Dual Wielding vs Big Weapon, Simulation analysis

Hi all,

Wanted to teach myself a new stat program, so i tried working out which is better.

This is strictly illustrative and not meant to be definitive

dual wielding a d6 weapons (say a double axe)

or a 1d12 weapon (great axe)

so let us now make assumptions

50% chance to hit on a given attack (simulated as a uniform distribution between 0 and 1)

not this is different to just halfing the damage as it interacts with deadly strike and alters the variation.

no strength or dex modifier to damage (this should make too much of a difference but that can come later)

these would i imagine only change the influence slighly

so these are pseudo-random draws made using a highly advanced random number generator

1,000,000 draws

so first go

2d6 
Mean (3.499689)
SD (3.006233)




1d12
mean( 3.258002)
sd(4.068299)




so as you can see, at this point the 2d6 is more consistent and provides better average damage.

But this changes with deadly strike

So, deadly strike let you have 2d for one sucessful attack per round. so the advantage is a bigger dice for the d12 but you get twice the chance to use it for dual wield. These simulation correctly account for deadly strike only being used once by a dual wielding player.

So let us see

2d6 with deadly strike
mean(6.124233)
sd(4.432612)



1d12 with deadly strike
mean(6.515468)
sd(7.364581)



Now you see that dual wielding is more consistent but less on average once the systems comes into play
This contuines on with the next level

Now there always going to be some subjectives but that is good, i like the balance

great weapon. critical hits are bigger, more likely to give you a big hit which could save the day (which would have saved one party i know)

dual wield, slighly more flexible in weapon choices, higher ac with feat, seperate targets so less overkill.

So i think dual wielding feels right. like two handed or any other fighting but not


 
Nice. You could improve the program a bit so that when it selects 1, there will be an additional 1 to 10 chance of critical hits. Wonder what the difference would be with a million rolls.

EDIT: This all is generally pretty acceptable data in itself, but completely unobservable and irrelevant in a practical session. The barbarian in my party uses a maul and has trouble hitting stuff. But when he does, he throws a LOT of 10+ damages. He's just lucky like that. Good job though.

IMAGE(http://www.nodiatis.com/pub/20.jpg)

But the actual chance of a critical sucess is one in 20? a critical failure in this context does not matter (damage is still 0)

It is possible i just figured it out, this is meant to be more illustrative. 
But the actual chance of a critical sucess is one in 20? a critical failure in this context does not matter (damage is still 0)

It is possible i just figured it out, this is meant to be more illustrative. 



A chance for critical failure is 1 in 10 because there are ten rolls on a 20-sided die that would result in a failure. But it doesn't matter and I know this. I've done some programming, I realise the logic behind it.

A chance for critical hit is 1 in 10 because there are 10 rolls that would result in a hit. But only one that does the maximum(and then some) damage.

IMAGE(http://www.nodiatis.com/pub/20.jpg)

ahh, you were talking conditionally while i was refering to the joint probablity.

i think i am going to simulate a D20 roll and set the AC at 11 as a better approach to handling criticals 
Yes, it will be a 1 out of 20 scenario if you make 20 rolls available for the program, instead of 2.

But why were you referring to joint probability when you had conditional requirements in the first place?

IMAGE(http://www.nodiatis.com/pub/20.jpg)

Who's the optimization challenged person using only d6 for dual wield?
Who's the optimization challenged person using only d6 for dual wield?


Without feats or stat bonuses. This is meant to be a "pure" comparison of dual vs two-handed.

IMAGE(http://www.nodiatis.com/pub/20.jpg)

exactly, and that would be originally my wife using a double axe.

Min maxing is not as much fun as flavour 
Personally, and I've said this before, the accuracy of dual wielding is actual 75% as opposed to 50%, and frankly, Big Weapon should be far an away the option if you want massive damage.

Dual should be about consistent hitting, while Big Weapon should about making sure the guy falls down in one hit or less.

If only because Cleave is selectable by all weapon types.
Personally, and I've said this before, the accuracy of dual wielding is actual 75% as opposed to 50%.


No. Math doesn't work that way. Diminishing returns, you know.

It's 75% IF you hit with both weapons. That one time you hit with both weapons, it had a 75% chance of happening. On a larger scale, your statement is completely wrong.

 If proffessor_e would add a hit/miss counter to his program, it would probably show a lower to hit % PER ROLL on double-handed(i would guess the combined percentage from both hands would fall around 40%) vs two-handed(slightly less/more than 50%).

For now, this program shows the average damage roll for either fighting style.

