Weapon Balance - A Statistical Analysis

[Crazydwarf]

Crazy dwarf. I'm probably one of the ones that has confused you in this thread. I have a very simple way of explaining some things.

Indeed, I'm thankful for taking this down a notch so I can follow along better

Alex is not saying that a +2 or so to damage equals a -2 to AC.

I know, that is my argument.
Or more presice, my argument is that it does NOT equal out in relative "worth", but it SHOULD.

To understand the relationship, you have to understand what these two modifiers mean.

-2 to AC means, basically, that you will be hit an extra 2 times per 20 times you are attacked.

+1.5 to damage means, that basically, you will be doing an extra 15 points of damage per 20 attacks per [w].

I assume we are using a stable calculation here wich has the random element accounted for, averages or such ?

Plain bad luck can mess with outcomes a whole lot.
Mauls can roll 8 for damage and warhammers 10, lucky streaks can come and go, dice can even have factory flaws to favor an outcome and the player might not know it. (very unlikely though I guess)
I might go through a whole session and the DM rolls so poorly I might aswell have gone buck naked, of course a twohander would be better in that certain instance

But fact remains that the AC bonus from shields are constant, and the damage bonus from twohanders are randomized twice.
And maybe it's just me, but I would give more "worth" to something certain than something uncertain.

So, the more you are attacked, the better to go Sword and Board. However, unless you are a defender, just having a shield probably means you are being attacked less. This does not necessary help your team (though thinking about it, it is beneficial for the team if the leader is not attacked as much because losing the medic is bad for everybody.)

Understood, but these are also variables we cannot account for.
I cannot forsee which will be the most beneficial at any given time to me.
When I create a PC, I must choose my strengths and hope they will be beneficial at some point.

But it seems to me that one of the two options is better at what it does than the other, wich limits my choices to one that I fluffwise may not like.
Wich is the basis of my problem, I like twohanders, but sword 'n board just seems like a better option overall, even in instances where more damage would be preferable.

But, the more you use high [w] attacks the better to go Two-Handed Weapon Fighting. The reason for this is that for every [w] your original damage bonus effectively doubles! Think about that for a second. For the 1st level brute strike, your damage bonus triples! And it's reliable, so you're guaranteed to land it at some point when you decide to use it.

3*0 = 0 (I know the bonus is not zero just tossing this here as food for thought)

Yes I understand how twohanders benefit more from multiple [W] powers.
But is it still enough damage ?
if brute strike causes 30 damage with a warhammer (no bonuses accounted for) then it would be 36 with a maul.
+6 HP damage. Not bad for a lvl 1 daily I guess...At lvl 1.

As PC's and enemies level up HP goes up fast aswell right ?
Making this bonus smaller and smaller in "worth" while the worth of more AC just keeps climbing.

And there is still that pesky random element to account for.
I can unload that power and have it come up minimum of 6 HP with a maul and 3 with a warhammer.

Now, as you might have guessed, it's very hard to give an accurate mathematical estimation as to whether or not this is balanced. There are too many variables

Excatly, I have no way to prove my concept mathematicly, all I have is "gut feeling" to go by.

EDIT: And reaping strike is a very good power. It's pretty much the quintessential two handed weapon power. It basically allows you to do your str modifier x10 per 20 rounds. This could be an extra 40 points at 1st level. This is, of course, useless against minions, but it's great against soldiers, elites, and solo's (all hard to hit).

Reaping strike is an excellent power, especially for twohanders..I never doubted this.

It is a bit less useful to sword 'n boarders, and since the shield seems to outpreform twohanders, then it might rarely come into play, I cant really say it makes twohanders any better since they cannot benefit from iron vanguard at all. EDIT: And by Iron vanguard I of course mean tide of iron...I gots my stuff confused.

Thanks to all here though, loving this discussion.
Just wish I could follow the mathy bits better

 

[Old Gumphrey]

Sorry if this was covered, but the greatsword and glaive, while they have the lowest damage of the two-handers, also allow you to use Heavy Blade Opportunity, which, if you're a 2H weapon guy, is positively awesome sauce.

