion vs Greatsword:
Umm, crit factor of Falchion is 0.3 and the one of Greatsword is 0.2
So you deal 1.2 vs 1.3 times basedamage.
If both weapons are enlarged the difference in damage is 1d6, 3.5 damage. As far as the factor of the falchion is 0.1 higher (1.3/1.2) you need about 35 basedamage to make up for the 1d6.
Ok, when not large the difference is only 2 - idk why I considered them being large. Then they are equal at +20 basedamage.
Is there math on this?DPH= average damage * ToHit * (1 + (1-multiplier) * ToCrit) assuming that anything in your threat range hits (which it usually does). So every 1 higher in range adds 5% (like wise for a 20xX weapon every 1 higher of multiplier above 1 adds 5%).
Now assuming improved critical or keen and no vital strike we get 15-20 => 30% and 17-20 => 20%, so if (7+X)*1.2<(5+X)*1.3 it makes sense to switch to Falchion. So at 0.1*X=1.2*7-1.3*5, X=19. So, including the base damage from the Greatsword the crossover point is at 26 points of damage.
[edit]Sorry, my calculations were wrong.
About the scrythe: It has the same crit math as the falchion (reason: see first part of the post) so you do need the same bonus in base damage.
[edit]There is no 14-20/x2, it should have been 15-20/x2
Your math is wrong.
And what is power critical?
Your math is wrong.
And what is power critical?
You can't just state it's wrong, you have to show it.
Power critical=critical focus (from D&D/NWN days).
Because the number of confirmation rolls does not change the average damage at all.
And you cannot have 14-20/x2
Because the number of confirmation rolls does not change the average damage at all.
And you cannot have 14-20/x2
Hmm... just checked again, you're right, it's 15-20/x2
And I just saw my calculations are messed up as well since I added up the base damage of the greatsword for all possibilites while keeping the possibility for a single roll with the falchion :(
Ok, I redid my calculations. I assume you roll 20 times (easier to calculate that way since every to hit roll will have occurred once by then) and sum up all the damage both weapons do over the complete possibility tree.
a=chance to hit (0.9>=a>0, 0.05|a )
b=chance to confirm the critical you roll on 17 with falchion
c=extra damage for the greatsowrd in all possibilites
d=damage bonuses needed to outshine the greatsword
b=a (<- low probability to score [b]more[b] crits then the greatsword making the damage bonus required high)
c=2*20a+2*2*a (2*20*a=base extra damage over the tree, 2*2*a=extra base damage for crit chance with the greatsword)
(d+5)*b=c (5=avarage base damage of falchion)
<=> d=c/b-5
<=> d=39
@Wasum: As you can see, the extra damage needed is not dependent on the chance to hit and thus not dependent on your chance to confirm crits.
It makes sense to calculate this way if you want to know how things go with power crit. You will end up with a bonus damage value needed that is dependent on your chance to hit.
I'm sure something like this has been done multiple times. One really good example is here. essentially, as long as the attacker can deal above 20 points of base damage, the larger threat range weapon will deal more avg. damage. As in the falchion, especially it's keen ( as it widens the gap between the falchion and greats word), vs the greatsword threat ranges.
I'm sure something like this has been done multiple times. One really good example is here. essentially, as long as the attacker can deal above 20 points of base damage, the larger threat range weapon will deal more avg. damage. As in the falchion, especially it's keen ( as it widens the gap between the falchion and greats word), vs the greatsword threat ranges.
There seems to be an error in that example, 18-20/x2 should be the same as 20/x4, (just like 19-20/x2=20/x3)
Hmm, is it not? I haven't checked it recently though on the math, or even the error.. Even still, of the growing threat range, or higher crit match up as you point out, then even so, the base damage has to b roughly near what had been mentioned, of base 20 damage before it pulls in favor of the higher threat range weapon.
Edit: just checked the site. A LOT was removed. There were pages of math and calculations for figuring out the numbers. Guess the author removed all but the meat & potatoes. Still, of the calculations they did were right, even if the 20/x4= 18-20/x2 seem to follow the pattern as the lower range and crit weapons of 19-20/x2= 20/x3, the numbers there seem to show otherwise. The difference between the 20/x4= 18-20/x2 calculations seems to be an avg. DPR of .5 dmg, in favor of the higher threat range weapon.
Hmm, is it not? I haven't checked it recently though on the math, or even the error.. Even still, of the growing threat range, or higher crit match up as you point out, then even so, the base damage has to b roughly near what had been mentioned, of base 20 damage before it pulls in favor of the higher threat range weapon.
