crit multiplier and crit range and impr crit, overpowered?? [Archive] - Wizards Community

crit multiplier and crit range and impr crit, overpowered?? [Archive] - Wizards Community

Post/Author/DateTime Post
Kroll
10-21-04, 05:46 AM I made a miscalculation in this..so read my last post for the TRUTH!!!!

<edited for stupidity >...too bad it is mine ;)

SO I sat down and pondered...about the above headline..sat down in front of excel and made some numbers on different weapons

in this test I compare scimitar longsword and battel axe vs a target with 25% 50% and 95% hit chance, with a zero dam bonus and with a +6 damage bonus and with the impr crit feat.

so first table coming up..
http://users.cybercity.dk/~dsl37620/table1.bmp
so this shows that the longsword is the winner of test 1.

table 2:
http://users.cybercity.dk/~dsl37620/table2.bmp
so here, with a +6 damagebonus, battel axe blows the competition out of the water.

in conclusion: low damage fighters would be best served with high crit range weapons, but with just a modest damage bonus would be better off switching to a high multiplier weapon.
The conclusion of this test is that the gnome hooked hammer has to be the absolute best weapon at high level, followed by probably the greataxe.

ofcourse therea re other factors to consider, power attack with 2handed and so on and so forth, and not to forget..the ROLEplay..but looking purely at numbers the above holds true.
Nom
10-21-04, 09:15 AM Can you explain how you got these numbers? Mathematically, 19-20/x2 is identical average damage output to 20/x3, as long as the roll required to hit is less than 19.

In contrast 1d6 18-20/x2 or 20/x4 is better than 1d8 19-20/x2 or 20/x3 once the bonus damage (not from the die roll itself) exceeds 18.5. With improved crit (for example), the bonus damage need only exceed 8.5. With a double improvement, the bonus needed drops to 5.17.

Formula for average damage:

h: to-hit chance
c: crit range (18-20 -> 15%)
m: crit multiplier
d: expected damage given a standard hit
D: average damage

D is chance of regular hit (h-c) * damage (d)
plus chance of failed critical threat (c * (1-h)) * damage (d)
plus chance of successful critical (c * h) * damage (d) * multiplier (m)

D = { (h-c) * d } + { c * (1-h) * d } + { c * h * d * m }
expanding
D = { h * d - c * d } + { c * d - c * h * d } + { c * h * d * m }
cancelling and factoring h*d
D = h * d * (1 - c + c * m) = h * d * (1 + c * (m-1))

b = damage bonus (Str, magic, ...)

Longsword: 1d8 19-20/x2
d = 4.5 + b; c = 0.1; m = 2
D = h * (4.5 + b) * (1.1)

Battleaxe: 1d8 20/x3
d = 4.5 + b; c = 0.05; m = 3
D = h * (4.5 + b) * 1.1

Scimitar: 1d6 18-20/x2
d = 3.5 + b; c = 0.15; m = 2
D = h * (3.5 + b) * 1.15

Pick: 1d6 20/x4
d = 3.5 + b; c = 0.05; m = 4
D = h * (3.5 + b) * 1.15

Scimitar / pick = longsword / axe when ...
h * (3.5 + b) * 1.15 = h * (4.5 + b) * 1.1
=> 3.5 + b = (4.5 + b) * (1.1 / 1.15)
=> (0.05 / 1.15) * b = 4.5 * 1.1 / 1.15 - 3.5
=> b = (4.5 * 1.1 - 3.5 * 1.15) / 0.05 = (4.95 - 4.025) * 20 = 18.5

With double value crit (eg double multiplier):
1d8 19-20/x3 => D = h * (4.5 + b) * 1.2
1d6 19-20/x4 => D = h * (3.5 + b) * 1.3

3.5 + b = (4.5 + b) * (1.2 / 1.3)
=> b = (4.5 * 1.2 - 3.5 * 1.3) / 0.1 = (5.4 - 4.55) * 10 = 8.5

With triple value crit:
1d8 18-20/x3 => D = h * (4.5 + b) * 1.3
1d6 18-20/x4 => D = h * (3.5 + b) * 1.45

3.5 + b = (4.5 + b) * (1.3 / 1.45)
=> b = (4.5 * 1.3 - 3.5 * 1.45) / 0.15 = (5.85 - 5.075) / 0.15 = 5.16...
Enaloindir
10-21-04, 09:19 AM Something must be wrong with the way you conducted your test. I did the same thing, but approached it theoretically (this might be boring).

