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magic8BALL
2007-01-08, 12:34 AM
I don't know if this has been done before, but here's a feat based on Improved Critical, a spell based on keen edges, and a weapon ability based on keen. You can get a battle axe to 1d8 19-20/x3, so here's how to get a longsword there.



New Feat:

Augment Critical

You swing your weapon with such might and skill, you deal more damage than usual with a true blow.
Requirements: Weapon Focus, BAB +8
Benifit: Choose a weapon you have taken the Weapon Focus feat for. You double the extra dice of damge dealt by this weapon on a critical hit. A crit from a shortsword deals x3 damge, a crit from a battleaxe becomes x5, a crit from a scythe becomes x7.
Special: You can take this feat multiple times. Its effects do not stack. Each time you take it, choose a new weapon with wich you also have the weapon focus feat.
A fighter may take this as a bonus feat.



New Spell:

Augment Weapon
Transmutation
Level: Sor/Wiz 3
Components: V, S
Casting Time: 1 standard action.
Range: Touch
Target: Weapon Touched
Duration: 1 round/level
Saving Throw: Will negates (harmless, object)
Spell Resistance: Yes (harmless, object)

You transform one weapon such that it deals damage more efficiently when it strikes true. The critical mulitplier of the weapon is doubled* for the duration of the spell. This increase dose not stack with similar effects, such as the Augment Critical feat or an augmented weapon. This effect may only be set upon a bludgeoning or slashing weapon.
*remembering that doubling multipliers is different in D&D to normal arithmatic



New Weapon Abilitys:

Augmented: The critical multiplier for this weapon is doubled. (Remember that doubling multipliers is different in D&D than normal arithmatic) This effect dose not stack with similar effects, such as the Augment Critical feat, or the augment weapon spell. This effect can only be placed on a bludgeoning or slashing weapon. This effect, and the keen effect cannot be placed on the same head of the same weapon (for this, see greater threat).
Moderate Transmutation; CL 10th; Craft Magic Arms and Armor, augment weapon; Price +1 bonus.

Greater Threat: Many tales are told of a hero's blade, all all fear the eventaul comming of Deaths Scythe. These are a few exsamples of greater threat weapons.
The threat range for this waepon is doubled (as per the keen edges spell), and the critical multiplier increased (as per the augment weapon spell). These effects do not stack with similar effects, such as the Improved Critical feat or the Augment Critical feat. This effect can only be placed on a slashing weapon.
Moderate Transmutation; CL 16th; Craft Magic Arms and Armor, augment weapon, keen edges; Price +3 bonus.

Lord Iames Osari
2007-01-08, 12:53 AM
Mmmm, augmented keen scimitars...

Peregrine
2007-01-08, 01:59 AM
Augmented critical is underpowered. The correct equivalent to keen is to increase the multiplier by itself, following D&D multiplier-stacking rules, i.e. x2 becomes x3, x3 becomes x5, x4 becomes x7.

Unfortunately I have to run out right now, so a further analysis (and any support for my above statement :smalltongue:) will have to wait, sorry!

magic8BALL
2007-01-08, 03:09 AM
...so my augmented scythe dose x7 on a crit?

I thought of that... but... whoa! That's heaps over powered!

Say a 16th lvl fighter with Greater Spec (Scythe), STR 22, and a +2 Augmented Scythe... thats 14d4+105... a mean of 140... ouch...

I kept it to "add one to the crit muliplier" to try to keep balanced... doubling the crit multiplier is... well... ouch...

...on the other hand... keen scimitars are ouch too... (15-20!). I'd love to see what evedince your analysis shows up... I shall atempt to do my own. Thanks for the input.

...but the multiplier is already a multiplier... x3 being twice as good as x2, x4 beinhg three times as good... this feat increases the muliplier...but so dose improved crit... and that doubles the alsready increased multipliers...I'll get onto my maths programs...

Ok. From what I see so far... Peregrine, you're right.
Below is a list of weapons, with their normal value's, improved crit values and augmented values listed beside them. The numbers representing mean damage assume a +5 total bonus to damage, and 1/2 of the threats scored are confirmed.

Morning Star
normal (1d8+5, 20/x2) --> 9.7375
imp. crit. (1d8+5, 19-20/x2) --> 9.975
aug. crit. (1d8+5, 20/x3) --> 9.975

Longsword
normal (1d8+5, 19-20/x2) --> 9.975
imp. crit. (1d8+5, 17-20/x2) --> 10.45
aug. crit. (1d8+5, 19-20/x3) --> 10.45

Battleaxe
normal (1d8+5, 20/x3) --> 9.975
imp. crit. (1d8+5, 19-20/x3) --> 10.45
aug. crit. (1d8+5, 20/x4) --> 10.2125 (my version)
aug. crit. (1d8+5, 20/x5) --> 10.45 (Peregrine's version)

well... for these three weapons, your are right... I will update the post above. Thanx!

Demented
2007-01-08, 05:16 AM
The feat doesn't specify that the weapon must be bludgeoning or slashing.

magic8BALL
2007-01-08, 05:29 AM
neither does improved critical.

Peregrine
2007-01-08, 11:16 AM
Yup. As you can see, while x7 sounds impressive, it's on par with a threat range of 15-20, which is what you get when you keen an 18-20 weapon. (The only difference is that with a high threat range, you might run into enemies whom you can't hit on a roll of, say, 16 or worse, which cuts out some of your 15-20 threat range. A 20/x7 weapon, however, is good against all ACs. I have had pointed out to me that a high-multiplier weapon is 'wasted' on multiple weak enemies though... if normal damage isn't enough to take down an enemy, but x2 is, and x3 is overkill, then you're better off with a sword than an axe.)

So yes, just adding 1 to the multiplier is underpowered. However, one thing to keep in mind is that the core game doesn't let you stack any increases to threat range. Multiple increases to the multiplier (not that there are any others I know of) should be disallowed if you use this rule. And increasing both the threat range and multiplier should definitely be right out. That's very powerful, because the combined increases are not linear. If you have a threat range that's x steps past 20, and a multiplier that's higher than x2 by y, then your total improvement is as good as a weapon that's improved by x+y+xy steps in only one 'direction'.

