Weapon Balance - A Statistical Analysis

[Alex319]

1.52 damage per die is not nothing - by a long shot. The lower AC has an impact in 10% of all attacks, so if these attacks deal 15 damage a round (on a hit), then even if you attack with just 1[W] you're fine. If you're dealing more than 1[W] on average, (which you will) then you can take more and still be balanced. This is being optimistic in favor of the two-handed weapon, since a shield only raises your AC and ref, whereas attacks may come in on all defenses.

In other words, if you can avoid being hit too often, then the two-hander will have a fairly large advantage. If you're being attacked on your fortitude or will, you might as well take a two handed weapon. If you're getting hit a lot, pick a shield. This isn't broken - it's obvious - when you're not being attacked a lot, your defense is less important.

First of all, your math is a little bit off. You are correct that if enemy attacks deal 15 damage, and you are attacked on average once per round, then a shield (which blocks 10% of all attacks) means you take on average 1.5 less damage per round. You didn't take into account,however, that 1.5 additional points of [W] does not mean you deal 1.5 additional damage per round, because you don't hit every round. (Of course it could be more if you frequently attack with multiple [W] powers.)

On the other hand, my comment about "offense being more important than defense" refers to the following fact - suppose that you and an ally both have AC 20 without a shield. If you take a shield that raises your AC to 22, then an enemy could simply avoid you and target your ally, so you haven't really reduced the overall damage to your party. Of course this is not always true (you could have marked the enemy, the enemy could be unable to get to your ally, etc.) but in general defense bonuses are worth less than offense bonuses due to this "target substitution effect."

(Here's another way to look at this: if you had a choice between two minor action utility powers, one of which gave you +10 to attack for one round, and one of which gave you +10 to AC and reflex for one round, which one would you be more likely to choose?)

 

[Alex319]

This would also solve the slight oddity of a bastard sword being a better two-handed sword than a greatsword.

A bastard sword is a superior weapon, and a greatsword is a military weapon. Hence a bastard sword takes an extra feat to use, and as such is supposed to be more powerful.

 

[Siberys]

speaking of which, do the superior weapons seem worth the feat necessary to be proficient with 'em? At a glance, they didn't seem worth it, so I was considering upping their proficiency bonus a point...

 

[Alex319]

AC (and reflex) has sort of a boolean feel to them. it's either "get hit or don't get hit".
The scale it works on is relativly small, I cant cover all variables but I ballpark it at 10-35 (10 is minimum I belive and 35 is a lvl 30 generic person in mundane plate and heavy shield unless I'm mistaken)
Any bonus here, even one that seems minor, like +2 will have a significant effect on your character.

First of all, the highest AC you can get at 30th level is far more than 35. At 30th level you can have +6 godplate armor (total AC bonus 14+6=20), combined with the 10 base and 15 from level gives 45, and that's not even counting a shield or feats like Armor Specialization and Two-Weapon Defense. But this is a secondary point of relatively minor concern to the overall analysis.

HP (and thus damage) works in a different way.
It's not "live or die" but HP must be sequentially hacked off until it reaches 0. and the amount of HP can easilly reach 100+ when faced with several monsters or even one big nasty monster in the higher levels.
I dont have exact numbers here but I'm sure its a much bigger scale than the AC one.

A bonus on this scale must be quite large before it gives any substansial effect.
+2 doesnt seem to cut it to make up for a loss of 2 AC/Reflex, and its not even a stable +2 bonus, its a possible +2 bonus since it's just a bigger damage dice that might still roll poorly.

Am I overlooking something ?
Or is it just a case of "grass looks greener" ?

First of all, I explained a couple posts up about why offensive bonuses are in general better than defensive bonuses, which is why an extra +1 to attack is worth about 1.2 points of [W] while an extra +2 to AC/Reflex is worth far less than 2.4 points of [W]. (And don't forget that an extra +2 to AC/Reflex is worth nothing if an enemy targets your Fortitude or Will defense.) But in order to address the relationship between attack rolls and damage rolls, let's compare the effectiveness of a longsword (+3 prof, 1d8 damage) and warhammer (+2 prof, 1d10 damage).