Using the following symbols:

D = multiplied damage on a critical hit (base+Str+...)
d = extra damage dice, not multiplied on a critical
hit (flaming,...)
M = critical multiplier (2 for a longsword, 3 for a
battleaxe,...)
P = hit chance (50% if you hit on 11+ on a d20)
Pc = threat chance (5% = .05 for battle axe,
10% = .10 for longsword,...)
Ph = chance for a non-threatening hit (this is P-Pc)

I came to the following conclusions (for a single attack)

Average damage =
= Avg dmg (non-crit) + Avg dmg (crit)
= Avg dmg (normal hit) + Avg dmg (unconfirmed crit)
+ Avg dmg (crit)
= P(normal hit)*dmg(normal hit)
+ P(unconfirmed crit)*dmg(normal hit)
+ P(crit)*dmg(crit)
= Ph*(D+d) + Pc*(1-P)*(D+d) + Pc*P*(M*D+d)
= Ph*(D+d) + Pc*(D+d) - Pc*P*(D+d) + Pc*P*(M*D+d)
= (Pc+Ph)*(D+d) - Pc*P*D - Pc*P*d + Pc*P*M*D + Pc*P*d
= P*(D+d) + Pc*P*(M-1)*D
= P*(D+d+Pc*(M-1)*D)
= P*(d+D*(1+Pc*(M-1)))
= P*(d+D*CF)
with CF = 1+Pc*(M-1) the "critical factor"

If you are comparing two weapons, the hit chance P will be indentical. Extra damage dice damage d should alse be the same. So, the "quality" of the weapon is only determined by D*CF. Let's nog plug in a few values.

First, for weapons without improved critical and/or the keen enhancement
Longsword:
D = 4.5+X (1d8+X)
Pc = 0.10 (threat on 19-20)
M = 2 (x2 damage on a critical hit)
--> (4.5+X)*(1+0.10*(2-1)) = (4.5+X)*1.1
= 4.95+1.1*X average damage for each hit

Battle axe:
D = 4.5+X (1d8+X)
Pc = 0.05 (threat on 20)
M = 3 (x3 damage on a critical hit)
--> (4.5+X)*(1+0.05*(3-1)) = (4.5+X)*1.1
= 4.95+1.1*X average damage for each hit

Scimitar:
D = 3.5+X (1d6+X)
Pc = 0.15 (threat on 18-20)
M = 2 (x2 damage on a critical hit)
--> (3.5+X)*(1+0.15*(2-1)) = (3.5+X)*1.15
= 4.025+1.15*X average damage for each hit

You see that the damage for the battle axe and longsword are completely identical, with 4.95+1.1*X damage for each successful hit. The scimitar trails a bit behind with only 4.025+1.15*X damage for each hit.
However, once X = 18.5, the scimitar has caught up with and surpassed the longsword and battle axe in terms of damage.

Now, when you have improved critical and/or the keen enhancement:
Longsword:
D = 4.5+X (1d8+X)
Pc = 0.20 (threat on 17-20)
M = 2 (x2 damage on a critical hit)
--> (4.5+X)*(1+0.20*(2-1)) = (4.5+X)*1.2
= 5.40+1.2*X average damage for each hit

Battle axe:
D = 4.5+X (1d8+X)
Pc = 0.10 (threat on 19-20)
M = 3 (x3 damage on a critical hit)
--> (4.5+X)*(1+0.10*(3-1)) = (4.5+X)*1.2
= 5.40+1.2*X average damage for each hit

Scimitar:
D = 3.5+X (1d6+X)
Pc = 0.30 (threat on 15-20)
M = 2 (x2 damage on a critical hit)
--> (3.5+X)*(1+0.30*(2-1)) = (3.5+X)*1.30
= 4.55+1.30*X average damage for each hit

Again, the battle axe and longsword are completely identical, with the scimitar doind a little less damage if you have a low damage adjustment. Once X = 8.5, the scimitar surpasses them in terms of damage.

