Ok - so I think i'm a bit rusty in my math. Tell me if Im wrong?
Situation have to pick either greatsword (2d6/19-20/x2) or a falcion (2d4/18-20/x2)
We assume imp critical + cirtical focus.
Which is the better weapon?
Assuming 30% to hit a monster... (50% chance to confirm a hit)
Greatsword
2d6 = 7, x = base dam (PA, STR enchantments) so dam is (7+x), on a succesful cit (which will happen 10% af the time (20% of hits will be crits, only 50% will be comfirmed) is does extra dam.
So dam will be:
110(X+7)
Falcio
2d4 = 5, 15% of the hits will be comfirmed crits.
115(X+5)
So what should the base dam (x) be to make the two weapons equally good?
110(X+7) = 115(X+5)
110X +770 = 115X +575
5x = 195
x= 39
Is my math skills bad?
keen or non keen?
without crunching the numbers those extra 2 pts of dmg (avg'ed) with the GS works better for me.
Keen Falchion. Improving crit range to 15-20 is MUCH more dangerous
I think the 2d6 makes the greatsword better at lower levels. But at higher levels, as you increase your crit threat range, the falcion becomes a better choice.
@DazEvil
Let se if i get your math here :-)
1-14 will do 0 dam since they don´t hit
15-16 on great sword will do 2(7+11) = 36 dam
17-20 on the greatsword do 4(7+11) +(extra crit dam) = 72 dam + crit
Comfirmed Crit will do an extra (7+11) dam and we have 50% chance of comfirming så that ½x4(7+11) = 36
In all Great sword will do 144 dam
Falcion should then do the same.
1-14 = 0 dam
15-20 does 6(5+11)+ crit dam = 96 dam + crit dam
Crit dam is ½x6(5+11) = 48 dam
In all Falcion does 96+48 = 144 dam
Your math skills are better than mine :-)
So +11... That like lvl 4 with a full bab class. Me like!
Now with a Enlarge person it would be 2d6 vs 3d6...
Falcion (14*0+6*1,5)*(x+7)= 9x+63
Greatsword (14*0+2*1+4*1,5)*(x+10,5)= 8x+84
9x+63 = 8x+84
X = 21
making Greatsword a better choise until you have +21 dam
As the poster above stated 19-20/x2 compared to 18-20x2 is only ever better if your +damage is less than a certain number as the critical effect is multiplying all of your damage. The difference between 2d4 averaging 5 and 2d6 averaging seven is nothing compared to critting 10% more often with a larger static damage bonus.
All of this is affected by your hit chance but if you have a 50% chance to hit, 11 or more on a d20 you need to have +20 to your weapon damage to do more damage with a keen falchion over a keen greatsword, obviously improved crit is identical to keen mathmatically for this equation. Critical focus reduces the damage bonus required to +14, having a better hit chance is going to lower the number exponentionally.
((weapon damage+damage bonus)*hit percentage)+(((weapon damage+damage bonus)*crit percentage)*(hit percentage+crit focus percentage))=average damage per swing including miss chance.
So my above equation is ((7+14)*0.5)+(((7+14)*0.2)*(0.5+0.2))=13.44 for the greatsword.
((5+14)*0.5)+(((7+14)*0.3)*(0.5+0.2))=13.49 for the falchion.
The higher the higher the damage bonus the more the falchion pulls infront, however hit bonus smooths the damage and lets the greatsword keep up.
Eg with an 80% hit chance, 5+ on a d20 with the same +14 damage the greatsword averages 21 damage and the falchion averages 20.9 which means you need a higher damage modifier to take advantage of the crit rate.
If you factor in other modifiers such as power attack and crit feats and weapon enchantments these can further change the results, however once your character gets to level 8 to get access to imp crit and crit focus the falchion will always be better for an opt'd character. However even with a 70% hit chance and +30 damage the falcion only does 1.39 damage more, iterative attacks do also take a greater advantage of the critical rate as well.
In conclusion the falcion is better but only slightly, the critical effect feats will improve that as criticals are about more than pure damage.
If you don't factor in the hit chance you are not producing correct results, as i showed with the above equation since your to hit chance directly effects weather the potential crit you roll is actually a crit or not.
People with higher hit chances have smoother bell curves for damage when the equation is plotted as a graph so higher hit chances actually favour less spike damage crits to produce overall damage and thusly the greatsword over the falchion.
Edit: i should mention that this smoothing effect only works up to a certain +damage amount, after you hit the magic number for +damage all +hit bonuses increase the falchions damage at the same or better rate than the greatswords so towards higher numbers the graph will spike. I have not extrapolated the equation or graphed it out but i beleive the magic number to be around +40 damage.
It is a fact that for an opt'd character that a falchion is better than a greatsword and that as you increase in level and damage this just gets more and more true. However hit chance is more important overall to dpr calculations than either crit chance or damage bonus, keeping that in mind with you comparison and factoring for haste and iterative attacks is also something to think about, as are attacks of opportunity.
If you don't factor in the hit chance you are not producing correct results, as i showed with the above equation since your to hit chance directly effects weather the potential crit you roll is actually a crit or not.Only because you introduced critical focus, which I personally don't see too many people taking. If you take that out of your formula (and put in the crit multiplier) you get :
(weapon damage+damage bonus)*hit percentage+(weapon damage+damage bonus)*crit percentage*hit percentage*crit multiplier ...