 

[Crazydwarf]

Yay awesome sauce, I like awesome sauce !
Using cleave or reaping strike on an OA seems like it could be useful alot of times.
Maybe even sure strike if we really want that runner stopped, and how about tide of iron...Oops ?

We cannot really account for powers, feats and magic unless it applies to only one of the options right ?

And I find it poor practice to try and balance things out later on with strange bonuses than to get it right at the basic level.

 

[Stalker0]

A lot of good discussion here.

The current debate about THW vs S&B relies heavily on the question of how often is the S&B user going to get hit? Its easy to gauge a human reaction from a THW offense perspective. After all, its in a players best interested to strike often and kill monsters as quickly as possible, so they will strike in a way that best accomplishes that goal. And you don't need a lot of math to know that if a creature is really wounded, you want to take it out so it doesn't hurt you.

However, things get a little fuzzier on the defense side. For the pcs, defense boils down not on their choices, but the choices of the dm. As stated earlier, if the DM uses a lot of monsters that focus on will defense for example (perhaps a mind flayer campaign) then a shield has a weaker benefit. If a DM determines in his mind that the fighter and paladin's marks are very strong, and therefore will have his monsters hit the defenders frequently, then the utility of a shield greatly increases. If he has decided that the incentive isn't that strong, then the shield becomes an even greater deterrent not to hit the defender, and so its utility is very weak.

Further, the number of monsters makes a difference. If the party faces lots of solo's, then the number of attacks a party member receives vs how many attack he dishes out changes compared to if he's fighting hoards of minions, and that can have an impact on how important defense is.

And lastly, how important are skills in 4e? Remember that +2 AC/reflex defense costs a -2 to several skills. How useful are these skills in any given game?


So ultimately, while I appreciate the math being done to compare THW and S&B, there is one very large variable that must be taken into consideration, and that is how many attacks a shield user will actually take where his shield will be useful. Until people can agree on a general baseline for that, then any math equation done is meaningless.

Now there are some assumptions you can make. You can use the standard 5 monsters vs 5 PCs as a baseline, as that seems to be the standard given to use by the dmg. You could say that general 2 of them will attack the defender, or 3 or 4, but pick a general number. This of course is influenced by the difference in AC between the defender and the rest of the party. Further, you can look at the monster's manual, choose monsters that most people are going to use, and therefore get a guage of how many AC or reflex attacks the party will endure.

With all of that, you can guage a rough estimate, and from there do a true comparison. I'm not going to do it, but I encourage someone to take on the challenge

 

[Alex319]

And lastly, how important are skills in 4e? Remember that +2 AC/reflex defense costs a -2 to several skills. How useful are these skills in any given game?

Don't forget that you can unequip your shield before using skills to avoid the penalty. Therefore, the penalty only matters if you are using skills while in combat (or in a situation where you are afraid combat is imminent and don't want to get caught off guard and have to burn a standard action to equip your shield)

 

[Crazydwarf]

Well I do think, a calculation like this might not even be possible.
If we eliminate all variables then we have no numbers to work with..If we allow them we have too many.

Anyway, I made a longer post earlier but internet failure fluked it away, and I cant be bothered reposting all of it.

However I will repeat a theoretical houserule, I wouldnt use it because I don't like "nerfing" things, and it would add cumbersome complexity to combat.

If we imagine a skill check with the shield to block an attack, if the block was succesfull the shield would absorb 1D2 damage from that attack.

This would put heavy shields and twohanders on equal value right ?
And it would make shields pretty unpopular in the process I belive. :/

 

[Crashy75]

Well I do think, a calculation like this might not even be possible.
If we eliminate all variables then we have no numbers to work with..If we allow them we have too many.

Anyway, I made a longer post earlier but internet failure fluked it away, and I cant be bothered reposting all of it.

However I will repeat a theoretical houserule, I wouldnt use it because I don't like "nerfing" things, and it would add cumbersome complexity to combat.

If we imagine a skill check with the shield to block an attack, if the block was succesfull the shield would absorb 1D2 damage from that attack.

This would put heavy shields and twohanders on equal value right ?
And it would make shields pretty unpopular in the process I belive. :/

To make it closer, you'd have to make it 1d2 damage per die of damage received. But then, it is much easier to deal damage than it is to heal, so you can't really make a clear comparison.

