Calculating average damage for weapons? [Archive] - Wizards Community

Calculating average damage for weapons? [Archive] - Wizards Community

Post/Author/DateTime Post
Gemstone
04-14-06, 06:45 AM I've been trying to come up with a formulae that calculates the average damage that a weapon can deal with each hit, which includes critical hit damage. This far, my calculations have been incorrect, but they have proven useful. If anyone out there has a correct formulae for calculating hits, would you please share it with me?
claypigeons
04-14-06, 07:16 AM The average roll on a single y-sided die = (y+1)/2

Let's say you have a longsword. Let's assume you hit. You do (8+1)/2 damage, or 4.5 per hit. Add power attack and other things

The average roll on x y-sided dice is x((y+1)/2)

With this, let's say you crit. So you do 2((8+1)/2). Or, 9 damage, plus power attack and other things.

I hope this is somewhere in the realm of what you wanted.

The equations for all the variables concerning the topic (to hit vs varying AC and such) are beyond my sleep deprived brain.
Gemstone
04-14-06, 07:42 AM Well, quite close, but simple probability math is something even I can handle :) I was after a formulae that takes critical hits into the calculations. This far I've used:

Average damage equal to
(p+x/2)+y*z*(x/2)

p=strength bonus
x=size of die
y=critical hit multiplier
z=chance of getting a critical

thus, the average damage for a str 15 fighter with a longsword is:
2+(8/2)+0,10*2*4,5=7,4

this formulae is incorrect as far as I know, but at lesat it gives a handle :)
claypigeons
04-14-06, 08:08 AM A critical hit is just 2/3/4/whatever times as much damage. So just take the average damage of a hit. Add your modifiers to this number. And then multiply it out.

longswords do 4.5 average damage. Add in a +4 strength bonus, and it does 9.5 average. (5-13, rather than 1-8..)

Multiply by 2 and a longsword crit should do around 19 damage on average with a +4 strength mod.

Either my train of thought is WAY off, or you are trying to over complicate things. (bear with me, im going 2 days on 2 hours of sleep :mad: )
Vaelan
04-14-06, 08:22 AM D = Average damage; (Min roll + Max roll) / 2 + modifiers
H = Chance to hit
C = Chance to score a threat
M = Critical multiplier

(H-C)(D) + (C)(H)(D)(M) + (C)(1-H)(D)

Expressed verbally:

1. Find the chance of hitting and subtract the chance of scoring a threat, then multiply that number by the damage dealt on a hit. This gives you the amount of damage dealt by normal hits.

2. Find the chance of scoring a threat and multiply it by the chance of hitting, then multiply that number by the damage dealt on a hit and the weapon's critical multiplier. This gives you the amount of damage dealt by successful critical hits.

3. Find the chance of scoring a threat and multiply it by the chance of missing, then multiply that number by the damage dealt on a hit. This gives you the amount of damage dealt by unconfirmed critical threats.

4. Sum the results of 1-3.

For example a Longsword-wielding fighter with 16 Strength and Weapon Specialization deals an average of 9.5 damage per hit. Let us give him a 75% chance to hit.

(H-C)(D) + (C)(H)(D)(M) + (C)(1-H)(D)
(.75-.10)(9.5) + (.10)(.75)(9.5)(2) + (.10)(.25)(9.5)
.65(9.5) + .075(9.5)(2) + .025(9.5)
.65(9.5) + .15(9.5) + .025(9.5)
9.5(.65+.15+.025)
9.5(.825)
7.8375
tarkin
04-14-06, 10:40 AM Please note that 75% chance to hit is fairly inaccurate.

It is based on:

1) Only using your highest BAB

2) Ignoring non-ac based protections, such as incorporealness, concealment, mirror images, etc.

=======

As a general rule, when playing in a Strict or Loose game, people doing a Full Attack hit 50% of the time. Single attacks are harder to generalize, but at high levels, a single attack hits around 80% of the time.

While at certain levels, this number will fluctuate, it is a very good rule of thumb.