Yes, it should be roughly 20 base damage bonus for 1 point of weapon base damage, about 10 base damage with improved crit (more if you do not hit your threat range, may happen with 15-20/x2), slightly less (depending on hit chance, I'd say approximately 2 less) with crit focus.
I got to do something else now, maybe if I find the time to calculate it accurately. There is a formula where you input avarage base damage and crit class of two weapons in and get the required bonus damage out.
Falcata is clearly the best crit weapon (not considering static crit feats) since 19-20/x3=20/x5
Except the falcata is 1 handed, so less damage than a 2 handed, and it's exotic, which many classes and builds don't want to waste feats/ traits for. But in that regard, yes it's the best, otherwise for everyday martial weapon, it's the falchion at 18-20/x2.
My thoughts are as they have been: high multiplier favors the underdog and gives large swings, while a high crit range favors the stronger and smooths the curves out more.
That's why enemies with high multiplier weapons always terrify me ): They typically have a small sample size of attacks, but a single crit can EASILY be a PC kill. I'm sure this is one reason orcs in 3.5 were changed to have falchions. In 3.0 they had greataxes and I'm *sure* they killed many a PC ):
|
| 1 person marked this as a favorite. |
@Silent Saturn: you can calculate average damage per hit to seewhich weapon fits best. And therefor, yes, multiplier matters.
I'm fully aware that you can calculate average damage per hit. I'm not claiming that the multiplier doesn't matter. I'm claiming that it doesn't matter ENOUGH.
|
Yeah, I have a serious love for earth breakers. And a soft spot for the thundering weapon property on them. Just to make the crits feel especially fun!The Earthbreaker is the best weapon.I tend not to worry too much about a weapon's crit multiplier when I choose a weapon, since at best crits are unpredictable and there's always the possibility of rolling 1's on the damage dice.
There's other factors to look at. The weapon's base damage dice, any special qualities it has, what type of damage it deals, and most importantly-- whether or not you think you'd have fun wielding it!
I like you. We can be friends.
One thing I haven't seen mentioned yet which can be a point in favor of higher crit multipliers is that there are a couple (admittedly high-level) archetypes features and class abilities that allow someone to cause an automatic critical threat. Those could get downright brutal with an x4 crit weapon.
One thing I haven't seen mentioned yet which can be a point in favor of higher crit multipliers is that there are a couple (admittedly high-level) archetypes features and class abilities that allow someone to cause an automatic critical threat. Those could get downright brutal with an x4 crit weapon.
Yeah in the case where you can guarantee a crit (or greatly increase the chance that a single threat will crit), the 3x/4x weapons are superior. In fact, many people point to the level 20 fighter ability and claim it is better for falchions. It's actually best when crits happen less frequently (you REALLY want them to confirm) and hit harder. If you have a larger sample size of crits, it becomes less important if they confirm because they deal less damage.
Let's say I have 2 crits in one combat with a greatsword and 1 crit with a scythe. If I don't have one crit confirmed from the greatsword, oh well, it only gave me 1 extra attack worth of damage. If I don't confirm with the scythe, I lose out on 3 additional attacks worth of damage. So it's 3 times more important for me to confirm that scythe crit than with the greatsword.
But waiting for a capstone ability to do this is a bit silly |: The barbarian Mighty Swing ability is pretty good for this, but level 12 is quite a distance to go for some people. Most people would prefer to have more consistency with the early-level crits than inconsistent massive crits.
Interesting discussion.
But of course, if you are advocating the Falchion, wouldn't you prefer the Nodachi? It does 1d10 instead of 2d4 and has the same threat range.
Peet
Interesting discussion.
But of course, if you are advocating the Falchion, wouldn't you prefer the Nodachi? It does 1d10 instead of 2d4 and has the same threat range.
Peet
If your GM will allow it, yes, it's a superior sword to the falchion in practically every way |:
+ .5 additional damage
+ brace property
+ slashing OR piercing damage
same weight
- 5 extra gold (who cares?)
I tried to determine if it was considered a hafted weapon, but I can't really tell one way or another. I would assume it isn't |:
It does not matter at all how often you have to confirm a critical hit. Even if you had to confirm every single point of damage, rolling 30+ dice the average outcome would not change.
Why would the Nodachi be disallowed?
Some GMs dont allow Oriental weapons.
|
One thing I haven't seen mentioned yet which can be a point in favor of higher crit multipliers is that there are a couple (admittedly high-level) archetypes features and class abilities that allow someone to cause an automatic critical threat. Those could get downright brutal with an x4 crit weapon.