My conclusions:

The term D*CF = D*(1+Pc*(M-1)) determines weapon balance. This means that 19/x2 and 20/x3 weapons are completely equivalent. Same goes for 18/x2 and 20/x4 weapons... Of course, this is only true if the base damage of those weapons is equal (no point comparing a longsword with a greatsword)
Even though most 18/x2 and 20/x4 weapons have a slightly smaller damage compared to 19/x2 and 20/x3 weapons, they do more damage once you get your strength high enough
When creating a feat that increases a weapon's critical multiplier M, you need to be careful: this increased multiplier should only apply in the weapon's original threat range. Otherwise, the combination of both an increased thret range and critical multiplier would be much stronger than the combination of two feats would allow.
The critical factor CF goes 1.1-1.2-1.4. when applying these feats. You can clearly see that the second increase is much greater than the first one. When comparing this with the pricing for magic items, where an increasing bonus becomes more expensive instead of cheaper, this is clearly unbalanced. Applying the increased multiplier only in the original threat range (so you can have a 17-19/x2-x3 weapon :D) keeps this under control to a certain extent (CF = 1.1-1.2-1.3).
Of course, simply not allowing those two feats to stack is another option (probably the safest one)

I hope you're still awake now,
Enaloindir
Enaloindir
10-21-04, 09:20 AM Seems like both Nom and me were typing the same thing at the same time :D

Enaloindir
Kroll
10-21-04, 09:57 AM I'm absolutly no mathematical genius, so here goes (gets in the line of fire ;) )

ok...

I took 3 incidens, one with a hit probability of 95% (alll except 1's hit) one with 50% and one with 25%

I then use the following calculation, exampel with 50% hit prob and +6 dam
10% crit probability (19-20)

((base dam x (chance to hit) ) + dam bonus
+
((base dam x crit multiplier+(crit multiplier x dam bonus)) x crit probability) x chance to hit

with numbers for the longsword with a hit probability of 50% I would get theese numbers

((4,5+6) x 0,5)+(((4,5+6) x 2) x 0,1 x 0,5)= 20,7

hope that clarifies that, again I'm a doctor not a statistician ;)
tarkin
10-21-04, 10:39 AM You counted the crit twice, and did the math wrong.

You did:

with numbers for the longsword with a hit probability of 50% I would get theese numbers

((4,5+6) x 0,5)+(((4,5+6) x 2) x 0,1 x 0,5)= 20,7

First of all, that equation is equal to 6,3 not 20,7

Secondly, that math is for having the crit do x3 damage because you are adding the x2 damage AFTER already adding the damage for a regular hit as well.

To do it right it should be:
((4,5+6) x 0,5)+((4,5+6) x 0,1 x 0,5)= 5,775

or to those of us that live in the USA:
((4.5+6) x 0.5)+((4.5+6) x 0.1 x 0.5)= 5.775
Enaloindir
10-21-04, 10:43 AM or to those of us that live in the USA:
((4.5+6) x 0.5)+((4.5+6) x 0.1 x 0.5)= 5.775

Hey, some people live in Europe and still get a decimal . on their keyboards... ;)
Kroll
10-21-04, 11:05 AM found out by the x2 crit counting on the bike trip home ;)

going back to my excel and trying to find some loop outof saying I was wrong ;)
Kroll
10-21-04, 11:16 AM ((base dam x (chance to hit) ) + dam bonus
+
((base dam x crit multiplier+(crit multiplier x dam bonus)) x crit probability) x chance to hit

with numbers for the longsword with a hit probability of 50% I would get theese numbers

((4,5+6) x 0,5)+(((4,5+6) x 2) x 0,1 x 0,5)= 20,7

sorry wrote the formular I use wrong

((base dam(avg) + dam bonus) x (chance to hit))
+
((base dam(avg) + dam bonus) x crit multiplier) x crit prob x hit prob.

with exampel
((4,5 + 6) x 0,5) + (4,5 + 6) x 0,1 x 0.5 x 2 = 6,3

and for some reason my table dosen't show that..so here eare the revised tables..

http://users.cybercity.dk/~dsl37620/table3.bmp

table 2
http://users.cybercity.dk/~dsl37620/table4.JPG

so I have to eat my words ..SORRY!!!..

seems like my conclusion were way off...with scimitar being a better weapon at high level with dam bonus than the x3 weapons, guess I'll have to make some huse rule.

thansk for helping me out figuring this out :)
Nom
10-22-04, 12:22 AM Unfortunately for clean analyses, there are a few more quirks:

Purely from damage, a 12-20/x2 weapon is weaker than 18-20/x4. Both have a CF of 1.9, but it's significantly more likely for 12-20/x2 to miss within the critical range (eg need 15 to-hit) than for 18-20/x4.