If you play in a Power Game, that number might go as high as 75%.
JadeSpider9643
04-14-06, 11:40 AM you can't include crits when calculating the "average" damage output of a weapon because that's based off the attack roll not the damage roll. Then it becomes a matter of the average damage of a specific character attacking a specific target using a specific weapon, at which point the data becomes so specialized that it's essentially useless.
Kage_Ryu
04-14-06, 11:51 AM you can't include crits when calculating the "average" damage output of a weapon because that's based off the attack roll not the damage roll. Then it becomes a matter of the average damage of a specific character attacking a specific target using a specific weapon, at which point the data becomes so specialized that it's essentially useless.

That's a good point. You can calculate damage seperately, as individual scores, but not together. When you start putting the damage together you must include chance to hit critical, chance to not hit, enemies that can't be hit, boosts from str and other abilities, DM's preference on monsters/ac of monsters/abilities of monsters, and so on and so on.

You're best off just considering each seperately.
dragonseth
04-14-06, 12:05 PM I can see what formula you're trying to generate, but there is a fatal flaw. Getting a crit threat and getting a crit are way different. You can say a Longsword has a 10% chance of getting a crit, but you'd be wrong. Confirming is something you didn't take into account.
Gemstone
04-14-06, 01:13 PM The point with calculating damage output by including critical damage is that I need a formulae to calculate the critical average damage. There has to be some correct way to calculate critical damage when you compare it towards the average humanoid without immunities, special abilities or Damage reduction :) The argument arose when we discussed a falcion or a longsword+shield.

To Vaelan: I really like your formulae :) thanks for the help. It was just the thing I needed
dragonseth
04-14-06, 01:20 PM Okay, well assuming we're somewhere where crits are auto, no confirming, its fairly simple.
Damage + (% chance of crit)(Additional Damage From Crits) This bonus is same as damage for most weapons, but could be different
Where, damage is (1+die type)/2 + Damage Bonuses
Gil Gwath
04-14-06, 06:44 PM Hello to you all.

I'll try to explain myself at best i can, even if i'm not an english speaker.
Here is a formula to calculate the average damage to be expected knowing these factors:

p = chance to hit (i.e.: if you need a 16 on your die to hit p=5/20=0,25)
d = average damage for your weapon (i.e.: (max+min)/2 . For a longsword d=4,5)
b1 = bonuses to hit that multiply on a crit (i.e.: strenght bonus, weapon enhancement, …)
b2 = bonuses to hit that DON'T multiply on a crit (i.e.: sneak attack bonus, precision bonus…)
t = threat range for your weapon (t=1 for a 20/x2 weapon, t=2 for a 19-20/x2 weapon and so on)
m = weapon multiplier (i.e. for a longsword m=2)

Average damage for a single attack

p*(d+b1+b2)+0,05*t*p*(m*(d+b1)+b2)

If you have 2 attacks and use the full attack action:

p*(d+b1+b2)+0,05*t*p*(m*(d+b1)+b2)+(p-0,25)*(d+b1+b2)+0,05*t*(p-0,25)*(m*(d+b1)+b2)

I suppose you understood the way to do to calculate for people with 3 or 4 attacks.... ;)
I hope there are no major flaws in my formulae, couse here is 0.44 am and i'm going to sleep ;)
supernerd8916
04-14-06, 08:00 PM (x+1)/2+y+z*o +n*o*p
_____________________
20

x= sides on the dice
y= strength
z= miscellaneous addons
n= total amount of rolls you can get and still critical threat
o= total amount of rolls you can get and still hit
p= critical multiplier

this formula shows the average roll in a series of 20 rolls
Gemstone
04-15-06, 04:07 AM THanks for the help everybody :) I've been looking for such a thing for a long time
Mitchell
04-15-06, 04:09 AM (x+1)/2+y+z*o +n*o*p
_____________________
20

x= sides on the dice
y= strength
z= miscellaneous addons
n= total amount of rolls you can get and still critical threat
o= total amount of rolls you can get and still hit
p= critical multiplier

this formula shows the average roll in a series of 20 rolls

But isn't this multiplying add-ons that shouldn't be multiplied?