Let me illustrate. A battleaxe (20/x3, so y = 1) and a longsword (19-20/x2, so x = 1) are on par, right? So you'd expect their keen versions to be on par, too: a keen battleaxe (19-20/x3, x = 1, y = 1) is as good as a keen longsword (17-20/x2, x = 3). So, one step each way is as good as three steps only one way.

Now let's look at a scythe in a game that has keen and augmented available, and able to be put on one weapon. This is now a 19-20/x7 weapon (x = 1, y = 5), which is as good as eleven steps in one direction (i.e. a 20/x9 weapon or a 9-20/x2 weapon). What you've gotten with just two enhancements, would take three keen-like improvements (say, keen, Improved Critical, and something else) on top of a falchion -- if you let them stack. (And if you followed normal 'doubled doubling' rules; normal is 18-20, doubled once is 15-20, doubled twice is tripled or 12-20, doubled thrice is quadrupled or 9-20. If you made an exception and let a doubled double be a quadruple, then you would have any mix of improvements in either direction be equal -- but you'd be making some crazy powerful weapons.)

So yeah. Only one improvement to crits should be allowed. (Yeah, I've done this analysis before... had debates on the power of crit improvements before... also created an enhancement similar to augmented, which I called crushing.)

Edit: Oh, by the way. You've called the new, revised increase to the multiplier 'doubling'. Actually, it's squaring. Doubling a multiplier, by D&D rules, means adding one to it, which is what you had before. What you're doing is applying the multiplier again (x4x4), thus squaring it (and applying D&D arithmetic, so it's x7, not x16). Of course, telling people to square their multipliers would just confuse them even worse... perhaps just say something like, 'add the multiplier twice, following the D&D rules of arithmetic for stacking multipliers'?

PS ...that thri-keen pun was not intended. :smallfrown:

Closet_Skeleton
2007-01-08, 11:34 AM
The old 3.0 Weapon Master/Kensei class increased your multiplier by x2 and even then it was limited to so many uses per day. Squaring Crits seems wrong. Keen only doubles your threat range.

Peregrine
2007-01-08, 11:44 AM
'Only' doubles your threat range? Think of the multiplier more like a 'range' as well. x2 is 'one extra damage roll', x3 is 'two extra', and so on, just like 20 is 'one outcome of the attack roll', 19-20 is 'two outcomes', etc. Doubling the range and D&D-squaring the multiplier are then exactly the same. Augmenting a x3 means doubling the 'two extra' to give 'four extra', or x5; just the same as doubling a range of 19-20 means doubling the 'two outcomes' to 'four outcomes' or 17-20.

Arbitrarity
2007-01-08, 04:27 PM
This, and keen, or improved critical, is a baad, baad idea.

15-20 x3 crit, 19-20 x7 crit.

magic8BALL
2007-01-08, 11:46 PM
I realise that increasing both a weapons threst range AND augmenting the critical multiplier may lead to some very powerful weapons.

But at the moment, you need a combination of factors to get you there, and there are limitations on both keen edges and augment weapon. (only a slashing weapon can have both spells cast on them)

To buy a keen augmented weapon would cost at least 18 000gp in enhancments alone (remebering the +1 minimum magic weapons need), and you are dependant on a crit (even though your chances are good) to deal out large amounts damage. You need to remeber that undead, constructs, oozes, plants and so forth are imune to the extra damage, and some fortification on your opponents armor renders your new "super slashy scimitar" almost useless.

...so...

...any constructive thoughts, or just more "thats a real advantage" coments, becouse of cause it's an advantage to have multiple complementary enhancements on a weapon.

ok... here's 4 ways to enhance a scythe to a +3 total bonus.The numbers representing mean damage assume a strength score of 20, the weapon specialisation feat and 1/2 of the threats scored are confirmed.

+3 scythe (2d4 +12, 20/x4) --> 18.275

+2 keen scythe (2d4+11, 19-20/x4) --> 18.4

+2 augmented scythe (2d4+11, 20/x7) --> 18.4

+1 keen augmented scythe (2d4+10, 19-20/x7) --> 19.5

Well, hey looky-here! the extra +1 bonus actually deals an point of damage! Too bad the +1 keen augmented scythe has one less to hit than a +2 augmented scythe or +2 keen scythe.

Surely this is balanced?

Peregrine
2007-01-09, 01:00 AM
But at the moment, you need a combination of factors to get you there, and there are limitations on both keen edges and augment weapon. (only a slashing weapon can have both spells cast on them)

Oh, woe. It only works for my scythe, or my falchion, or my scimitar, or... :smalltongue:


To buy a keen augmented weapon would cost at least 18 000gp in enhancments alone (remebering the +1 minimum magic weapons need), and you are dependant on a crit (even though your chances are good) to deal out large amounts damage. You need to remeber that undead, constructs, oozes, plants and so forth are imune to the extra damage, and some fortification on your opponents armor renders your new "super slashy scimitar" almost useless.

We must balance our additions against the core game's assumption that better criticals are a good enough situational bonus that they're as good as an equivalent general bonus. (Actually, as we shall see, my analysis calls even this into question.)


...any constructive thoughts, or just more "thats a real advantage" coments, becouse of cause it's an advantage to have multiple complementary enhancements on a weapon.

You think my comments thus far have not been constructive? I'm afraid you stand to be disappointed, as I'm going to basically state the same things again, only with more depth.

Yes, of course it's an advantage. But it's too much of an advantage, on these grounds: keen and augmented are two improvements to a weapon's crits (one to range, one to multiplier), that are equivalent to three improvements to only range or only multiplier. And the core game forbids stacking multiple improvements to range (and has no improvements to multiplier). Stacking these two things is as good as stacking three things that you're not allowed to stack anyway.


ok... here's 4 ways to enhance a scythe to a +3 total bonus.The numbers representing mean damage assume a strength score of 20, the weapon specialisation feat and 1/2 of the threats scored are confirmed.