There's also the Teamwork feat "Outflank". Not only does that increase your flanking to hit bonus from +2 to +4, it gives your flanking buddy an AoO whenever you score a critical hit.
This works out pretty well for our Monk/Rogue strike team. If the monk scores a critical hit, there's a fair chance that the rogue will succeed with the AoO (dealing sneak damage as well!). And if the rogue gets a threat (18-20 with a rapier) and confirms (quite likely with a +4 flanking bonus, especially if the monk succeeded in tripping the enemy) the monk can add his small contribution (and, with combat reflexes, can even do it every time the rogue scores a critical).
Bless weapon Vs. evil enemies, auto crit hit. Fighters capstone ability, of increasing the multiplier, and auto crit.
|
Bless weapon Vs. evil enemies, auto crit hit. Fighters capstone ability, of increasing the multiplier, and auto crit.
I'm not sure what you mean. It could be:-
• each hit vs. an evil foe with a weapon so blessed is automatically a threat (not true)• each threat vs. an evil foe with a weapon so blessed is automatically confirmed (true)
Why would the Nodachi be disallowed?
Why should a weapon do more damage just because the are invented by far eastern cultures? I just do not understand the hype about japanese weapons and samurai, they were just sabers and knights.
|
Golarion is filled with Tian people, and many are prominent NPCs in several Adventure Paths.
The Dragon Empires is basically a mesh of Asian cultures and suddenly deciding it does not exist is a bit weird.
Nobody is "hyping" Asian weapons, but simply pointing out one good one.
A Nodachi is no more out of place than an Elvish Curve blade, Barbazu Beard, or Piston Maul.
I enjoy the x3 weapons.
Everyone at the table loves screaming KABOOM when someone lands one on an enemy (including me)
Why would the Nodachi be disallowed?Why should a weapon do more damage just because the are invented by far eastern cultures? I just do not understand the hype about japanese weapons and samurai, they were just sabers and knights.
Kinda have to agree. Some of the Eastern weapons (Like the Nodachi) are just so much better than anything else that it carries a whiff of fanboyism.
Oh it's not fanboyism if its true! ^_^
Wonder whether Japanese are like that about Longswords and Greataxes as well:O
Although a sweeping generalization that loses accuracy relative to its volume I'd say on the large, no. Asians do like claymores and english longswords but most often in the form of putting them up against katanas in an effort to prove they believe the katana is better.
The percentage of japanese people who believe the finest crafted scottish claymore would be prefereable to a mastercrafted tamahagane katana is likely pretty low. Especially for the asian body type. Not that the anime community doesnt have a thing for giant spatula blades, but in terms of real world comparisons I believe they stand strongly on the side of prefering katanas.
Same cant be said for america or china though. I don't believe america has a distinct preference between english and asian blades or at least the preference isnt as pronounced. Perhaps there are more martial arts fans than larpers which could create a distinct sway here in the states... Only to be slightly offset by the renaissance festival weaponsmiths who make claymores out of lawnmower blades, which depending on what your goal is will certainly produce a resilient if not comically flexible blade that could barely be considered traditional european....
And china of course probably holds the belief that 'made in china' means superior out of hand but i'd be interested in seeing what the demographic layout of preference in china *really is*...
It's all theoretical, but I believe the Japanese largely agree that katanas are superior to english longswords and claymores unless the person wielding it is a cartoon character.
I think you'd even be hard pressed to find a japanese person who'd choose a fencing sword over a katana though there's a very legitimate argument to be made that a fencer could hold his own against a samurai.
Personally I come down on the side of katanas. I've got a Paul Chen Tiger Katana myself. 45" total length so longer than the cas ibera musashi blade. Paul Chen is one of the few non japanese swordsmiths that is allowed to work with tamahagane. My tiger katana isn't tamahagane of course. Its assab k120 swedish steel but thats ok. I cant afford to spend more on a sword than a car. Over 1000 folds. I figure musashi's blade was so big because among asians he was considered 'very big' and i consider myself taller than most 'tall asians' so I'll need an even bigger blade for the same reason. Amazingly balanced and feels lighter than it should as a result. It kind of is my personal version of the 'claymore of katanas'... And yet i can still use it quickly one handed.