And Gil, no worries. You type better english than some english speakers. :)

I just wonder why this matters that much? That's alot of math to figure out that weapon "A" will provide you with a .00365 damage boost over weapon "B" if the AC is "X" or lower, but if it is "Y" or higher, then you need to go to weapon "B", because it will do .00125 more damage per swing.
And then you have to factor in what you lose by going to a two-handed weapon... Are you doing more damage than you are taking now because of the lost AC? Maybe you would be better off using a shield and one-handed weapon "Q" since they are using weapon "G", because you know that the shield will put your AC over the critical threshold assuming that their attack bonus is "T" or less. Then again, if their armor is enhanced at all, then weapon "U" becomes your best choice no matter what... :confused:

I leave this sort of thing to the optimizers. :)
Ghostwheel
04-15-06, 05:56 AM I've been trying to come up with a formulae that calculates the average damage that a weapon can deal with each hit, which includes critical hit damage. This far, my calculations have been incorrect, but they have pr oven useful. If anyone out there has a correct formulae for calculating hits, would you please share it with me?

There is no way to iterate a single equation to cover all of the variables that can arise. To determine such an equation, some parameters must be established. And once such parameters are set, any weapon vs. weapon comparisons have to be conducted using the same parameters at all times.

Variables that only affect one side of such an equation are easy to deal with; they will normally be a simple +/- to a single factor. Variables that affect both sides of such an equation must be handled with great care. The feat Power Attack is probably the most common example of such a variable. Power Attack not only affects "to hit" chance on one side of such an equation (in a 1 to 1 manner), but also affects damage potential (often not in a 1 to 1 manner) on the other side of the equation. Both sides of the equation must always be taken into account, so that what is done to each side of the equstion is also done to the other.
supernerd8916
04-15-06, 08:21 AM But isn't this multiplying add-ons that shouldn't be multiplied?

my equation assumes that if you power attack, you always power attack (along with other addons, such as flaming weapons). but your right, if they dont always power attack dont multiply that part out, just add it on before you divide