My own analysis takes into account the to-hit bonus. For simplicity I ignore any damage above the weapon's own, auto-confirms crits and just sets a target roll to hit. (These are the same assumptions I used in the thread on Vorpal Tribble's paragon enhancement, which I said I was pretty sure were valid, but didn't go into. If you want, I can test them. But I'm quite confident that they're valid for comparing weapons, rather than figuring out what you're actually going to achieve in combat.)

+3 scythe (2d4+3, 20/x4, needs 9 to hit)
1-8 (40%): 0
9-19 (55%): 2d4+3 = 8 mean
20 (5%): 2d4+3 x 4 = 32 mean
Total: 6 mean

+2 keen scythe (2d4+2, 19-20/x4, needs 10 to hit)
1-9 (45%): 0
10-18 (45%): 2d4+2 = 7 mean
19-20 (10%): 2d4+2 x 4 = 28 mean
Total: 5.95 mean

+2 augmented scythe (2d4+2, 20/x7, needs 10 to hit)
1-9 (45%): 0
10-19 (50%): 2d4+2 = 7 mean
20 (5%): 2d4+2 x 7 = 49 mean
Total: 5.95 mean

+1 augmented keen scythe (2d4+1, 19-20/x7, needs 11 to hit)
1-10 (50%): 0
11-18 (40%): 2d4+1 = 6 mean
19-20 (10%): 2d4+1 x 7 = 42 mean
Total: 6.6 mean

Two interesting results: +2 keen and +2 augmented are not better than +3 (and since they're situational and +3 is general, you'd expect they would be), and +1 augmented keen is much better than any of them (10% more damaging than +3 alone).


Well, hey looky-here! the extra +1 bonus actually deals an point of damage! Too bad the +1 keen augmented scythe has one less to hit than a +2 augmented scythe or +2 keen scythe.

Surely this is balanced?

Is it balanced against +3, being a situational bonus (only against enemies vulnerable to crits) rather than a general bonus like +3? Maybe. Is it balanced against the existing crit enhancements? Heck no.

Of course, those existing enhancements may actually, by this analysis, be rather weaker than they should be. But justifying the stacking on these grounds is bolting on a fix to a broken system.

(And saying they're too weak is ignoring the old truth that greater magic weapon makes all +x enhancements above +1 redundant... just get a +1 keen augmented blasting nuking weapon and use GMW to make it anywhere up to a +5 keen augmented blasting nuking weapon!)

magic8BALL
2007-01-09, 01:12 AM
You think my comments thus far have not been constructive?

Far from it, thank you very much for your input.

Your analysis disreguards the chance for a threat comfimation to miss, inflating the effectiveness of both the weapons threat range and critical multiplier. Otherwise, it is very in depth. Of cause, these hyperthetical analysis' are just that: untill we can get a real AC to hit, it's worth just about anyones guess. My analysis assumes also that you hit. (you can't deal damage on a miss, and no good saying you roll damage on a miss anyway)

Here's an idea...

You cannot magically enhance a weapon with both keen and augmentation... instead, you must spend a +3 bonus to grab the both of them (or just use a feat, or get the mage to cast a spell... dose anyone do that anymore?)

New Weapon Ability:

Greater Threat: Many tales are told of a hero's blade, all all fear the eventaul comming of Deaths Scythe. These are a few exsamples of greater threat weapons.
The threat range for this waepon is doubled (as per the keen edges spell), and the critical multiplier increased (as per the augment weapon spell). These effects do not stack with similar effects, such as the Improved Critical feat or the Augment Critical feat. This effect can only be placed on a slashing weapon.
Moderate Transmutation; CL 16th; Craft Magic Arms and Armor, augment weapon, keen edges; Price +3 bonus.

Hence a +1 greater threat scythe would be coparable to cost and effectiveness to a +4 scythe... is that closer?

Peregrine
2007-01-09, 01:29 AM
Your analysis disreguards the chance for a threat comfimation to miss, inflating the effectiveness of both the weapons threat range and critical multiplier.

Yes, I know. As I said, the numbers themselves do not represent what damage a given character will do in actual combat. But they accurately represent the relative damage of each weapon. I can demonstrate that auto-confirming crits is valid in this way, if need be.


Otherwise, it is very in depth. Of cause, these hyperthetical analysis' are just that: untill we can get a real AC to hit, it's worth just about anyones guess.

Again, my assumption of a roll needed to hit is valid for comparison purposes. It will show the same relative standings for all rolls that do not impinge on a weapon's threat range. (If you have a 19-20/x2 weapon, but you can only hit on a natural 20, your weapon is no better than a 20/x2.)


My analysis assumes also that you hit. (you can't deal damage on a miss, and no good saying you roll damage on a miss anyway)

No, but when working out the average damage (errm, that is, the mean damage, let's not start the 'average' debate here... :smallwink:), you need to take into account those times that there is zero damage. At least one result in 20 is 0 damage against any AC, thanks to our friend the natural 1.

And I fear I have to run out again (it seems to keep happening to me in this thread), so I can't give greater threat much analysis right now. Sorry!

magic8BALL
2007-01-09, 02:13 AM
Why would you need to take into account the times you miss? You missed! Thats to do with your BAB and the opponents AC and all sorts of conditional modifiers like cover and concealment and spells and weather - YUK!

I my view, if your comparing mean damage of a few weapons, compare the mean damage they dish out, not the "aww, but what if I miss" factor.

On the other hand, a +3 scythe dose have a (roughly) 10% better chance to hit than a +1 (insert favouite filler here) scythe, and that should be accounted for, just I couldn't be bothered doing that much for a proposition of an addition to a recreation... yet :smallwink:

Roderick_BR
2007-01-09, 05:52 AM
I'll have to agree it seems overpowered. And I don't care much for those math things. Who here has dealt "average" damage all campaign long? :p
If there is an equivalent in 3.5, then that would be fine, otherwise, it should only rise the multiplier in +1 multiplier, like those PrC's abilities, and others effects the Feat Spirited Charge, Although I need to re-read how that one works now.
But a nice idea to use.