A good way to think of this is in terms of "expected damage per round." This is the probability the attack will hit times the expected damage if it does hit. Also note that the expected damage includes both the damage from the weapon and any damage bonuses (from attributes, magic weapons, feats, powers, etc.)

So our formula is:

Expected Damage = H*(XW+B)

where H is the hit probability, X is the number of [W] the power has, and B is any bonuses to damage or additional damage other than the [W].

So suppose that the probability of hitting is 0.5 with the warhammer, and so it is 0.55 with the longsword. We want to see under what conditions the longsword and warhammer will have an equal amount of damage per round.

Expected Damage from Warhammer = 0.5*(5.5X + B)
Expected Damage from Longsword = 0.55*(4.5X + B)

Setting these equal we get:

0.5*(5.5X+B) = 0.55*(4.5X+B)
2.75X + 0.5B = 2.475X + 0.55B
0.275X = 0.05B
5.5X = B

A higher value of B in comparison to X makes the longsword a better choice, while a lower value of B in comparison to X makes the warhammer a better choice.

Consider the case of a paladin attacking a marked target with Holy Strike (damage is 1[W] + Str + Wis). Assuming a 1st-level paladin with 18 Str and 16 Wis, this gives B=7 and X=1, making the longsword the better choice. Now suppose the paladin is now 30th level. He will have added 8 points to both Str and Wis, giving him a 26 Str (+8) and 24 Wis (+7), and will probably have a +6 weapon and an additional +3 from Weapon Focus, giving him B=24. Even though X is now 2, the very high value of B means that the longsword is still the better choice.

This is not always true, however. Consider a 30th level fighter using No Mercy (7[W] + Str damage), and also with a 26 Str, +6 weapon, and weapon focus. He now has X=7 and B=17, making the warhammer by far the better choice. (Additionally, No Mercy is Reliable, so that even if the difference in proficiency bonuses makes the attack miss instead of hit, the fighter can try again next round.)

And back to the topic of two-handed weapons: another very good reason to take a two-handed weapon is Reaping Strike, which does more damage on a miss if the weapon is two-handed. If Reaping Strike is one of your primary at-wills this is a very good benefit. Another benefit is that if you have a Warlord in your party with Commander's Strike, the Warlord can go sword-and-shield and use your melee basic attack (plus the Warlord's Int modifier to damage), so the Warlord can get the additional damage from the two-handed weapon as well as the shield bonus to his own AC and Reflex!

 

[Alex319]

speaking of which, do the superior weapons seem worth the feat necessary to be proficient with 'em? At a glance, they didn't seem worth it, so I was considering upping their proficiency bonus a point...

I actually addressed this point in my first post, when I calculated that superior weapons have an average damage about 1 point more than similar military weapons, and so the extra damage granted by the superior weapon proficiency feat is about in line with the extra damage granted by Weapon Focus, the closest comparable feat.

Upping the proficiency bonus by 1 (to +4) would make superior weapon proficiency way too powerful. It would essentially be a heroic tier feat that gives +1 to attack and +1 per [W] to damage - all the time! Note that the only feats which give attack bonuses at all give them in very restricted situations (such as only when using particular abilities, or when making OAs). The closest feat comparable to what you would be making is Back to the Wall, which is a paragon tier feat that gives +1 attack, damage, and AC (about the same size as the benefit you are granting) but only when you are adjacent to a wall. Your superior weapon proficiency would be a heroic tier feat that would grant close to this benefit all the time, making it much more powerful.

 

[Crazydwarf]

First of all, the highest AC you can get at 30th level is far more than 35. At 30th level you can have +6 godplate...