Post/Author/DateTime	Post
Gemstone 04-14-06, 06:45 AM	I've been trying to come up with a formulae that calculates the average damage that a weapon can deal with each hit, which includes critical hit damage. This far, my calculations have been incorrect, but they have proven useful. If anyone out there has a correct formulae for calculating hits, would you please share it with me?
claypigeons 04-14-06, 07:16 AM	The average roll on a single y-sided die = (y+1)/2 Let's say you have a longsword. Let's assume you hit. You do (8+1)/2 damage, or 4.5 per hit. Add power attack and other things The average roll on x y-sided dice is x((y+1)/2) With this, let's say you crit. So you do 2((8+1)/2). Or, 9 damage, plus power attack and other things. I hope this is somewhere in the realm of what you wanted. The equations for all the variables concerning the topic (to hit vs varying AC and such) are beyond my sleep deprived brain.
Gemstone 04-14-06, 07:42 AM	Well, quite close, but simple probability math is something even I can handle :) I was after a formulae that takes critical hits into the calculations. This far I've used: Average damage equal to (p+x/2)+yz(x/2) p=strength bonus x=size of die y=critical hit multiplier z=chance of getting a critical thus, the average damage for a str 15 fighter with a longsword is: 2+(8/2)+0,1024,5=7,4 this formulae is incorrect as far as I know, but at lesat it gives a handle :)
claypigeons 04-14-06, 08:08 AM	A critical hit is just 2/3/4/whatever times as much damage. So just take the average damage of a hit. Add your modifiers to this number. And then multiply it out. longswords do 4.5 average damage. Add in a +4 strength bonus, and it does 9.5 average. (5-13, rather than 1-8..) Multiply by 2 and a longsword crit should do around 19 damage on average with a +4 strength mod. Either my train of thought is WAY off, or you are trying to over complicate things. (bear with me, im going 2 days on 2 hours of sleep :mad: )
Vaelan 04-14-06, 08:22 AM	D = Average damage; (Min roll + Max roll) / 2 + modifiers H = Chance to hit C = Chance to score a threat M = Critical multiplier (H-C)(D) + (C)(H)(D)(M) + (C)(1-H)(D) Expressed verbally: 1. Find the chance of hitting and subtract the chance of scoring a threat, then multiply that number by the damage dealt on a hit. This gives you the amount of damage dealt by normal hits. 2. Find the chance of scoring a threat and multiply it by the chance of hitting, then multiply that number by the damage dealt on a hit and the weapon's critical multiplier. This gives you the amount of damage dealt by successful critical hits. 3. Find the chance of scoring a threat and multiply it by the chance of missing, then multiply that number by the damage dealt on a hit. This gives you the amount of damage dealt by unconfirmed critical threats. 4. Sum the results of 1-3. For example a Longsword-wielding fighter with 16 Strength and Weapon Specialization deals an average of 9.5 damage per hit. Let us give him a 75% chance to hit. (H-C)(D) + (C)(H)(D)(M) + (C)(1-H)(D) (.75-.10)(9.5) + (.10)(.75)(9.5)(2) + (.10)(.25)(9.5) .65(9.5) + .075(9.5)(2) + .025(9.5) .65(9.5) + .15(9.5) + .025(9.5) 9.5(.65+.15+.025) 9.5(.825) 7.8375
tarkin 04-14-06, 10:40 AM	Please note that 75% chance to hit is fairly inaccurate. It is based on: 1) Only using your highest BAB 2) Ignoring non-ac based protections, such as incorporealness, concealment, mirror images, etc. ======= As a general rule, when playing in a Strict or Loose game, people doing a Full Attack hit 50% of the time. Single attacks are harder to generalize, but at high levels, a single attack hits around 80% of the time. While at certain levels, this number will fluctuate, it is a very good rule of thumb. If you play in a Power Game, that number might go as high as 75%.
JadeSpider9643 04-14-06, 11:40 AM	you can't include crits when calculating the "average" damage output of a weapon because that's based off the attack roll not the damage roll. Then it becomes a matter of the average damage of a specific character attacking a specific target using a specific weapon, at which point the data becomes so specialized that it's essentially useless.
Kage_Ryu 04-14-06, 11:51 AM	you can't include crits when calculating the "average" damage output of a weapon because that's based off the attack roll not the damage roll. Then it becomes a matter of the average damage of a specific character attacking a specific target using a specific weapon, at which point the data becomes so specialized that it's essentially useless. That's a good point. You can calculate damage seperately, as individual scores, but not together. When you start putting the damage together you must include chance to hit critical, chance to not hit, enemies that can't be hit, boosts from str and other abilities, DM's preference on monsters/ac of monsters/abilities of monsters, and so on and so on. You're best off just considering each seperately.
dragonseth 04-14-06, 12:05 PM	I can see what formula you're trying to generate, but there is a fatal flaw. Getting a crit threat and getting a crit are way different. You can say a Longsword has a 10% chance of getting a crit, but you'd be wrong. Confirming is something you didn't take into account.
