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Rheebus
03-12-2009, 07:01 PM
I am playing with some formulas to calculate Average Damage per Hit for multiple weapon types. I started with Bastard Swords vs. Khopeshes, because I was trying to work through which I should pick up for my battle cleric.

Assumptions:

Average damage for a weapon was based on randomly rolling the dice for damage, example: 1d6 would average 3.5 damage per hit because each number 1, 2, 3, 4, 5, 6 should be rolled an equal number of times. (1+2+3+4+5+6) / 6 = 3.5
I am assuming a hit on a 5+ on average. Monster AC is variable. Also, this is very difficult to predict because as you progress in your attack sequence you get huge bonuses to hit. As they get to their 3rd and 4th attacks the bonus to hit goes up by 5 each time. This dramatically improves the chance to hit on those last two (and any subsequent attacks).
All critical hits are confirmed. For most melee toons, this is a 95% chance.

Definitions
WD = Weapon's Average Base Damage
BONUS = Any Damage Bonus applied BEFORE critical multiplier on a critical hit.
FDB = Average first damage bonus from alignment burst (always 7 - Holy Burst, Anarchic Burst, Axiomatic Burst)
SDB = Average second damage bonus from a secondary source (always 3.5 - pure good, lesser X bane)
%H = Percent chance any swing will do normal damage
CM = Critical Multiplier (x2, x3, x4)
BDB = Average burst damage bonus (5.5 for x2 critical multiplier weapons, 11 for x3s, and 16.5 for x4s)
%CH = percent chance of a critical hit (assumes they are confirmed)

Formula

Average Damage per Hit = (((WD + BONUS) + FDA + SDA) * %H) + ((((WD + BONUS) * CM) +FDB + SDB +BDB) * %CH)

Now, let's see it in action.

Khopesh
Damage: 1d8
Critical Threat Range: 19-20
Critical Multiplier: x3

Bastard Sword
Damage: 1d10
Critical Threat Range: 19-20
Critical Multiplier: x2

These two weapons have the same threat range. The bastard sword has a higher base damage and the khopesh has a higher critical multiplier. My hypothesis is that they will have similar Average Damage per Hit at low damage bonuses and that the khopesh's average damage per hit will increase faster than the bastard sword's because of its higher Critical Multiplier.

This hypothesis seems to be correct. On average, the Khopesh will outperform the bastard sword at higher damage bonuses. At +15 to damage, the Khopesh will do 11% more damage per swing on average (38.5 and 34.65 respectively).

Tell me what you think. I am currently working to make this simpler and include every weapon in my analysis. If you have any questions. Please do not hesitate to ask.

I will not answer flame replies.

The Rheeb

Aganazer
03-13-2009, 10:25 AM
I'd be curious to see the effects of auto-crit when MOB's are CC'd in some way. Include an extra 5-10% to the crits and see the difference it could make.

For me, the one thing that is making me consider a bastard sword is the availability of them. There are usually three times as many BS's on the auctioneer than khopeshes. As a casual gamer who will never have ideal gear, that is a serious consideration.

elraido
03-13-2009, 10:41 AM
I don't know why they didn't keep the khopesh the same as pnp. x2 crit with a bonus to trip

Rev-1
03-24-2009, 03:19 PM
I am playing with some formulas to calculate Average Damage per Hit for multiple weapon types. I started with Bastard Swords vs. Khopeshes, because I was trying to work through which I should pick up for my battle cleric.

Assumptions:

Average damage for a weapon was based on randomly rolling the dice for damage, example: 1d6 would average 3.5 damage per hit because each number 1, 2, 3, 4, 5, 6 should be rolled an equal number of times. (1+2+3+4+5+6) / 6 = 3.5
I am assuming a hit on a 5+ on average. Monster AC is variable. Also, this is very difficult to predict because as you progress in your attack sequence you get huge bonuses to hit. As they get to their 3rd and 4th attacks the bonus to hit goes up by 5 each time. This dramatically improves the chance to hit on those last two (and any subsequent attacks).
All critical hits are confirmed. For most melee toons, this is a 95% chance.