IMAGE(http://www.nodiatis.com/pub/20.jpg)

1) THanks for posting the distributions.  We've been over the averages ad nauseum, but it's nice to actually see the distribution instead of thinking to ourselves, "yeah, 2d6 is going to be more bell curved."

2) Did you factor in that, with deadly strike, you can apply the extra d6 after you've determined which of your attacks have hit and therefore have a 75% chance of hitting with that extra die?

3) While I'm willing to agree that that there are levels at which the math works out pretty well, the problem with the current system is that it doesn't work out at all levels.  Early on, TWF is strictly better.  Not by much in average, but higher probabilities to get high-end damage is no more likely to save the day than lower probabilities to get low-end damage, so even a slightly better average will save your bacon more times than a lucky crit.  When you get one DS die, 2 hander pulls ahead in damage but TWF has other advantages, especialy if you invest feats.  But then when you get a second DS die, 2 handers are far and away better (barring some of the more obviously overpowered TWF feats, and even those rely on a reaction bottleneck and using up the entirety of your feat slots just to keep up).  If you think it's "about right" at any one level, it is necessarly nowhere near right at other levels, and the optimal play is to switch weapon styles half way through your career.  That can't be right, regardless of the damage/distribution ratios you or anyone else prefers.  We can argue over what the correct ratios are, but they really ought to be constant.
1) THanks for posting the distributions.  We've been over the averages ad nauseum, but it's nice to actually see the distribution instead of thinking to ourselves, "yeah, 2d6 is going to be more bell curved."

2) Did you factor in that, with deadly strike, you can apply the extra d6 after you've determined which of your attacks have hit and therefore have a 75% chance of hitting with that extra die?

3) While I'm willing to agree that that there are levels at which the math works out pretty well, the problem with the current system is that it doesn't work out at all levels.  Early on, TWF is strictly better.  Not by much in average, but higher probabilities to get high-end damage is no more likely to save the day than lower probabilities to get low-end damage, so even a slightly better average will save your bacon more times than a lucky crit.  When you get one DS die, 2 hander pulls ahead in damage but TWF has other advantages, especialy if you invest feats.  But then when you get a second DS die, 2 handers are far and away better (barring some of the more obviously overpowered TWF feats, and even those rely on a reaction bottleneck and using up the entirety of your feat slots just to keep up).  If you think it's "about right" at any one level, it is necessarly nowhere near right at other levels, and the optimal play is to switch weapon styles half way through your career.  That can't be right, regardless of the damage/distribution ratios you or anyone else prefers.  We can argue over what the correct ratios are, but they really ought to be constant.




1. Yes, i know this. but what i want to show is that there isn't any major source is complaint and that i like the new dual wield rule.

2. Yes i did, the results do not change much without it but i did include that deadly strike is a hit. If anyone wants the R script, just ask. i trying to teach myself the program.

3. I agree but i don't like munchkining, i like the fact that dual wield has more flavour benefits. 
Whether you like munchkining shouldn't enter into it.  You shouldn't be mechanically penalized for going with the more flavorful choice, whether you decide to go with it or not.  It's the old "does balance matter" debate: if you don't care, then you shouldn't mind if those who do care get what they want.
Surprisingly enough, I admit that this iteration rules for dual wielding are pretty much interesting while still kept simple. I think this is an elegant solution.

The only fear I have is toward vertical feat progression that could really throw away all this elegancy quite fast.
The only fear I have is toward vertical feat progression that could really throw away all this elegancy quite fast.


What do you mean by vertical feat progression? That only one set of feats would be optimal for dual wielding or what?

IMAGE(http://www.nodiatis.com/pub/20.jpg)

The only fear I have is toward vertical feat progression that could really throw away all this elegancy quite fast.


What do you mean by vertical feat progression? That only one set of feats would be optimal for dual wielding or what?

basically it means that feats will be used  to become more powerful, rather than more versatile, +1 to a stat as opposed to "now i can attack in a different way" (which would be lateral feat progression).

"Trying to run gritty gothic horror with 4e is like trying to cut down a tree with a hammer, likewise trying to run heroic fantasy with 1e is like trying to hammer a nail with a chainsaw."

 
 

 This is what i get when i hit the Quote button:  http://community.wizards.com/%23

 

  

Yes exactly.

A feat which would allow you to use non-light weapons would totally screw the cool math. This would be a vertical feat.

A feat that would allow you use your shield as a light weapon would not mess with the math, because you would still have to have another light weapon in the other hand for dual-wield to work. This would be an horizontal feat.