Peregrine
2007-01-09, 09:54 AM
On the other hand, a +3 scythe dose have a (roughly) 10% better chance to hit than a +1 (insert favouite filler here) scythe, and that should be accounted for, just I couldn't be bothered doing that much for a proposition of an addition to a recreation... yet :smallwink:

Exactly. You need to consider your chance of missing inasmuch as the weapon itself influences that. (That's the short justification of why we don't have to worry about BAB and AC and cover and whatnot: these apply equally to both weapons. But the weapons themselves have enhancement bonuses to attack rolls, so we have to account for that.)

And on the matter of it being recreation... yeah... I... I, umm... I kind of like doing this sort of analysis. :smallfrown:

magic8BALL
2007-01-10, 07:02 AM
Well... yes and no.

Your attack modifier and your opponents AC determine what you need to roll on a d20 to hit. No suprise there, but the point is that if you only need a 2 to hit, a critical accounts for a smaller percentage of the mean damage than in a situation where you need to roll a threat just to get that auto-hit thing going, and a comfirmation is out of the question. When we are dealing with bonuses to threat ranges, and useing that as a benchmark for balancing a new proposal to increase the critical multipliers themselves, the percentage of the mean damage actually dealt by a critical should be at the top of the list of thiongs we should worry about.

However, actually lives are not at stake. My numbers, and your numbers, are good enough for me. "doubleing the extra dice of damage on a crit" is in line with "doubling the threat range of the weapon".

The new question is: is it balaned to have a +3 enhancement that magically does both for slashing weapons, when there are other ways to get the same effect on all kinds of weapons?

...I also enjoy these analysis'... it's the only maths I've done for months :smallfrown:

Peregrine
2007-01-10, 11:14 AM
Your attack modifier and your opponents AC determine what you need to roll on a d20 to hit. No suprise there, but the point is that if you only need a 2 to hit, a critical accounts for a smaller percentage of the mean damage than in a situation where you need to roll a threat just to get that auto-hit thing going, and a comfirmation is out of the question. When we are dealing with bonuses to threat ranges, and useing that as a benchmark for balancing a new proposal to increase the critical multipliers themselves, the percentage of the mean damage actually dealt by a critical should be at the top of the list of thiongs we should worry about.

On the contrary, what percentage of a weapon's damage is from crits is irrelevant and, as you point out, totally dependent on the enemies you fight. What is relevant is simply whether it's higher or lower than some other possible weapon. Then we can balance new things by finding the closest match in the core rules.


The new question is: is it balaned to have a +3 enhancement that magically does both for slashing weapons, when there are other ways to get the same effect on all kinds of weapons?

Yes, I think so. However, on the flavour text, I'm not sure that Death's scythe would be a greater threat weapon... I always rather pictured it as a you die now weapon. :smallbiggrin:

Ultimatum479
2007-01-10, 06:23 PM
...there are limitations on both keen edges and augment weapon. (only a slashing weapon can have both spells cast on them)
On that note, the weapon damage type is mentioned in the weapon enhancement and spell, but not in the feat. So that's not all that much of a limitation unless you meant to have it in the feat as well.

magic8BALL
2007-01-11, 12:03 AM
Well, to have the feat, you need to have the prereqs, and use a feat. For a magic weapon, you just hand over a share of the latest dragons hoard. There is no limitation on which weapons Improved Critical can be used with, yet keen edges stipulates that the spell dose not work on bludeoning weapons. So similarly, I have stipulated that peircing weapons cannot be augmented through magic.

Demented
2007-01-11, 01:41 AM
For the most part, keen edge's restrictions are justified by bludgeoning weapons not having much of an edge to make keen. Though, that could be either ancillary fluff or a subtle balancing issue being covered up by fluff.

magic8BALL
2007-01-11, 02:24 AM
very true... so my fluff is something like "the effect increases the power of the blow, a piercing weapon punches a hole through your opponent, but putting the weapon further through deals no extra damage" or something. Just to play it safe, I assumed it was a balancing issue of some sort...

Roderick_BR
2007-01-11, 07:21 AM
Hmm.. I think that opening a hole in the other side of the body does deal more damage :P
You ARE pushing it deeper into the person's inner organs.

Vik
2007-01-11, 08:17 AM
Some math about crit influence on damage :
I call :
- X the chance to hit
- D the average damage that can be multiplied by a crit
- A the additionnal damage
- R the range of crit threat
- M the crit multiplier
I assume that X >= R, that is a crit threat is a hit (it's usually true for most weapons).

The the average damage is :
AVG = X.(D+O) + R.X.D.M
AVG = X. ( D + O + R.D.M )

Average damage gain with additional bonuses are :
Gain_AVG(+1 alteration) = 0.05.AVG + X.(1+R.M)
Gain_AVG(Keen) = R.X.D.M
Gain_AVG(Augmented)= R.X.D.M

Keen and augmented are the same, and Keen is better than +1 bonus if :
0.05 (D + O + R.D.M) + X.(1+R.M) < R.X.D.M
that is :
0.05 (D+O) < RDM(X-0.05) - X - RMX
If there is no additionnal damage (flaming or the like), and RM = 0.10 (case of most martial weapons) that's :
0.05 . D < 0.10*D*(X-0.05) - X - 0.10*X
0.045.D < X(0.1*D-1.1)
0.045*D / (0.1*D-1.1) < X
If D <= 20, that's impossible, which means that the +1 bonus is better.
If D = 30, then the keen bonus is better for X>0.7 (hit at least at 6).
If D = 60, then the keen bonus is better for X>0.55 (hit at least at 9).

So we can say that in most cases with usual weapons, the +1 bonus is better than the keen one, except for very strong attackers using Power attack.

I'll put the math of Keen+Augmented later ^^

Edit : for a good crit weapon (falchion, rapier, scythe), RM = 0.15
And then the condition is
0.05*D < 0.15*D*(X-0.05) - X - 0.15*X
0.0425*D < X*(0.15*D-1.15)
If D<=10.75 that's impossible.
If D = 15, then Keen is better that +1 if X > 0.55 (hit at least at 9)
If D = 25, then Keen is better that +1 if X > 0.40 (hit at least at 12).