At which point you can just divide out hit percentage, it's a common term, if the number for one weapon is larger it stays larger whether to hit is taking into account or not.
the OP involved critical focus, so i did the equations correctly to demonstrate the mathematics behind the difference in the two weapons. while i understand what your saying and you are right its perfectly acceptable to do quick working out with the method you have put forward its not what the OP asked or anything to do with the question which we are answering.
In the equation you posted the part for crit multiplier should be x*(crit multiplier-1)=
just so you get the correct result, i didn't include it in my previous workings as it has no bearing on either the greatsword or the falchion as they are both x2 weapons. for an axe or pick with a x3 or x4 multiplier you want to add on the damage*(crit multiplier-1) at the end of the equation since the initial damage includes the basic hit but i digress.
if you would like to discuss the benefits of crit focus (which many people will take if they take the xxx critial feats as its a prereq) or if you would like to correct any of the equations i have posted i will happily discuss this further, however i feel that all of the information i have posted is correct as pertaining to the OP and while i can see that your trying to simplify the equation and help you are infact providing incorrect information at the moment.
So, I made a quick spreadsheet, based off Egoish's formulas, with minor adjustments to make sure everything worked right at the high and low ends. (Making sure the confirmation roll is never more than a 95% chance and taking into account the fact you can't score a critical threat if you don't hit.) After a little playing about, I've come up with the following minimum damage bonuses for a falchion to be at least as good as a greatsword, damage wise.
0.95 : 19 : 19
0.90 : 18 : 19
0.85 : 17 : 19
0.80 : 16 : 19
0.75 : 15 : 19
0.70 : 15 : 19
0.65 : 15 : 19
0.60 : 14 : 19
0.55 : 14 : 19
0.50 : 14 : 19
0.45 : 13 : 19
0.40 : 13 : 19
0.35 : 12 : 19
0.30 : 11 : 19 <- the 30% to hit asked about in the OP
0.25 : 26 : 43
0.20 : Never : Never
0.15 : Never : Never
0.10 : Never : Never
0.05 : Never : Never
(7+x)*(0.3+(0.3+0.2)*0.2)=
(7+x)*(0.3+(0.5)*0.2)=
(7+x)*(0.3+0.1)=
(7+x)*0.4=
2.8+0.4x
Falchion
(5+x)*(0.3+(0.3+0.2)*0.3)=
(5+x)*(0.3+(0.5)*0.3)=
(5+x)*(0.3+0.15)=
(5+x)*0.45=
2.25+0.45x
Compare the two
2.8+0.4x=2.25+0.45x =>
0.05x=0.55 =>
x=11
PS. ignoring Vital Strike, because it's a waste of feat slots.
I'm no kind of optimiser, but could you elaborate? I've always thought the Vital Strike chain were useful for increasing your options, rather than for upping your dps in general. I.e. they let you either full attack, or, if you had other stuff to do, at least compensate for some of the lost damage. Is there a differing consensus on them?
Nice work on the spreadsheet, good catch on the high end to hit as well. Didn't account for it in the equation. Good to see it all works out, +11 damage isn't hard to reach at low levels but only having a 30% chance of connecting is quite low, most creatures have relatively low AC. Using that info to draw conclusions i'd guess at level 8 with those feats you'd best of in the +15 or more damage area since with power attack between 65% and 75% to hit is about right for most fighter types.
Of course reaching +15 damage at level eight is very easy so as has been said an opt'd character is better off with a falchion.
In the case of vital strike you can see that hitting for an extra 2d6 with a greatsword vital strike at level 8 when your +damage can be more than double that, theres better things to do with feats than add little damage to standard actions.
Falchion.
Oh you want math and stuff? Falchion's just better because I enjoy rolling crits. :-)
Just what i thought when I picked weapon focus falcion
When i picked a Falsion I knew I never roll a natural 20 on an attack roll - my natural 20 always comes when I make saves :-) so figured i would go with my gut. But then the optimizer in me wanted to know if i made the right choise. Should get over the magic +11 in a level or two.
Yar.
It all depends on what you want, what you feel is important, and how you play. (style is important for some, as are themes, in game regional preferences/accuracy, critical hit feats, consistent damage vs lower regular damage with higher bursts of damage, etc).
If all you want is the numbers crunching, I did some a while ago.
and
It compares 12 different weapons when used with 5 different attack routines (Charge, regular/cleave, vital strike, full-attack, and hasted) performed by a (what I think is a basic) fighter at 12th level, as well as at 1st level for (base weapon) comparisons. Those calculations also include to hit/miss chances appropriate for those levels, crit.ranges and multipliers, etc.
As you can see, depending on your build and your attack routine/choice for that round, sometimes the Falchion is better, sometimes the Greatsword is better.
~P
@ JIGGY: LOL
Wow, I'm glad to see I'm not the only nerd to sit down with pen & paper or a spreadsheet and figure this crud out!
As for the general thread, though, I think Eldorn summed it up nicely.
If your character is optimized and hitting your target isn't a problem, having a better crit range will always be superior, at least once you hit that +dmg threshold.
That said, if your character is only going to hit with the reduced crit range anyways, the better base weapon damage is always going to be better.
I actually plan for this with most of my characters anyway by carrying a keen greataxe or scythe in a bag of holding on my martial character. I won't be dropping my damage (depending on my starting weapon), but the x3 or x4 dmg comes in mighty useful on boss fights!
Thanks for all the math, guys! I'd been calculating it that way for years, but never actually had anyone confirm my madness, er... method before.