Gemstone 04-14-06, 01:13 PM	The point with calculating damage output by including critical damage is that I need a formulae to calculate the critical average damage. There has to be some correct way to calculate critical damage when you compare it towards the average humanoid without immunities, special abilities or Damage reduction :) The argument arose when we discussed a falcion or a longsword+shield. To Vaelan: I really like your formulae :) thanks for the help. It was just the thing I needed
dragonseth 04-14-06, 01:20 PM	Okay, well assuming we're somewhere where crits are auto, no confirming, its fairly simple. Damage + (% chance of crit)(Additional Damage From Crits) This bonus is same as damage for most weapons, but could be different Where, damage is (1+die type)/2 + Damage Bonuses
Gil Gwath 04-14-06, 06:44 PM	Hello to you all. I'll try to explain myself at best i can, even if i'm not an english speaker. Here is a formula to calculate the average damage to be expected knowing these factors: p = chance to hit (i.e.: if you need a 16 on your die to hit p=5/20=0,25) d = average damage for your weapon (i.e.: (max+min)/2 . For a longsword d=4,5) b1 = bonuses to hit that multiply on a crit (i.e.: strenght bonus, weapon enhancement, …) b2 = bonuses to hit that DON'T multiply on a crit (i.e.: sneak attack bonus, precision bonus…) t = threat range for your weapon (t=1 for a 20/x2 weapon, t=2 for a 19-20/x2 weapon and so on) m = weapon multiplier (i.e. for a longsword m=2) Average damage for a single attack p(d+b1+b2)+0,05tp(m(d+b1)+b2) If you have 2 attacks and use the full attack action: p(d+b1+b2)+0,05tp(m(d+b1)+b2)+(p-0,25)(d+b1+b2)+0,05t(p-0,25)(m*(d+b1)+b2) I suppose you understood the way to do to calculate for people with 3 or 4 attacks.... ;) I hope there are no major flaws in my formulae, couse here is 0.44 am and i'm going to sleep ;)
supernerd8916 04-14-06, 08:00 PM	(x+1)/2+y+zo +no*p _____________________ 20 x= sides on the dice y= strength z= miscellaneous addons n= total amount of rolls you can get and still critical threat o= total amount of rolls you can get and still hit p= critical multiplier this formula shows the average roll in a series of 20 rolls
Gemstone 04-15-06, 04:07 AM	THanks for the help everybody :) I've been looking for such a thing for a long time
Mitchell 04-15-06, 04:09 AM	(x+1)/2+y+zo +no*p _____________________ 20 x= sides on the dice y= strength z= miscellaneous addons n= total amount of rolls you can get and still critical threat o= total amount of rolls you can get and still hit p= critical multiplier this formula shows the average roll in a series of 20 rolls But isn't this multiplying add-ons that shouldn't be multiplied? And Gil, no worries. You type better english than some english speakers. :) I just wonder why this matters that much? That's alot of math to figure out that weapon "A" will provide you with a .00365 damage boost over weapon "B" if the AC is "X" or lower, but if it is "Y" or higher, then you need to go to weapon "B", because it will do .00125 more damage per swing. And then you have to factor in what you lose by going to a two-handed weapon... Are you doing more damage than you are taking now because of the lost AC? Maybe you would be better off using a shield and one-handed weapon "Q" since they are using weapon "G", because you know that the shield will put your AC over the critical threshold assuming that their attack bonus is "T" or less. Then again, if their armor is enhanced at all, then weapon "U" becomes your best choice no matter what... :confused: I leave this sort of thing to the optimizers. :)
Ghostwheel 04-15-06, 05:56 AM	I've been trying to come up with a formulae that calculates the average damage that a weapon can deal with each hit, which includes critical hit damage. This far, my calculations have been incorrect, but they have pr oven useful. If anyone out there has a correct formulae for calculating hits, would you please share it with me? There is no way to iterate a single equation to cover all of the variables that can arise. To determine such an equation, some parameters must be established. And once such parameters are set, any weapon vs. weapon comparisons have to be conducted using the same parameters at all times. Variables that only affect one side of such an equation are easy to deal with; they will normally be a simple +/- to a single factor. Variables that affect both sides of such an equation must be handled with great care. The feat Power Attack is probably the most common example of such a variable. Power Attack not only affects "to hit" chance on one side of such an equation (in a 1 to 1 manner), but also affects damage potential (often not in a 1 to 1 manner) on the other side of the equation. Both sides of the equation must always be taken into account, so that what is done to each side of the equstion is also done to the other.
supernerd8916 04-15-06, 08:21 AM	But isn't this multiplying add-ons that shouldn't be multiplied? my equation assumes that if you power attack, you always power attack (along with other addons, such as flaming weapons). but your right, if they dont always power attack dont multiply that part out, just add it on before you divide