So for a good weapon, it's reasonnable to take the Keen enchantment (or augment).

Vik
2007-01-11, 08:40 AM
For a Keen + Augment enchantment, the gain is 3.R.X.D.M, that's 3 times the gain of a single Keen (as already noted by Peregrine).

The gain of a +3 enchantment is also 3 times the one of a +1 enchantment :
Gain_AVG(+1 alteration) = 0.15.AVG + 3.X.(1+R.M)
Meaning that if one consider a Keen equivalent to a +1 enchantment, then a Keen+Augment enchantment should be rated at +3, the math is exactly the same.

Note : if there are additionnal damage, the relative efficiency of Keen and Augment drop. Also, too high crit range is not so good due to the fact that the X>R assumption won't be valid anymore.

magic8BALL
2007-01-11, 11:59 PM
Ok, so the +3 enhancement bonus for greater threat is balanced. Thanks!

Here's somthing I have thought of too...
Augmented Weapon can be placed on a morning star becouse it deals bludgeoning damage.
Keen can also be placed on a morning star becouse it also deals piercing damage.
...so, should I include morning stars in the list of weapons that can be enhanced with greater threat? Or just keep slashing weapons only?

Vik
2007-01-12, 09:29 AM
Keep slashing only.

Yakk
2007-01-12, 10:27 AM
This is not at all balanced.

Criticals in D&D quickly fall out of balance.

First, start with the concept of a "crit pip". A crit pip is the crit-damage-increase-amount times the width of the threat range.

Most simple weapons have 1 crit pip, most martial weapons have 2 crit pips, and some martial weapons that do less damage have 3 crit pips.

Keen is an acceptable enchantment because weapons with 3 crit pips are heavily nerfed in order to make keen balanced.

Suppose someone pulls off a total of +30 damage modifier.

Keen Longsword average damage: 4.5+30 * (1.2) = 41.4 average per hit.
Keen Scimitar average damage: 3.5+30 * (1.3) = 43.55 average per hit.

The Scimitar does 2.15 more damage per hit, on average, or 5.2%. In exchange, it has worse variance, and requires a serious setup to deliver it.

Now let's take the same situation, and change it to a Keen Augmented (via feat or enchantment) weapons.

AK Longsword average damage: 4.5+30 * (1.4) = 48.3 average per hit.
AK Scimitar average damage: 3.5+30 * (1.6) = 53.6 average per hit.

The gap grows to 5.3, or 11% more damage from the AK Scimitar than the AK Longsword.

Weapons like the Scimitar already have problems in that they are gimpy at low power levels, and once you pile on the modifiers they become better than the more standard weapons. This feat/enchantment only makes it worse.

If you could only have one of "crit damage augmentation effect" and "keen effect" on a weapon at once, then the difference would be one of flavour more than balance.

...

Another way of making this less insane would be limiting the augmentation to the base weapon damage dice only.

magic8BALL
2007-01-14, 12:27 AM
...so you would also limit crits as a result of a keen effect (or Improved Critical for that matter) to base weapon damage only?

I realise that having an increased threat chance AND an increased crit result is pretty... well... nashy to say the least, thats why I have limited it to but a few weapons, made the magic path to get there more expensive than it otherwise would be (one +3 enhancement instead of two +1 enhancements), and you really need to take a feat (or two) to get it relatively cheap.

Yes, weapons such as the scimitar, falcion, scythe, and other 18-20/x2, and 20/x4 weapons get the edge with enhancements like keen and augmentation, but these usually have smaller base dice, a higher price, and a higher cost to maintain (wich people generally ignore anyway... when was the last time you actually shapened your sword after hacking through someones fullplate and chopping them up...?) and lower bonuses to damage due to the weilders strength("I can't hit often, so I'll increase my chance for a threat...").

...still... your keen augmented scimitar with +30 to damage... verse my keen agumented longsword with +40 to damage becouse I can use it in two hands...

My point is, things in base rules are generally pretty balanced, my sugestion of augmentation is exactly balanced with keen... the only problem arises when these are happening at the same time. Remember: no keen effect can be stacked with another, as it was unbalancing... but is there a price at wich the nashyness of it is balanced with the cost?

Yakk
2007-01-14, 08:06 PM
It increased the average damage per hit on a +30 damage scimitar swing by +10. This damage increase is physical, and hence very difficult to block (compared to elemental damage), and it works on every kind of target.

It also works beyond the +5 enhancement bonus limit. I'd price an enchantment that said "do 10 more damage on every hit, based off the weapon type of the sword" as a +4 or +5 enchantment.

Now, let's take a look at a keen scythe, leap attack
+5 enhancement
+2 to hit +4 to damage (spec)
+20 BaB
+12 strength to hit bonus
+18 strength damage bonus
----
+39 to hit
+27 to damage

10 points of power attack at x3 to damage:
+29 to hit +57 to damage

Just keen: 62 * 1.3 = 80.6 average damage per attack
Keen+AK: 62 * 1.6 = 99.2 average damage per attack

AK (Augment Critical) gave a +18.6 average damage per attack increase. That would be valued at a +9 to +10 enchantment.

...

So, how about the cost of a +9 enchantment?

Naturally, you should cost out enchantment assuming the person in question is optimally enchanting an item. Hence your problem -- on a keen scythe wielded by a power attack build, the average damage increase from an Augment Critical is huge.

And then if you throw in stuff like Oil that auto-confirms crits, or boost crit confirmation chance, and you get a really sick build.

magic8BALL
2007-01-15, 06:42 AM
Your maths... baffles me...

Have you not read either Perigrines or my own analysis? Got a grasp of what I'm actually proposing? Sorry to sound cinical, but Augmented Weapon is exsactly the same maths as Keen.

Combining keen and augmentation is a multipliying effect, not an addition, as far as the combined effects on mean damage output. So whatever the mean damage output increase is for either of them (as they will be identical), the mean damage output increase for an effect wich combines the two will be it's square.