I own a very long no dachi as well but I promise they are not as well balanced and I'd choose the katana over it in a heartbeat, but truly i'm faster than most youtubers with a bokken so i'd even choose that in home defense against a claymore. The bokken is my version of a 'fencing katana' but even i'm not fast enough to feel good about taking a bokken against a fencing sword. At least with the katana theres a good chance that my hit will be worse than their hit. I'll take bokken over shinnai 10 times out of 10 though.
Back to the original topic I'd always pick a katana over anything else just because its my personal style, so even if the math made it an inferior choice I'd pick it anyway.
Over time and all other things being equal (keen or not, crit confirmation or not) the math is starkly in favor of the larger crit range over the larger multiplier so keen katana gives me the warm fuzzies. If you're an optimizer and you have a choice between say a d8(18-20(x2)) and a d8 (x4) the better choice is still the better crit range even over the whomping x4. It takes feats that help autoconfirm crits to make the x4 even in the same neighborhood as a larger crit range. Once you made both weapons keen its no contest. a 15-20 crit range far outperforms big modifiers over time.
As a matter of fact in terms of keen bonus, the mathematic difference is so stark that if you wanted to match a d8:15-20:x2 with something that being keen means only having a crit range of 18-20, to even get in the *neighborhood* of achieving damage parity over time you'd need that weapon to be a d8:18-20:x8!!!
Thats not true.
Unless 15-18 are considered misses it's totally true.
I've made a spreadsheet that rolls d20 strike rolls, d20 confirmation rolls and a d8 damage roll. It makes these rolls 3000 times.
Presuming that any roll of 14 misses, and playing out what each roll means given the possibilities of either a d8:15-20:x2 or a d8:19-20:x8.
out of 3000 damage rolls The 15-20x2 column is greater than the 19-20x8 column.
Then I tap the f9 key to recalculate the spreadsheet with 3000 new rolls. Same result time and time and time again. in sets of 3000 rolls, only once in 23 did the 19-20x8 column provide greater damage than the 15-20 column as long as the initial 15 strike roll is a hit.
The only way the greater multiplier gets an advantage is if you presume that a 15-18 is a miss. So if you're fighting something that you can only hit with a 19 or a 20 then sure. the second weapon will definitely do better. Lets bring it back down so that 18 misses and the second weapon is a x4... There we go. now they're evening out. So yeah. The higher multiplier only achieves damage parity with the better crit range if the 18 to strike would have missed in the first place. Even then the 15-20x2 still has better numbers over the course of 3000 rolls most of the time.
Then you did something wrong because math doesnt make any difference between 18-20/x2 and x4.
Well here ya go. using excel...
a2: =ROUNDUP(RAND()*(20),0)
This is the strike roll
b2: =ROUNDUP(RAND()*(20),0)
This is the confirmation roll
c2: =IF(A2>18,1,0)
did the first strike roll hit. in this example an 18 misses
d2: =IF(A2>14,1,0)
this asks if the attack roll was enough for the first weapon to crit. in this example 15 crits
e2: =IF(B2>14,1,0)
this asks if the confirmation roll was enough to confirm. in this case also a 15 confirms.
f2: =D2+E2
only a roll within the crit range that confirms is considered a crit hit
g2: =IF(F2=2,2,1)
if both the threat range and confirmation apply damage multiplier is in this case 2 else normal damage
h2: =ROUNDUP(RAND()*(8),0)
the damage roll. in this case a d8
i2: =G2*H2*C2
damage is a multiplier of the damage roll, the crit multiplyer and is zero if it missed.
-------
j2 =IF(A2>18,1,0)
second weapon crits only on 19 or 20
k2 =IF(B2>18,1,0)
second weapon only confirms on 19 or 20
l2 =J2+K2
did it crit and confirm?
m2 =IF(L2=2,4,1)
critical multiplier for the second weapon is in this case x4 or normal if the crit doesnt confirm.
n2 =M2*H2*C2 damage is the damage roll * crit multiplier (again x0 if it misses)
Stretch those columns out as long as you feel you need to to establish significance
Total columns I and N. Hit f9 to recalculate as many times as you like.
But if you change c so that a 15 hits instead of an 18 then you stretch the first weapons advantage so far out that the second weapon doesnt line back up until it gets a modifier of at least +8
If you change column c so that you only miss on a 1 the first weapon still has a clear advantage.
I've gotta get some sleep but let me know if there's something wrong with the sheet.
Bottom line is if you can hit with a 15-18 then having a threat range of 15-20 is far superior to multipliers with tiny crit ranges. The only time small crit ranges even come close is if you'd have been missing completely anyway.