Yes I knew this, I made a rough estimate and did not account for magic or feats etc. And I took care in mentioning this aswell.
However I disagree that 45 is "far more" when a monster (or group of monsters collectivly) may have 1000+ HP in comparison.

First of all, I explained a couple posts up about why offensive bonuses are in general better than defensive bonuses

Right, can you try again, and keep it simple for my stupidity's sake
All these formulas and math only cause me confusion rather than helping me grasp the concept.

I'll try to make a simple example:
A fighter has his plate armour and a one handed weapon. Now he's looking to "upgrade" by mundane means.

His options are:
1. Grab a shield to boost his defence
2. Grab a bigger weapon to boost his offence
3. Grab a secondary weapon to boost both "half-way"

The problem as I see it is that 1 seems to outshine 2 by quite some margin (and certainly 3 since that eats some feats before it can even become an option)

I have some houserules in mind (I wont go into detail about them to avoid derailing and hogging the thread).
But before I present them to my group and DM I feel I need to know if my opinion is true or imagined.

Otherwise I risk unbalancing the game completly, since they will likely agree to my houserules without much thought.
Sadly besides the DM, I'm the only one in the group that even know any rules at all

And back to the topic of two-handed weapons: another very good reason to take a two-handed weapon is Reaping Strike, which does more damage on a miss if the weapon is two-handed. If Reaping Strike is one of your primary at-wills this is a very good benefit.

But since shields seems to have this great advantage, and we assume a powergamer style wich chooses advantage > fluff at all times.
Then reaping strike is unlikely to end up as one of the at-wills....Ever.

Another benefit is that if you have a Warlord in your party with Commander's Strike, the Warlord can go sword-and-shield and use your melee basic attack (plus the Warlord's Int modifier to damage), so the Warlord can get the additional damage from the two-handed weapon as well as the shield bonus to his own AC and Reflex!

Cool, I'll admit to not knowing more about the warlord class other than a quick read through.
But that still seems very situational.

I must assume that I will rarely have knowledge of what class/race my friends will play at all times, my group atleast doesnt really plan our characters together, and let personal preference go before balanced out group. This might be a bad thing overall, and particularly in AD&D..But thats just how we roll
I also assume to have no prior knowledge about the DM's plans and cannot account for what enemies we will face or where.

There is so much uncertainty other than what my PC's strengths and weaknesses will be, and when the game presents my options as "defense or stupidity" rather than "defence or offence" I get a bit grumpy

 

[Alex319]

Yes I knew this, I made a rough estimate and did not account for magic or feats etc. And I took care in mentioning this aswell.
However I disagree that 45 is "far more" when a monster (or group of monsters collectivly) may have 1000+ HP in comparison.

This is a meaningless comparison. You are comparing the AC with the total number of hit points of a monster. This has no meaning because what is important is the amount of damage done on each attack. For example, doubling the hit points of a monster simply doubles the number of rounds it will take to kill it regardless of what weapons are used, and does not change the relative value of the weapons. (Actually this is not completely true, due to "overflow" of damage above that necessary to kill the monster - for example if all you were fighting was minions then damage wouldn't matter at all. But this would, if anything, make higher damage more important when fighting higher HP monsters, not less.)

Because the additional damage applies on every attack that hits, the appropriate comparison is with the amount of damage of each attack, not the total HP of the monster.

Right, can you try again, and keep it simple for my stupidity's sake
All these formulas and math only cause me confusion rather than helping me grasp the concept.

I'll try to make a simple example:
A fighter has his plate armour and a one handed weapon. Now he's looking to "upgrade" by mundane means.

His options are:
1. Grab a shield to boost his defence
2. Grab a bigger weapon to boost his offence
3. Grab a secondary weapon to boost both "half-way"

The problem as I see it is that 1 seems to outshine 2 by quite some margin (and certainly 3 since that eats some feats before it can even become an option)

I have some houserules in mind (I wont go into detail about them to avoid derailing and hogging the thread).
But before I present them to my group and DM I feel I need to know if my opinion is true or imagined.