Definitions
WD = Weapon's Average Base Damage
BONUS = Any Damage Bonus applied BEFORE critical multiplier on a critical hit.
FDB = Average first damage bonus from alignment burst (always 7 - Holy Burst, Anarchic Burst, Axiomatic Burst)
SDB = Average second damage bonus from a secondary source (always 3.5 - pure good, lesser X bane)
%H = Percent chance any swing will do normal damage
CM = Critical Multiplier (x2, x3, x4)
BDB = Average burst damage bonus (5.5 for x2 critical multiplier weapons, 11 for x3s, and 16.5 for x4s)
%CH = percent chance of a critical hit (assumes they are confirmed)

Formula

Average Damage per Hit = (((WD + BONUS) + FDA + SDA) * %H) + ((((WD + BONUS) * CM) +FDB + SDB +BDB) * %CH)

Now, let's see it in action.

Khopesh
Damage: 1d8
Critical Threat Range: 19-20
Critical Multiplier: x3

Bastard Sword
Damage: 1d10
Critical Threat Range: 19-20
Critical Multiplier: x2

These two weapons have the same threat range. The bastard sword has a higher base damage and the khopesh has a higher critical multiplier. My hypothesis is that they will have similar Average Damage per Hit at low damage bonuses and that the khopesh's average damage per hit will increase faster than the bastard sword's because of its higher Critical Multiplier.

This hypothesis seems to be correct. On average, the Khopesh will outperform the bastard sword at higher damage bonuses. At +15 to damage, the Khopesh will do 11% more damage per swing on average (38.5 and 34.65 respectively).

Tell me what you think. I am currently working to make this simpler and include every weapon in my analysis. If you have any questions. Please do not hesitate to ask.

I will not answer flame replies.

The Rheeb

I love that your one of the only other people I've seen that actually take the time to calculate the difference between the bastard swords and kopeshes and I really like what you've come up with. But I regret saying that your formula is actually incorrect and also a little extravagant for the comparison.

Now I'm not going to do any damage averages to actually pull out numbers for a data table. But I will simplify the formula so that it is plainly visible to see the difference.

Average Damage per Hit = (((WD + BONUS) + FDB + SDB) * %H) + ((((WD + BONUS) * CM) +FDB + SDB +BDB) * %CH)

It is incorrect because you are actually increasing the crit multiplier by one on each weapon. Your first series of brackets is added to the second serious of brackets (which is already being multiplied by the crit modifier.)

So to simply things quite a bit I will break down the comparison in order to really see what the difference will be.

As most of you already know, the damage that is included in the critical hit multiplier is (str + magical weapon bonus + base weapon damage) All other magical effects are separate and added afterwards. The only exception to this rule is a burst weapon based upon the critical multiplier.

Now to clarify what we are comparing I will repost your stats for these weapons:

Khopesh
Damage: 1d8
Critical Threat Range: 19-20
Critical Multiplier: x3

Bastard Sword
Damage: 1d10
Critical Threat Range: 19-20
Critical Multiplier: x2

Now to maintain a controlled experiment we must assume that the character using these two weapons has the exact same feats and attributes.

We will say "John Doe" Fighter is wielding a +5 Kopesh then afterward a +5 Bastard Sword so that the weapons will remain equal. John also gains the same str bonus to damage. (obviously)

He has a 10% chance to crit with either weapon, (assuming no Keen or Improved critical feat, which I will do afterwards.) roll a 19 or 20, that is 2 possible rolls out of 20 = 10% to crit

When John crits the difference between the damage of the kopesh and the bastard sword is 33%.The reason being is that the bastard sword will do X2 damage and the kopesh will do X3.

So 10% of the time the kopesh will do 33% more damage. This means that .10 x .33 = .033

or 3.3% more average dps.

Since the only damage modifiers included in the critical hit damage are: weapon dmg + Str + Magical Weapon Bonus. The higher these values on your character the greater this 3% increase will be seen.