And china of course probably holds the belief that 'made in china' means superior out of hand but i'd be interested in seeing what the demographic layout of preference in china *really is*
It's not representative but from what I have been told from people in china japan is quite hated amongst the Chinese and other mainland Asians. Mostly because their premier still honors the war criminals of WW2 (and they ravaged the Asian mainland as much as the Germans ravaged eastern Europe), there is no sign of remorse.
About the sword crafting skills: Many cultures possessed great smithing skills. But only the japanese preserved them, then the media mystified them.
First: Why the heck would you do it that way instead of just calculating the average over an endless amount of attempts? Seriously, I dont get that:P
But your method is kinda flawed further as you do not really consider average AC and scaling damage modifiers.
Did you include critical focus (as the crit is confirmed at 14+ while the attack hits at 18+)?
I'm kind of in a hurry right now - I will check your excel-thing later.
Why would the Nodachi be disallowed?
Why would anyone use the falchion?
I know there is an element of flavor with the eastern weapons, but why make a mechanically superior weapon as a flavor weapon? It's just a mechanics gripe on my part. I could understand it better if the weapon was hafted (that would cut the hardness by 5), but it's never mentioned if this is done. Otherwise, it looks like Paizo says the brace weapon property, the ability to choose piercing or slashing damage, and .5 extra weapon damage is worth 5 gold. At least the greatsword versus greataxe disparity (.5 avg damage) is 30 gold (:
I like doing it that way because its truly random. Instead of assuming an average I create one. Realistically if I pulled my sheet out to a sample size of 3200 theres a good chance that every possible combination of rolls would come up at least once, giving a true 'average' and a larger sample size might become statistically insignificant.
Plus it allows me to change values on the fly to test different scenarios. As you suggest I could modify one column and test your crit confirm 14 with critical focus with practically no effort at all, as well as check your suggested scaling modifiers on the fly, and if i feel like the sample is biased i just hit F9 and poof. 3200 new rolls!
In this format not only do I get a realistic result based on real rolls instead of an average, but instead of looking for the 'theoretical average based results' I can both see frequency and magnitude of the disparity, which tells a much different story than theoretical averages.
It does not matter at all how often you have to confirm a critical hit. Even if you had to confirm every single point of damage, rolling 30+ dice the average outcome would not change.
It's not an issue of how often critical hits get confirmed. It's an issue of the importance of confirming the critical hit. If the following situation happened:
* You confirm a critical hit, combat ends.
* You fail to confirm a critical hit, combat doesn't end, next round TPK.
Confirming the critical hit is pretty important.
Over time, you are correct that the average outcome doesn't change. We're not talking about average outcome. We're talking about the tempo of damage in a combat. If you can guarantee the 4x crit will hit, it's better than guaranteeing a 2x crit will hit.
| 1 person marked this as a favorite. |
Over time and all other things being equal (keen or not, crit confirmation or not) the math is starkly in favor of the larger crit range over the larger multiplier so keen katana gives me the warm fuzzies. If you're an optimizer and you have a choice between say a d8(18-20(x2)) and a d8 (x4) the better choice is still the better crit range even over the whomping x4. It takes feats that help autoconfirm crits to make the x4 even in the same neighborhood as a larger crit range. Once you made both weapons keen its no contest. a 15-20 crit range far outperforms big modifiers over time.
That's not true.
Here is why (example 18-20/x2 vs 20/x4):
a= chance to hit (1>=a>0, 0.05|a)
d= damage you deal on a normal hit
20/x4:
You have a 1/20 chance rolling 20 on a d20 right? You still need to confirm your crit, then you do 3 times extra damage. So your extra damage from crits is 1/20*a*3*d right?
18-20/x2:
Now you have 3/20 chances to threaten with a crit right? You still need to confirm, then you do one time extra damage. So the extra damage from crits is 3/20*a*1*d
1/20*a*3*d=3/20*a*1*d
you can do the same thing with 19-20/x4 vs 15-20/x2
q.e.d
[edit]I think I know why your spreadsheet is flawed: If your weapon does x2 damage on crit, it only adds its damage one time (the other time it's base damage it would do anyways since you hit already). If your weapon does x4 damage on crit, it adds its damage three times.
It does not matter at all how often you have to confirm a critical hit. Even if you had to confirm every single point of damage, rolling 30+ dice the average outcome would not change.
It does if you consider critical focus. If you edit the values for critical focus into my calculations on greatsword vs falchion you will get a bonus damage value dependent on hit chance.