Well, I can't tell you if your houserules are balanced without knowing what they are. But anyway, I'll try to explain a little bit better my point about offense being more important than defense.

Suppose I have a choice between two powers: one of which gives me +10 to all attacks for X rounds per encounter, and one of which gives me +10 to AC and reflex for X rounds per encounter. Which one is better?

If I choose the attack one, I can end up hitting on almost every attack. Since I control who I attack, I can target these attacks to the places where they will do the most good - to the monsters that are the biggest threat. And I can even increase the value of the attack bonus by using action points and multi-target encounters and dailies to apply the attacks to more targets.

If I choose the AC and reflex one, then I will be extremely difficult to hit, but that has only limited use, because it only applies when an enemy chooses to attack me, so the enemy has many countermeasures. He can attack someone else first. He can attack my fortitude or will. He can use a power that deals damage on a miss, so that my high AC won't completely protect me.

Of course, the bonuses we are dealing with here are much less than +10, and they are passive rather than active. But the point remains the same.

Otherwise I risk unbalancing the game completly, since they will likely agree to my houserules without much thought.
Sadly besides the DM, I'm the only one in the group that even know any rules at all.

But since shields seems to have this great advantage, and we assume a powergamer style wich chooses advantage > fluff at all times.
Then reaping strike is unlikely to end up as one of the at-wills....Ever.

Reaping strike can be quite good when faced with very high AC monsters or monsters that only have a few hit points left.

Cool, I'll admit to not knowing more about the warlord class other than a quick read through.
But that still seems very situational.

I must assume that I will rarely have knowledge of what class/race my friends will play at all times, my group atleast doesnt really plan our characters together, and let personal preference go before balanced out group. This might be a bad thing overall, and particularly in AD&D..But thats just how we roll
I also assume to have no prior knowledge about the DM's plans and cannot account for what enemies we will face or where.

There is so much uncertainty other than what my PC's strengths and weaknesses will be, and when the game presents my options as "defense or stupidity" rather than "defence or offence" I get a bit grumpy

Try this experiment. Play the game as normal, and have two fighters on the front lines - one sword and shield, one two-handed weapon.

Each time the sword-and-shield man gets attacked vs. AC or Reflex, roll damage for the attack, divide it by 10, and add it to a running tally. This is the expected amount of damage that was prevented by the shield. (To figure out the actual amount of damage prevented, don't divide it by 10 but only include attacks that miss, but miss by 2 or less, so without the shield they would have hit. But the first method gives a result with less variance.)

Each time the two-handed weapon man hits, take 1.5 times the number of [W] of the attack and add that to a separate running tally. This is the expected amount of additional damage done by the two-handed weapon. Also, if the two-handed weapon man has Reaping Strike, add the difference between his Strength mod and half his Strength mod to the tally each time he misses with Reaping Strike (against a target that is not a minion). For example, if he has Strength mod +4, then add 2 each time, because the two-handed weapon made Reaping Strike do 4 damage instead of 2.

Try this for several encounters and see what your results are.

 

[Crazydwarf]

This is a meaningless comparison. You are comparing the AC with the total number of hit points of a monster. This has no meaning because what is important is the amount of damage done on each attack. For example, doubling the hit points of a monster simply doubles the number of rounds it will take to kill it regardless of what weapons are used, and does not change the relative value of the weapons. (Actually this is not completely true, due to "overflow" of damage above that necessary to kill the monster - for example if all you were fighting was minions then damage wouldn't matter at all. But this would, if anything, make higher damage more important when fighting higher HP monsters, not less.)

I don't think its meaningless, what I'm trying to get at is that the AC and HP systems work differently. And a +2 bonus to one system is plain better than a +2 bonus to the other.
This is made even more clear if we take your example and assume we fight nothing but minions.
This would render the AC bonus of a shield much MUCH better than the damage bonus of a twohander, since we have a bonus vs no bonus.