Elemental burst weapons gain bonus damage on a critical hit. Burst is balanced between 19-20/x2 and 20/x3 due to multiplying damage to match critical multiplier, but an 18-20/x2 weapon is obviously a better burster than 19-20/x2.

You also need to consider whether average or point damage is more valuable. A high range x2 weapon will crit more often, but the crits won't hurt nearly as much as on a x4 weapon. A high crit multiplier exacerbates luck effects, by creating a rare chance of going from "pretty good" to "dead". Which works better for overcoming DR depends on the magnitude of the DR (and whether the creature has fast healing).
Frozen Yakman
10-22-04, 01:49 AM Pretty much what Nom said, the x4 and x3 end up being better than all the rest of their cousins because their crit-range is less effected by chance to-hit. The true average damage of a weapon is probably best figured as Sum(ad(x), 1, 20)/20 where ad(x) is the average damage a weapon has for a given number needed to roll on the d20 to hit.
ad(x) = chance-to-hit(x) ((1 - chance-to-crit(x))avg-normal-hit-damage + chance-to-crit(x)avg-crit-damage + avg-bonus-dice-damage).

I did some calculations awhile ago with the Scythe, Falchion, and Greatsword (and one Greataxe test as well). The numbers shouldn't be too different for 1h weapons or other comparisons.

What follows is what minimum damage bonus is need for the Scythe and Falchion exceed a similarly enchanted Greatsword.