As Perigrine so elegantly pointed out to me, it matters not the strength of the weilder, for the price of a +2 Longsword is the same for everyone, hence you can disreguard BAB, STR, Feats, and anything else that will effect damage other than the enhancement bonus to damage provided by the weapon itself.

Also, as a footnote, there is a +5 points of damage enhancement presented in the expanded psionics handbook. It is a +2 bonus.

Yakk
2007-01-15, 11:20 AM
Ok. So there are some weapons which have large crit ranges, but otherwise suck. They are balanced assuming that the only way to leverage that large crit range into multiplying damage is keen, and you can only take it once.

Once you can leverage large crit ranges more than once, those weapons are no longer balanced. The Scythe, Rapier, Falchion, Scimitar -- once you get to high levels, they are already better than the traditional Greatsword, Longsword, etc.

This is because large amounts of bonus damage, plus keen, makes them better than traditional low-level weapons.

Adding augment critical increases this effect even more...

Scimitar: 3.5+Bonus damage, +15% crit damage.
Longsword: 4.5+Bonus damage, +10% crit damage.

Scim edge: 5% on crit, -1 on die.

Keen Scimitar: 3.5+Bonus damage, +30% crit damage.
Keen Longsword: 4.5+Bonus Damage, +20% crit damage.

Scim edge: 10% on crit, -1 on die.

AK Scimitar: 3.5+Bonus Damage, +60% crit damage.
AK Longsword: 4.5+Bonus Damage, +40% crit damage.

Scim edge: 20% on crit, -1 on die.

The reason why Keen is balanced is because the stats of weapons like scimitar already take it into account. Without keen/improved crit, they are gimpy weapons. With keen and enough bonus damage, they are slightly-better-than the "default" weapons.

Toss in Augment Critical, and Scimitars and other "high crit" weapons rapidly become the only weapons worth considering.

Now, you can balance this in a number of ways.

You can gimp high-threat weapons knowing the existance of augment critical. Ie, change longswords to d10 and scimitars to d4 weapons.

You can price augment critical based off the assumption that people will use it effectively. This places it as at about a +9 enchantment, based off using it on two-handed high-threat weapons.

You can change the ability, so that the ability to leverage it into insane extra power at the high end doesn't exist, while the usefulness at the low end is mostly unchanged. Ie, limit it to delivering extra weapon bonus dice.

You can change the ability, so it doesn't stack with keen. This makes it into, mechanically, a "keen with a different flavour".

You can completely redo how crits and keen and augmented critical weapons work, so you end up with a different balance.

Or, you can ignore it, and add an unbalanced feat/enchantment to the game, hoping it doesn't do that much damage to gameplay.

magic8BALL
2007-01-16, 12:17 AM
Scimitar: 3.5+Bonus damage, +15% crit damage.
Longsword: 4.5+Bonus damage, +10% crit damage.

Scim edge: 5% on crit, -1 on die.

Keen Scimitar: 3.5+Bonus damage, +30% crit damage.
Keen Longsword: 4.5+Bonus Damage, +20% crit damage.

Scim edge: 10% on crit, -1 on die.

AK Scimitar: 3.5+Bonus Damage, +60% crit damage.
AK Longsword: 4.5+Bonus Damage, +40% crit damage.

Scim edge: 20% on crit, -1 on die.


The maths you present is... well slightly off. Just becouse you roll a threat dosnt mean you crit. The +x% bonus to mean damage should be 1/2ed, to allow for non-confirmed threats. Otherwise, it is exactly the same maths that I did to prove that Augmentation was exactly balanced with Keen.

Your 'Scim edge' is only an advantage if your 10% is greater than 1, so you need +10 to damage for it to be an advantage. (1/2 these if you want more accurate maths)

Is this AK you talk of an Augmented Keen Greater Threat weapon?

If so, you need to have +20 to damage for the scim to be better. (angain, half this for acuracy)

Yes, I know this is a way to get around the "an effect that increases potential bonus critical damage can only be applied once on a weapon" thing the base rules have, but it is at a fairly large cost, unless you take either of the feats (Improved Crit, or Augment Crit), and the opposing weapon enhancement. Remeber also, that if you take the +3 enhancement Greater Threat instead of this, you are at -2 to attack and damage, potentially.

By itself, you would agree that Augment Critical is balanced, yes? Scoreing a threat twice as often (keen edges)is better than dealing slightly less than double damage on a crit (augment weapon), if only for the fact that a threat is a hit wheather you confirm or not.

Yakk
2007-01-16, 05:15 PM
Threats do not auto-hit, at least not in the d20 rules I've read.

If your threat range is smaller than your hit range, you actually lose threat range.

Take your effective threat range width. Divide by 20. That percentage of hits become crits. Really, the math works out that way.

So, take (threat range) times (multiplier-1), divide by 20. That is the percentage increase in average damage that your ability to crit gives you.

This is true in any situation so long as your threat range isn't shrunk by the difficulty to hit the target. On someone you need a 1 to hit, a keen scimitar has a 30% average damage boost from crits. On someone you need an 11 to hit on, a keen scimitar has a 30% average damage boost from crits. On someone you need a 15 to hit on, a keen scimitar has a 30% average damage boost from crits.

If you want to dispute me, go ahead. Run the numbers for any of the above situation with and without crits. You get 30% more damage when you factor in scimitar crits (not counting bonus die damage from sneak attacks/flaming/etc, naturally).

...

Extra-wide threat ranges have the problem that they can be cut off by hard-to-hit targets.

Extra-narrow threat ranges with high multipliers have the problem that they are a source of high variance damage. That is fancy stats talk for "you can't rely on them very well, and when they do go off they are often overkill".

High crit multiplier weapons also have an advantage when executing a coup de grace.

In the design of D&D weapons, these two are considered equal. A 19x2 and a 20x3 weapon tend to have the same damage dice.

Based off this, if only one critical improvement feat and/or enchantment of any kind where allowed on a weapon, then your augment critical effects are balanced with keen type effects.

Once you allow the possibility that two such effects can exist, the impact on game balance is much larger. To understand this, one needs to grasp that scimitar, scyth, falcion, rapier etc. stats are designed with the existance of effects like keen in mind.