I think it is possible to make some assumptions. First of all, I think it is reasonable to assume that the DM is throwing a mix of monsters at the party. This is pretty much an assumption that must be made for any sort of analysis.

Also, defenders do affect the dm's choices on who the npc can attack. The mark effectively gives a heavy shield to everybody else(or an additional one if they already have one) and the Challenge abilities give the enemy other reasons to attack the defender. Therefore, it is reasonable to assume that the monster's choice problem is mitigated, at least a bit, when you are talking about defenders.

Going back to the 20 attack model, one is tempted to compare the average damage that a monster could do x2 and compare with the average extra damage done over 20 attacks, but this is probably not an accurate comparison. It is likely that you will be attacked 20 times before you can make 20 attacks, especially if you are a defender.

Also, another thing that is hard to guage is that the extra damage from 2-handed weapons should have an affect on the damage you receive because, simply, if you take a monster down quicker, he'll make less attacks (vs. you and your party).

Now, perhaps these two cancel each other out, but how can one be sure. I'm really tempted to create another formula here...

(Oh CrazyDwarf, to answer your earlier questions, really both the affects of an ac penalty and damage bonus will vary. Just as you might roll poor damage with your big great axe, your DM could roll poorly (or really well) with his d20 and your big shield means nothing (the dm never misses you by 2 or less). This is why we can only really use averages, for the most part. You could hit 20 out of 20 times and effectively double your damage from using your 2 hander or hit 0 out of 20 negating it completely. These two possibilities basically cancel each other out.

One think to keep in mind (and one of the reasons I like to go with a 20 attack model) is that, over time, the averages will pan out. I'd suggest you do that experiment Alex suggested. You could just set up a random encounter and control all creatures for a mock combat just to see.)

 

[chitzk0i]

What miffs me is that shield-users get access to Tide of Iron, whereas Two-handed weapon fighters don't get access to a push power until level nine dailies with Shift the Battlefield. Then, at 13, you finally get Silverstep and at 17, Mountain Breaking Blow. But shield guys get an at-will push since day 1.

 

[Crazydwarf]

To make it closer, you'd have to make it 1d2 damage per die of damage received.

Yes thats correct, good catch !
But it's still quite a bit of shield nerfage I'd wager.
Just incase I wasnt clear (I think I was though) the "houserule" was not intended for use, only show my abstract way of thinking...Sort of

I think it is possible to make some assumptions. First of all, I think it is reasonable to assume that the DM is throwing a mix of monsters at the party. This is pretty much an assumption that must be made for any sort of analysis.

Also, defenders do affect the dm's choices on who the npc can attack. The mark effectively gives a heavy shield to everybody else(or an additional one if they already have one) and the Challenge abilities give the enemy other reasons to attack the defender. Therefore, it is reasonable to assume that the monster's choice problem is mitigated, at least a bit, when you are talking about defenders.

Agreed.

Also, another thing that is hard to guage is that the extra damage from 2-handed weapons should have an affect on the damage you receive because, simply, if you take a monster down quicker, he'll make less attacks (vs. you and your party).

Exactly, this is very much my line of thinking.
It would seem to me that the extra damage output is too minor to cancel out the shield. But I'm not sure, it is just a gut feeling.

It could be remnants of other systems is haunting me though.
The systems I used to play had twohanders close to doing twice the damage of one handed weapons, but had fewer attack oppertuneties.
However it had the same:ish flaw where dualwielding came out on top, twohanders where okay and shield users where laughed at.
No balance at all.

Now, perhaps these two cancel each other out, but how can one be sure. I'm really tempted to create another formula here...

Please do, I wouldnt even be sure how to.

(Oh CrazyDwarf, to answer your earlier questions, really both the affects of an ac penalty and damage bonus will vary. Just as you might roll poor damage with your big great axe, your DM could roll poorly (or really well) with his d20 and your big shield means nothing (the dm never misses you by 2 or less). This is why we can only really use averages, for the most part. You could hit 20 out of 20 times and effectively double your damage from using your 2 hander or hit 0 out of 20 negating it completely. These two possibilities basically cancel each other out.