Base weapon
Scythe +59
Falchion +59

w/ Keen
Scythe +29
Falchion +30

w/ Flaming Burst
Scythe +53
Falchion +53

w/ Keen and Flaming Burst
Scythe +23
Falchion +24

3e only
w/ Keen and Imp Crit
Scythe +19
Falchion +20

w/ Keen and Imp Crit and Flaming Burst
Scythe +13
Falchion +15
Greataxe +529

Post/Author/DateTime	Post
Kroll 10-21-04, 05:46 AM	I made a miscalculation in this..so read my last post for the TRUTH!!!! <edited for stupidity >...too bad it is mine ;) SO I sat down and pondered...about the above headline..sat down in front of excel and made some numbers on different weapons in this test I compare scimitar longsword and battel axe vs a target with 25% 50% and 95% hit chance, with a zero dam bonus and with a +6 damage bonus and with the impr crit feat. so first table coming up.. http://users.cybercity.dk/~dsl37620/table1.bmp so this shows that the longsword is the winner of test 1. table 2: http://users.cybercity.dk/~dsl37620/table2.bmp so here, with a +6 damagebonus, battel axe blows the competition out of the water. in conclusion: low damage fighters would be best served with high crit range weapons, but with just a modest damage bonus would be better off switching to a high multiplier weapon. The conclusion of this test is that the gnome hooked hammer has to be the absolute best weapon at high level, followed by probably the greataxe. ofcourse therea re other factors to consider, power attack with 2handed and so on and so forth, and not to forget..the ROLEplay..but looking purely at numbers the above holds true.
Nom 10-21-04, 09:15 AM	Can you explain how you got these numbers? Mathematically, 19-20/x2 is identical average damage output to 20/x3, as long as the roll required to hit is less than 19. In contrast 1d6 18-20/x2 or 20/x4 is better than 1d8 19-20/x2 or 20/x3 once the bonus damage (not from the die roll itself) exceeds 18.5. With improved crit (for example), the bonus damage need only exceed 8.5. With a double improvement, the bonus needed drops to 5.17. Formula for average damage: h: to-hit chance c: crit range (18-20 -> 15%) m: crit multiplier d: expected damage given a standard hit D: average damage D is chance of regular hit (h-c) * damage (d) plus chance of failed critical threat (c * (1-h)) * damage (d) plus chance of successful critical (c * h) * damage (d) * multiplier (m) D = { (h-c) * d } + { c * (1-h) * d } + { c * h * d * m } expanding D = { h * d - c * d } + { c * d - c * h * d } + { c * h * d * m } cancelling and factoring hd D = h d * (1 - c + c * m) = h * d * (1 + c * (m-1)) b = damage bonus (Str, magic, ...) Longsword: 1d8 19-20/x2 d = 4.5 + b; c = 0.1; m = 2 D = h * (4.5 + b) * (1.1) Battleaxe: 1d8 20/x3 d = 4.5 + b; c = 0.05; m = 3 D = h * (4.5 + b) * 1.1 Scimitar: 1d6 18-20/x2 d = 3.5 + b; c = 0.15; m = 2 D = h * (3.5 + b) * 1.15 Pick: 1d6 20/x4 d = 3.5 + b; c = 0.05; m = 4 D = h * (3.5 + b) * 1.15 Scimitar / pick = longsword / axe when ... h * (3.5 + b) * 1.15 = h * (4.5 + b) * 1.1 => 3.5 + b = (4.5 + b) * (1.1 / 1.15) => (0.05 / 1.15) * b = 4.5 * 1.1 / 1.15 - 3.5 => b = (4.5 * 1.1 - 3.5 * 1.15) / 0.05 = (4.95 - 4.025) * 20 = 18.5 With double value crit (eg double multiplier): 1d8 19-20/x3 => D = h * (4.5 + b) * 1.2 1d6 19-20/x4 => D = h * (3.5 + b) * 1.3 3.5 + b = (4.5 + b) * (1.2 / 1.3) => b = (4.5 * 1.2 - 3.5 * 1.3) / 0.1 = (5.4 - 4.55) * 10 = 8.5 With triple value crit: 1d8 18-20/x3 => D = h * (4.5 + b) * 1.3 1d6 18-20/x4 => D = h * (3.5 + b) * 1.45 3.5 + b = (4.5 + b) * (1.3 / 1.45) => b = (4.5 * 1.3 - 3.5 * 1.45) / 0.15 = (5.85 - 5.075) / 0.15 = 5.16...
Enaloindir 10-21-04, 09:19 AM	Something must be wrong with the way you conducted your test. I did the same thing, but approached it theoretically (this might be boring). Using the following symbols: D = multiplied damage on a critical hit (base+Str+...) d = extra damage dice, not multiplied on a critical hit (flaming,...) M = critical multiplier (2 for a longsword, 3 for a battleaxe,...) P = hit chance (50% if you hit on 11+ on a d20) Pc = threat chance (5% = .05 for battle axe, 10% = .10 for longsword,...) Ph = chance for a non-threatening hit (this is P-Pc) I came to the following conclusions (for a single attack) Average damage = = Avg dmg (non-crit) + Avg