When you allow for multiple keen effects, or effects that boost crits in a multiplicative way like keen to stack with keen, you end up changing the assumptions around which weapons like the scimitar and the scyth where balanced.

That is why D&D banned the stacking of multiple keen type effects in the first place. If you want to remove this ban on stacking, by the back door of augmenting the critical damage, you should understand exactly how powerful it is.

By A.K., I mean "Augmented Critical Keen Weapon". By "Augmented Critical", I mean any effect or enchantment that increases the critical multiplier from X to (X-1)*2+1.


Scoreing a threat twice as often (keen edges)is better than dealing slightly less than double damage on a crit (augment weapon), if only for the fact that a threat is a hit wheather you confirm or not.

The Keen effect is equal to Augmented Critical Weapon. So long as no kind of one effect can exist on a weapon while any kind of another effect is on the weapon, everything is A-OK and flavourful.

Once you allow two crit-multiplying effects, things get rather out of balance.

Vik
2007-01-17, 02:28 AM
Just keen: 62 * 1.3 = 80.6 average damage per attack
Keen+AK: 62 * 1.6 = 99.2 average damage per attack

AK (Augment Critical) gave a +18.6 average damage per attack increase. That would be valued at a +9 to +10 enchantment. But, wait : the keen enchantment is, by itself, worth 62 * 0.15 = 9.3 points of damage, meaning by your very own calculation a +5 enchantment ?
Plus the fact that a +1 enchantment is more than worth a +5% of damage (in this case : +3 average damage per attack). If you gain 30% of damage, then at most you can consider it worth a +6 bonus. And when I say at most, that's because there are creatures immune to crits, and other that you will have a lesser chance to hit than your threat range. Your level 20 fighter, for instance, charges at +29 bonus to hit. Versus valuables opponent (CR 21 or more), that means he needs at least a 13 or more to hit - that's the AC of a dragon of appropriate CR with no spells or magic item, so it can easily raise to a 17+ to hit. Furthermore, crits wont multiply additionnal dice of damage.

Still, I'll agree about the fact that Augment critical has the slight problem of being stackable with a Feat or with a spell - but this can easily been modified (something like "if the weapon is augmented, it cannot benefit from any other effect affecting critical hits in a beneficial way").

magic8BALL
2007-01-17, 03:07 AM
No Yakk, your maths is flawed, you said it yourself...


Threats do not auto-hit, at least not in the d20 rules I've read.

but...



Take your effective threat range width. Divide by 20. That percentage of hits become crits. Really, the math works out that way.

...assuming you cornfirm the threat. Thats why you should divide by two... this assumes only 1/2 your threats are confirmed.

This means a Longsword deals a crit 5% of the time, even though it may score a threat 10% of the time.

This is me getting all defencive about maths though...

-=-=-=-=-=-

So basically, your argument, Yakk and Vik, (and it is a very valid one too, I agree, mathematically...) is that Keen and Augmentation should never stack: You cannot weild a keen weapon if you have the Augmented Dcritical feat, a wizard cannot cast keen edges on your scimitar if you have the Improved critical feat, Greater Threat should not exist, etc, based on game balance. Is this right?

If so... how do you, in games terms, enforce that?

"Aww... sorry, the spell failed... you must have Improved Critical as a feat trained hard to you this weapon effectivly..."

"I can teach you this feat trick... but it wont work if you use a magic weapin that is keen has this other particular effect wich is totally different in procedure, even though they deal the same mean damage but the maths of the outcome is the same... if you believe in you life being measured in numbers and all..."

"Yeah... nah... I can only enhance it one way or another... you cant have both... sorry..."

These are egsamples of the in game conversation as to why keen and augmentation cannot co-exist, and I for one find them silly.

Vik
2007-01-17, 03:52 AM
Well, exactly the same way you can't benefit from both Improved Critical and Keen.

Oh, by the way :

...assuming you cornfirm the threat. Thats why you should divide by two... this assumes only 1/2 your threats are confirmed.

This means a Longsword deals a crit 5% of the time, even though it may score a threat 10% of the time.No. Assuming that a threat is also a hit, and that there is no additionnal dice of damage :
The average damage you deal without crit is : Chance to hit x Damage per hit
The average damage you gain with a crit is : Chance to score a crit x Chance to hit again x Damage per hit x (Multiplier - 1)
So that, compared to the normal damage, the crit relative gain is Threat x (Multiplier - 1).

magic8BALL
2007-01-17, 06:14 AM
You seem to present your maths wrong too.

Let "Chance to hit" be x,
"threat range" be y,
"critical multiplier" be z,
"mean base damage" be d,
such that the mean base damage is the amount you roll on a standard hit(say 1d6+12 --> 15.5, for exsample)

Therefore, the mean damage delt by any attack over n trials as n becomes large is:

{1*0 + (19-y)x + y[xz+(1-x)]}d


For simplicity, I assume that you are only concered with the weapon makes contact, and that only 1/2 of the threats scored are confirmed, yielding this formula:

d*[1+(yz/40)]

This way you dont need to worry about all the variables that lead into what has been known as x.

-=-=-=-=-=-=-

You cant benifit from both keen and Improved Crit, becouse they do the same thing:

"I'd show you this trick to make your sword effectivly sharper than it is, but it has its limitations: you can only use it on a sword that isnt already sharper than its standard self."

"You do realise that by having this cast on the sword, its sharpness will only be equal to your training? You will recieve no added benifit..."

A whole lot more plausable.

Yakk
2007-01-17, 12:45 PM
Starting with your variables:
"Let "Chance to hit" be x,
"threat range" be y,
"critical multiplier" be z,
"mean base damage" be d,"

I'm defining two new ones. They turn out to be useful:
Let "threat chance" be t = y/20.
Let "crit damage bonus" be b = z-1.

And some random variables: (used formally -- in probability, random variables are placeholders for the thingy that generates random results, like an attack that can hit/miss then does a random amount of damage)
Let A be the random variable "attack without crits".
Let D be the random variable "damage on a hit without crits".