Now let us say that John Doe Fighter also has the improved critical feat:

The crit range on both weapons now becomes 17-20 which = 20% crit chance

.20 * .33 = .066

or 6.6% more average dps

********

So to sum up all of this in very simple terms. The only time you will see a significant difference in dps between using kopeshes and bastard swords is when you are using +5 weapons with no other magical enhancments and/or also have a HIGH str bonus. THIS DOES NOT INCLUDE THE 2 EXTRA BASE DAMAGE OF THE BASTARDS SWORDS. Which is 2. Almost the same as having an extra 4 str on a kopesh or an extra +2 on your kopesh. But since it is variable it is a little less. Another exception is the burst weapons which will add 1 more burst dice to your crits. Again a bonus that is variable and only minimally better then the bastard sword.

So in closure, for all of you out there that have been hating on bastard swords. STOP, not only are the cheaper then kopeshes but they are actually only 6% damage behind them with the Imp Crit feat and 3% without.

Nightflash - Khyber
Level 9 Fighter, Dual-wield Bastard Swords.

Borror0
03-24-2009, 03:38 PM
I love that your one of the only other people I've seen that actually take the time to calculate the difference between the bastard swords and kopeshes and I really like what you've come up with. But I regret saying that your formula is actually incorrect and also a little extravagant for the comparison.
Well, if we are assuming no Seeker damage, no on-crit damage (Bursts and Blasts) and no critical multiplier increases, the Green Steel Khopesh comes up ahead of a Green Bastard Sword at 15 base damage, which is very little. All other factors are biased toward the khopesh, so the real point where the two curves meet is actually lower.

1.15x+1.15*9=1.35x+1.35*5.5
1.15x+10.35=1.35x+7.425
0.20x=2.925
x=14.625
As for non-Green Steel, under the same conditions, khopesh beats a bastard sword at 2 base damage.

1.15x+1.15*5.5=1.35x+1.35*4.5
1.15x+6.325=1.35x+6.075
0.20x=0.25
x=1.25
If you wonder what 1.15 and 1.35 are, they are the critical power pf a bastard sword and a khopesh (respectively). A critical power the combination of the chance of getting a critical hit and how much damage it provides (averaged). It's an easy way to factor the critical multiplier and threat range in an equation.

I did not include other factors because 15 base damage is to easy to achieve it's not worth mentioning. A 10 base Str ranger (16) with Ram's Might has that much vs his favored enemies, using a masterwork weapon. I think it illustrates how easily it is to achieve. Any character with a 30 Str and a +5 weapon (which a Green Steel weapon is) will also pass that threshold, without any help from class feats or Power Attack.

Lewcipher
03-24-2009, 03:44 PM
There should have a been a warning posted that this thread contains math. I just got off work, and did math all day, and now? My brain is bleeding :D

gfunk
03-24-2009, 04:01 PM
I have the same charts myself, and have done them for most of the weapon types with different levels of improved crit (makes me wonder how many other people have also done this sort of thing)

. I've never posted them because when I made them I hadn't been subscribed to any photo hosting website (though I am now, but haven't revisited any of that stuff). You might also want to include the effect of various levels of fortification. I find that the bastard sword becomes about equivilant to the khopesh at around 50% fortification (at greater than ~50% fortification the greensteel bastard sword is superior). Of course, a bunch of this stuff changes now with all of the different enhancements to crit range and multiplier that are coming in mod 9.

Can't find a complete table atm, but here is one with some greensteel weapons (probably not all that legible... I never designed it to put on the web really.. it does show a similar relationship that you are describing with the bastard sword vs the khopesh):
** edit includes bloodstone.. or course
http://i621.photobucket.com/albums/tt297/cratonic/gsweapons.png

I also found a chart I made when I was looking at some lowbie weapons just for fun
http://i621.photobucket.com/albums/tt297/cratonic/lowbieweapon.png

Rev-1
03-24-2009, 11:17 PM
Well, if we are assuming no Seeker damage, no on-crit damage (Bursts and Blasts) and no critical multiplier increases, the Green Steel Khopesh comes up ahead of a Green Bastard Sword at 15 base damage, which is very little. All other factors are biased toward the khopesh, so the real point where the two curves meet is actually lower.