dmg (crit) = Avg dmg (normal hit) + Avg dmg (unconfirmed crit) + Avg dmg (crit) = P(normal hit)dmg(normal hit) + P(unconfirmed crit)dmg(normal hit) + P(crit)dmg(crit) = Ph(D+d) + Pc(1-P)(D+d) + PcP(MD+d) = Ph(D+d) + Pc(D+d) - PcP(D+d) + PcP(MD+d) = (Pc+Ph)(D+d) - PcPD - PcPd + PcPMD + PcPd = P(D+d) + PcP(M-1)D = P(D+d+Pc(M-1)D) = P(d+D(1+Pc(M-1))) = P(d+DCF) with CF = 1+Pc(M-1) the "critical factor" If you are comparing two weapons, the hit chance P will be indentical. Extra damage dice damage d should alse be the same. So, the "quality" of the weapon is only determined by DCF. Let's nog plug in a few values. First, for weapons without improved critical and/or the keen enhancement Longsword: D = 4.5+X (1d8+X) Pc = 0.10 (threat on 19-20) M = 2 (x2 damage on a critical hit) --> (4.5+X)(1+0.10(2-1)) = (4.5+X)1.1 = 4.95+1.1X average damage for each hit Battle axe: D = 4.5+X (1d8+X) Pc = 0.05 (threat on 20) M = 3 (x3 damage on a critical hit) --> (4.5+X)(1+0.05(3-1)) = (4.5+X)1.1 = 4.95+1.1X average damage for each hit Scimitar: D = 3.5+X (1d6+X) Pc = 0.15 (threat on 18-20) M = 2 (x2 damage on a critical hit) --> (3.5+X)(1+0.15(2-1)) = (3.5+X)1.15 = 4.025+1.15X average damage for each hit You see that the damage for the battle axe and longsword are completely identical, with 4.95+1.1X damage for each successful hit. The scimitar trails a bit behind with only 4.025+1.15X damage for each hit. However, once X = 18.5, the scimitar has caught up with and surpassed the longsword and battle axe in terms of damage. Now, when you have improved critical and/or the keen enhancement: Longsword: D = 4.5+X (1d8+X) Pc = 0.20 (threat on 17-20) M = 2 (x2 damage on a critical hit) --> (4.5+X)(1+0.20(2-1)) = (4.5+X)1.2 = 5.40+1.2X average damage for each hit Battle axe: D = 4.5+X (1d8+X) Pc = 0.10 (threat on 19-20) M = 3 (x3 damage on a critical hit) --> (4.5+X)(1+0.10(3-1)) = (4.5+X)1.2 = 5.40+1.2X average damage for each hit Scimitar: D = 3.5+X (1d6+X) Pc = 0.30 (threat on 15-20) M = 2 (x2 damage on a critical hit) --> (3.5+X)(1+0.30(2-1)) = (3.5+X)1.30 = 4.55+1.30X average damage for each hit Again, the battle axe and longsword are completely identical, with the scimitar doind a little less damage if you have a low damage adjustment. Once X = 8.5, the scimitar surpasses them in terms of damage. My conclusions: The term DCF = D(1+Pc*(M-1)) determines weapon balance. This means that 19/x2 and 20/x3 weapons are completely equivalent. Same goes for 18/x2 and 20/x4 weapons... Of course, this is only true if the base damage of those weapons is equal (no point comparing a longsword with a greatsword) Even though most 18/x2 and 20/x4 weapons have a slightly smaller damage compared to 19/x2 and 20/x3 weapons, they do more damage once you get your strength high enough When creating a feat that increases a weapon's critical multiplier M, you need to be careful: this increased multiplier should only apply in the weapon's original threat range. Otherwise, the combination of both an increased thret range and critical multiplier would be much stronger than the combination of two feats would allow. The critical factor CF goes 1.1-1.2-1.4. when applying these feats. You can clearly see that the second increase is much greater than the first one. When comparing this with the pricing for magic items, where an increasing bonus becomes more expensive instead of cheaper, this is clearly unbalanced. Applying the increased multiplier only in the original threat range (so you can have a 17-19/x2-x3 weapon :D) keeps this under control to a certain extent (CF = 1.1-1.2-1.3). Of course, simply not allowing those two feats to stack is another option (probably the safest one) I hope you're still awake now, Enaloindir
Enaloindir 10-21-04, 09:20 AM	Seems like both Nom and me were typing the same thing at the same time :D Enaloindir
Kroll 10-21-04, 09:57 AM	I'm absolutly no mathematical genius, so here goes (gets in the line of fire ;) ) ok... I took 3 incidens, one with a hit probability of 95% (alll except 1's hit) one with 50% and one with 25% I then use the following calculation, exampel with 50% hit prob and +6 dam 10% crit probability (19-20) ((base dam x (chance to hit) ) + dam bonus + ((base dam x crit multiplier+(crit multiplier x dam bonus)) x crit probability) x chance to hit with numbers for the longsword with a hit probability of 50% I would get theese numbers ((4,5+6) x 0,5)+(((4,5+6) x 2) x 0,1 x 0,5)= 20,7 hope that clarifies that, again I'm a doctor not a statistician ;)