Yes I have a basic understanding of averages.
But using them sort of masks a "immediate gratification" feeling, and you have to be good at seeing the big picture of things...Alas I'm not
wich as mentioned might be cause for my gut feelings here

I'd suggest you do that experiment Alex suggested. You could just set up a random encounter and control all creatures for a mock combat just to see.

I will at some point, as soon as I have the time.
I'm considering pitting two identical (except for weapons) fighters against eachother, all melee basic attacks, no powers or feats accounted for. Just to see who wins the most out of X numbers of mock fights.
Would this be a good way of doing a test ?

 

[Crashy75]

What miffs me is that shield-users get access to Tide of Iron, whereas Two-handed weapon fighters don't get access to a push power until level nine dailies with Shift the Battlefield. Then, at 13, you finally get Silverstep and at 17, Mountain Breaking Blow. But shield guys get an at-will push since day 1.

Yeah, that is a really good power...

Yes thats correct, good catch !
But it's still quite a bit of shield nerfage I'd wager.
Just incase I wasnt clear (I think I was though) the "houserule" was not intended for use, only show my abstract way of thinking...Sort of

Agreed.


Exactly, this is very much my line of thinking.
It would seem to me that the extra damage output is too minor to cancel out the shield. But I'm not sure, it is just a gut feeling.

Ok. Now I understand what you meant by comparing npc hp with pc AC. While I think there is something to this, there are mitigating factors. #1, killing an enemy 10% faster than normal is much better than being missed an additional 10% of the time IMO. An enemy that is alive longer can do plenty of terrible things and not just whittle down your HP with AC and Ref attacks. They can stun, inspire fear, dominate, and so on. I hadn’t thought of that before (though Alex had mentioned it) but it is very important. If THW did this, then they would be way better than Sword and Board.

It could be remnants of other systems is haunting me though.
The systems I used to play had twohanders close to doing twice the damage of one handed weapons, but had fewer attack oppertuneties.
However it had the same:ish flaw where dualwielding came out on top, twohanders where okay and shield users where laughed at.
No balance at all.

Sounds similar to 3.x.

Please do, I wouldnt even be sure how to.

Well, it turns out that it's a lot easier that I had thought (assuming I am doing it right- it almost seems too easy). Basically, the additional DPR added by the two-handed weapons must = about 10% of your enemies hp total to do this (cancel out the two attacks). The DPR bonus would be about .75[w]. So, about 1-2 at 1st level. I don't have the MM in front of me, but I think this probably less than 10% (1st level npc hp are usually >20 yes?). I'm thinking 5% might be better anyway (roughly enough to cancel one of those extra hits you'd suffer for not having a shield over 20 rounds) considering the above. 2[w] weapons would fit the bill for the most part here, but your 1[w] at wills are probably going to be less than even 5%.

I do wonder how this would scale. A 7[w] power(I think that's the highest) would add about 5 DPR which I'm sure is not 10% of an average epic critter and I'm doubtful that it is 5% either. Of course, there are other things that would add to 2HW DPR including weapon mastery (more so if you have high crit), reaping strike, +3 weapons, and I can't think of anything else off the top of my head.

Yes I have a basic understanding of averages.
But using them sort of masks a "immediate gratification" feeling, and you have to be good at seeing the big picture of things...Alas I'm not
wich as mentioned might be cause for my gut feelings here

Your gut feeling may be correct. I had already considered giving 2hw a sleight boost for other reasons, and this may become one more. In fact, I bought a d14 just for this purpose. I think I'll get another.

I will at some point, as soon as I have the time.
I'm considering pitting two identical (except for weapons) fighters against eachother, all melee basic attacks, no powers or feats accounted for. Just to see who wins the most out of X numbers of mock fights.
Would this be a good way of doing a test ?

I think it would be better to have them each face the same monsters rather than each other. I think it would be good to have them face a variety of monsters including some that target will and fort. Obviously, each other wouldn’t do this for the most part. I’d also do different levels (at least one per tier, but I’d do two per tier, one at a lower end of the tier and one at the higher end).