1.15x+1.15*9=1.35x+1.35*5.5
1.15x+10.35=1.35x+7.425
0.20x=2.925
x=14.625
As for non-Green Steel, under the same conditions, khopesh beats a bastard sword at 2 base damage.

1.15x+1.15*5.5=1.35x+1.35*4.5
1.15x+6.325=1.35x+6.075
0.20x=0.25
x=1.25
If you wonder what 1.15 and 1.35 are, they are the critical power pf a bastard sword and a khopesh (respectively). A critical power the combination of the chance of getting a critical hit and how much damage it provides (averaged). It's an easy way to factor the critical multiplier and threat range in an equation.

I did not include other factors because 15 base damage is to easy to achieve it's not worth mentioning. A 10 base Str ranger (16) with Ram's Might has that much vs his favored enemies, using a masterwork weapon. I think it illustrates how easily it is to achieve. Any character with a 30 Str and a +5 weapon (which a Green Steel weapon is) will also pass that threshold, without any help from class feats or Power Attack.

So your using made up formulas to actually compare these 2 weapons? If I were you I wouldn't try and over think this at all. What I posted earlier is very simple for anybody to understand and in mind is very accurate along with good tips to help people decide what they want to use. If your looking to show off with some math skills I suggest finding a different forum. I would perhaps believe what you just posted if A) I knew where you got these numbers from and what they represent, including your critical power numbers. (Which to me seem a little odd.) And B) if you'd provide a better summary of your findings involving the comparison. A percentage is always a simpler way to show just how much more effective another weapon. If I tell average Joe DDO player that kopeshes have 6% more overall dps then bastard swords, hes going to understand alot more then if you start giving him graphs and showing him algebra equations. I do appreciate what your doing, but personally I think your method is a bit off.

FluffyCalico
03-24-2009, 11:24 PM
So your using made up formulas to actually compare these 2 weapons? If I were you I wouldn't try and over think this at all. What I posted earlier is very simple for anybody to understand and in mind is very accurate along with good tips to help people decide what they want to use. If your looking to show off with some math skills I suggest finding a different forum. I would perhaps believe what you just posted if A) I knew where you got these numbers from and what they represent, including your critical power numbers. (Which to me seem a little odd.) And B) if you'd provide a better summary of your findings involving the comparison. A percentage is always a simpler way to show just how much more effective another weapon. If I tell average Joe DDO player that kopeshes have 6% more overall dps then bastard swords, hes going to understand alot more then if you start giving him graphs and showing him algebra equations. I do appreciate what your doing, but personally I think your method is a bit off.

Um what?
A proper Equasion graghed is the comparision. How can you get 5% better when how much better keeps changing? We invented math for a reason. It answers lots of things such as which is better DPS.

03-24-2009, 11:50 PM
I love that your one of the only other people I've seen that actually take the time to calculate
The reason you haven't "seen" other people calculate it is because you haven't looked. DDO is not a new game, and weapons like Khopesh have been unchanged for years. What you're talking about is ancient history.

If your looking to show off with some math skills I suggest finding a different forum.
As you've only made 5 posts, you apparently haven't read this forum for very long. It is monstrously obnoxious for a new user to come into a forum and start dictating to established members what they may or may not post there.

I would perhaps believe what you just posted if A) I knew where you got these numbers from and what they represent, including your critical power numbers. (Which to me seem a little odd.)
Your newness may also explain why you're so ignorant about this topic. It's a bad idea to go around making claims about what hasn't been said if you yourself haven't been paying attention (http://www.lmgtfy.com/?q=ddo+%22critical+power%22) to the site.

Borror0
03-24-2009, 11:57 PM
I also found a chart I made when I was looking at some lowbie weapons just for fun
Love how Star of Iran is so much higher than all others. :D

So your using made up formulas to actually compare these 2 weapons?
Those "made up formula" you referred to are actually describing perfectly how each weapon respectively affect DPS.