tarkin 10-21-04, 10:39 AM	You counted the crit twice, and did the math wrong. You did: with numbers for the longsword with a hit probability of 50% I would get theese numbers ((4,5+6) x 0,5)+(((4,5+6) x 2) x 0,1 x 0,5)= 20,7 First of all, that equation is equal to 6,3 not 20,7 Secondly, that math is for having the crit do x3 damage because you are adding the x2 damage AFTER already adding the damage for a regular hit as well. To do it right it should be: ((4,5+6) x 0,5)+((4,5+6) x 0,1 x 0,5)= 5,775 or to those of us that live in the USA: ((4.5+6) x 0.5)+((4.5+6) x 0.1 x 0.5)= 5.775
Enaloindir 10-21-04, 10:43 AM	or to those of us that live in the USA: ((4.5+6) x 0.5)+((4.5+6) x 0.1 x 0.5)= 5.775 Hey, some people live in Europe and still get a decimal . on their keyboards... ;)
Kroll 10-21-04, 11:05 AM	found out by the x2 crit counting on the bike trip home ;) going back to my excel and trying to find some loop outof saying I was wrong ;)
Kroll 10-21-04, 11:16 AM	((base dam x (chance to hit) ) + dam bonus + ((base dam x crit multiplier+(crit multiplier x dam bonus)) x crit probability) x chance to hit with numbers for the longsword with a hit probability of 50% I would get theese numbers ((4,5+6) x 0,5)+(((4,5+6) x 2) x 0,1 x 0,5)= 20,7 sorry wrote the formular I use wrong ((base dam(avg) + dam bonus) x (chance to hit)) + ((base dam(avg) + dam bonus) x crit multiplier) x crit prob x hit prob. with exampel ((4,5 + 6) x 0,5) + (4,5 + 6) x 0,1 x 0.5 x 2 = 6,3 and for some reason my table dosen't show that..so here eare the revised tables.. http://users.cybercity.dk/~dsl37620/table3.bmp table 2 http://users.cybercity.dk/~dsl37620/table4.JPG so I have to eat my words ..SORRY!!!.. seems like my conclusion were way off...with scimitar being a better weapon at high level with dam bonus than the x3 weapons, guess I'll have to make some huse rule. thansk for helping me out figuring this out :)
Nom 10-22-04, 12:22 AM	Unfortunately for clean analyses, there are a few more quirks: Purely from damage, a 12-20/x2 weapon is weaker than 18-20/x4. Both have a CF of 1.9, but it's significantly more likely for 12-20/x2 to miss within the critical range (eg need 15 to-hit) than for 18-20/x4. Elemental burst weapons gain bonus damage on a critical hit. Burst is balanced between 19-20/x2 and 20/x3 due to multiplying damage to match critical multiplier, but an 18-20/x2 weapon is obviously a better burster than 19-20/x2. You also need to consider whether average or point damage is more valuable. A high range x2 weapon will crit more often, but the crits won't hurt nearly as much as on a x4 weapon. A high crit multiplier exacerbates luck effects, by creating a rare chance of going from "pretty good" to "dead". Which works better for overcoming DR depends on the magnitude of the DR (and whether the creature has fast healing).
Frozen Yakman 10-22-04, 01:49 AM	Pretty much what Nom said, the x4 and x3 end up being better than all the rest of their cousins because their crit-range is less effected by chance to-hit. The true average damage of a weapon is probably best figured as Sum(ad(x), 1, 20)/20 where ad(x) is the average damage a weapon has for a given number needed to roll on the d20 to hit. ad(x) = chance-to-hit(x) ((1 - chance-to-crit(x))avg-normal-hit-damage + chance-to-crit(x)avg-crit-damage + avg-bonus-dice-damage). I did some calculations awhile ago with the Scythe, Falchion, and Greatsword (and one Greataxe test as well). The numbers shouldn't be too different for 1h weapons or other comparisons. What follows is what minimum damage bonus is need for the Scythe and Falchion exceed a similarly enchanted Greatsword. Base weapon Scythe +59 Falchion +59 w/ Keen Scythe +29 Falchion +30 w/ Flaming Burst Scythe +53 Falchion +53 w/ Keen and Flaming Burst Scythe +23 Falchion +24 3e only w/ Keen and Imp Crit Scythe +19 Falchion +20 w/ Keen and Imp Crit and Flaming Burst Scythe +13 Falchion +15 Greataxe +529