E(A) = x*E(D) = x*d

(The function E is known as "expectation", or "average". When applied to a random variable, it returns the mean. This kind of notation allows you to manipulate random variables algebraicly, quite useful!)

So, in english, neglecting crits your expected damage is chance to hit times average damage per hit. This seems pretty damn reasonable.

I am neglecting crits because it forms a baseline, plus damage with neglected crits is really easy to work out. My goal is to generate a simple formula that takes this baseline damage, and includes the effect of crits on average damage.

So, what happens when you add crits into the mixture?

Let C be the random variable "attack, including crit effects". Let's figure out how it evaluates:

You swing. Assuming the threat range is all a valid hit:
1-x chance of a miss
x-t chance of a hit, no threat
t chance of a threat

If you have a threat:
1-x chance to not confirm, do normal damage
x chance to confirm, do crit damage.

So, the entire result tree is:
1-x chance of a miss
x-t chance of a hit, no threat
t*(1-x) chance of a threat that didn't confirm
t*x chance of a crit

== Group the swings that result in a normal hit

1-x chance of a miss
x-t + t(1-x) chance of a normal hit
t*x chance of a crit

== Expand t(1-x) on the normal hit line

1-x chance of a miss
x-t + t-x*t chance of a normal hit
t*x chance of a crit

== Cancel the +t and the -t on the normal hit line

1-x chance of a miss
x-x*t chance of a normal hit
t*x chance of a crit

Now, for the damage done: Change normal hit/crit hit to the expected average damage

1-x chance of a 0 damage
x-x*t chance of d average damage
t*x chance of d*z = (b+1)*d

Which works out to: Now that everything is in damage, we can add them together
(x-x*t)*d + t*x*(b+1)*d
Spreading:
x*d - x*t*d + t*x*b*d + t*d*x
the two bold terms are identical with opposite signs. Cancel the like terms
x*d + t*x*b*d
Factor out x*d: Note that x*d is E(A), or the expected damage when you neglect crits
x*d (1+t*b)


So,
E(C) = x*d*(1+t*b)
= E(A) * (1+t*b)
t is threat chance, b is treat bonus.
t = "threat range"/20 = y/20, so
E(C) = E(A) * (1+ y*b/20)
I call "y * b" the number of crit pips the weapon has.

The threat width, times the bonus damage (above 1x) the weapon does on a crit.

E(attacks, counting crits) = E(attacks, neglecting crits) * (1 + "crit pips"/20)

Which is the result I was claiming: A weapon with 3 crit pips does +15% damage per hit over the weapon with 0 crit pips. It doesn't matter what your hit chance is, so long as your entire threat range is in the hit domain.


For simplicity, I assume that you are only concered with the weapon makes contact, and that only 1/2 of the threats scored are confirmed, yielding this formula:

d*[1+(yz/40)]

Your assumptions are unnessicary and result in an incorrect conclusion. You can just translate crit pips into a percent damage bonus, as demonstrated above. This boost is pips/20 * 5%.

Pips = (Bonus-1) * (Width).
20x2 weapons have 1 Pip.
20x3 weapons have 2 Pips.
19x2 weapons have 2 Pips
20x4 weapons have 3 Pips.
18x2 weapons have 3 Pips.

Keen and/or Improved crit doubles the number of Pips.

Your ability also doubles the number of Pips -- and it stacks, geometrically, with Keen and/or Improved crit.

By SRD, a keen rapier has a +30% crit damage bonus, and a keen longsword a +20% damage bonus. Your change boosts this to +60% and +40%.

This changes game balance, making high-crit-pip weapons signiciantly and massively better than low-crit-pip weapons, for the expenditure of only a small amount of enchanting and a single feat.

A ~ 25% average boost to melee damage output in all situations is not something that should cost a single feat (or a single +1 enchant).


You cant benifit from both keen and Improved Crit, becouse they do the same thing

No. You can't benefit from them both, because allowing both of them results in unbalanced game mechanics and weapons. Fixing the unbalanced game mechanics and weapons was not something D&D wanted to so, so they just banned it.

...

What happens is the percent bonus difference between crit-monkey weapons and non-crit monkey weapons grows. As it grows, the balancing gimping of the crit-monkey weapons doesn't scale, while the difference does.

In your case, the difference grows geometrically when both effects stack. This makes the imbalance worse and harder to account for.

Tortoise262
2007-11-14, 03:49 AM
x7 critical? I'd love that, but it's wacky. This is the way I see it: The feat should double the damage dealt on a critical hit. x4 doubled, by D&D rules, is x5... not x7, as much as I want it to be.

Hagentai
2007-11-21, 06:40 PM
Now this is just what I've done with my game.

Not being a fan of vorpal I made Augmented Critical a +4 enhancement that can go on any weapon.

A times 2 would go to times 3.

So a 1+ augment critical long sword is a +5 sword.

magic8BALL
2007-11-23, 05:23 PM
For:
"Chance to hit" be x,
"threat range" be y,
"critical multiplier" be z,
"mean base damage" be d,"

Your defined,
"threat chance", t = y/20, is ok, but
"crit damage bonus", b = z-1, is wrong, as the damage dealt in a succesful critiacl hit is zd, hence the bonus damage, b = zd-d = d(z-1). So your calculations are out by a factor of your base damage. I'm going to ignore the rest.


x7 critical? I'd love that, but it's wacky. This is the way I see it: The feat should double the damage dealt on a critical hit. x4 doubled, by D&D rules, is x5... not x7, as much as I want it to be.

No, it really is x7.

x4 means normal damage plus three times normal damage as extra damage.

The feat/spell/effect doubles extra damage (as keen spell/effect, improved crit doubles threat range), so the extra damage jumps from three times normal to six times normal, for a total of x7 damage.

Thats just how the game balances. Please see the long 'maths-type' posts above if you're unsure.

I think the problem there is more the case of a x4 crit range.

I tremble when this varient is used in conjunction with the Great Hammer (used by Longhorn Minotaurs in MM(3/4?)) Base crit 19-20/x3!