In the case of the normal khopesh versus the normal bastard sword, the left side represents the bastard sword and the right side represents the khopesh. For the bastard sword, the 5.5 is the base average of the weapon (1d10) and the 1.15 is the factor by which damage is increased (1*15/20+2*4/20). For the khopesh, 4.5 is the average of the khopesh's base damage (1d8) and the 1.35 is the factor by which damage is multiplied when using a khopesh (1*15/20+3*4/20).

Using these numbers, we can use basic algebra to figure out how much base damage do we need for a khopesh to be better than a bastard sword.

It's not "made up formulas" but very simple mathematics.

What I posted earlier is very simple for anybody to understand and in mind is very accurate along with good tips to help people decide what they want to use.
Well, my answer is even easier: khopesh will always be better DPS.

Only Green Steel bastard sword put a challenge to Green Steel khopesh, but it's not really a problem since the amount of damage require for a GS khopesh to be better DPS than a GS bastard sword is so small that any build thinking of using either of the two (ie Str-based) will do more damage with a khopesh since the meeting point is 15 damage. Since a GS weapon has a base +5, this means a mere 30 Str will allow the GS khopesh to beat the GS bastard sword.

Oh, and that's assuming no on-crit weapon enchantments nor any seeker damage (like Bloodstone) which are biased toward the khopesh!

[...] if you'd provide a better summary of your findings involving the comparison. A percentage is always a simpler way to show just how much more effective another weapon. If I tell average Joe DDO player that kopeshes have 6% more overall dps then bastard swords, hes going to understand alot more then if you start giving him graphs and showing him algebra equations.
Since that's always dynamic, giving a percentage is imprecise.

Crarites
03-25-2009, 08:41 AM
No maelstrom on that lowbie weapon guide. :D

unionyes
03-25-2009, 10:05 AM
Barbie to Ken; 'Gee math is tough'

gfunk
03-25-2009, 10:52 AM
Love how Star of Iran is so much higher than all others. :D

.

I was only looking at lvl 1 to 4 named weapons in that chart.. and assuming that someone might have access to a lvl 2 star of irian... pretty obvious why they changed it (I assume thats what you are refering to)

Borror0
03-25-2009, 11:00 AM
I assume thats what you are refering to
Yeah. I think that's the definition of "unbalanced", hehe

Gunga
03-25-2009, 11:11 AM
So your using made up formulas to actually compare these 2 weapons? If I were you I wouldn't try and over think this at all. What I posted earlier is very simple for anybody to understand and in mind is very accurate along with good tips to help people decide what they want to use. If your looking to show off with some math skills I suggest finding a different forum. I would perhaps believe what you just posted if A) I knew where you got these numbers from and what they represent, including your critical power numbers. (Which to me seem a little odd.) And B) if you'd provide a better summary of your findings involving the comparison. A percentage is always a simpler way to show just how much more effective another weapon. If I tell average Joe DDO player that kopeshes have 6% more overall dps then bastard swords, hes going to understand alot more then if you start giving him graphs and showing him algebra equations. I do appreciate what your doing, but personally I think your method is a bit off.

Nice Rev. I like your style.

Gunga
03-25-2009, 11:14 AM
The reason you haven't "seen" other people calculate it is because you haven't looked. DDO is not a new game, and weapons like Khopesh have been unchanged for years. What you're talking about is ancient history.

As you've only made 5 posts, you apparently haven't read this forum for very long. It is monstrously obnoxious for a new user to come into a forum and start dictating to established members what they may or may not post there.

Your newness may also explain why you're so ignorant about this topic. It's a bad idea to go around making claims about what hasn't been said if you yourself haven't been paying attention (http://www.lmgtfy.com/?q=ddo+%22critical+power%22) to the site.

No. I think it's perfectly fine for smart people to come in here and show their stuff. I think we should encourage new comers, rather than belittle them. Don't you agree, your grumpiness?

skyking613
03-25-2009, 11:31 AM
Um why not use something like this??

http://www.afterlifeguild.org/Thott/ddo/

Borror0
03-25-2009, 11:32 AM
Um why not use something like this??

http://www.afterlifeguild.org/Thott/ddo/
It's far from perfect.

LA_MIKE
03-26-2009, 04:46 PM
..