If we double the AC of the monster, do we double the amount of rounds...Or do we make the monster completly invincible ?

Because the additional damage applies on every attack that hits, the appropriate comparison is with the amount of damage of each attack, not the total HP of the monster.

Yes, if we want to compare the damage output of one handers vs twohanders.
That is of importance, but what I'm wondering is if the numbers add up when we compare the damage output of one handers + the defensive bonus of a shield VS the damage output of a twohanded weapon.
It would seem to me that twohanders fall behind due to not outputting enough damage to weigh up for the loss of a shield.

All that math and such you allready gone through probably have the answers..It's just a bit too much math for me to handle and comprehend.

Well, I can't tell you if your houserules are balanced without knowing what they are.

True, we could take that as a separate discussion if there is interest
My point was though that if the system is allready balanced by means I have yet to understand, then any houserule I would add would unbalance it in favor of twohanders, wich is not what I want.

Suppose I have a choice between two powers: one of which gives me +10 to all attacks for X rounds per encounter, and one of which gives me +10 to AC and reflex for X rounds per encounter. Which one is better?

These powers are equally (or atleast equal:ish) good because they give the same bonus on the same system, and also equally situational.

But what if it was +10 damage or +10 AC ?
It should be clear then that the +10 AC one is much better.
Atleast in the higher levels where a monster can eat the +10 damage and still be standing long enough to hit back.

If I choose the attack one, I can end up hitting on almost every attack. Since I control who I attack, I can target these attacks to the places where they will do the most good - to the monsters that are the biggest threat. And I can even increase the value of the attack bonus by using action points and multi-target encounters and dailies to apply the attacks to more targets.

If I choose the AC and reflex one, then I will be extremely difficult to hit, but that has only limited use, because it only applies when an enemy chooses to attack me, so the enemy has many countermeasures. He can attack someone else first. He can attack my fortitude or will. He can use a power that deals damage on a miss, so that my high AC won't completely protect me.

Lots of if's, can's and maybe's here.
As I said these are things beyond foresight, I can choose one or the other and have it be good or bad because the DM just randomly sets certain conditions against me.
And imho it's better to be good 50% of the time than bad 100% of the time...Hmm, hope thats understandable.

Reaping strike can be quite good when faced with very high AC monsters or monsters that only have a few hit points left.

Sure, but if I'm always using a shield I would still prefere cleave and the other one (iron vanguard is it ?) over reaping strike.
I'd guess I'd have use them more often.

Try this experiment. Play the game as normal, and have two fighters on the front lines - one sword and shield, one two-handed weapon.

Good one, I'll try running a simulation if I ever get the time.
As it is I don't get to play normally much anyway (school, job, wife, kids...You probably know the drill )

 

[Crashy75]

...
On the other hand, my comment about "offense being more important than defense" refers to the following fact - suppose that you and an ally both have AC 20 without a shield. If you take a shield that raises your AC to 22, then an enemy could simply avoid you and target your ally, so you haven't really reduced the overall damage to your party. Of course this is not always true (you could have marked the enemy, the enemy could be unable to get to your ally, etc.) but in general defense bonuses are worth less than offense bonuses due to this "target substitution effect."

The classes (so far) that will make the choice between sword and board and two handed weapons will be either defenders or leaders. Defenders can effectivly convey that +2 to AC bonus to their allies if the baddies have selected the 'wrong' target whether or not they themselves have a shield.
Defenders have other ways of punishing enemies for ignoring them. Given that, I don't think this holds for defenders. I will say that you have a point regarding leaders, however.

(Here's another way to look at this: if you had a choice between two minor action utility powers, one of which gave you +10 to attack for one round, and one of which gave you +10 to AC and reflex for one round, which one would you be more likely to choose?)

Clearly the +10 to attack is better but this doesn't apply to Two Handed Weapons vs. Sword and Board. You've already shown that a bonus to hit is much better than increased damage die. And you are not switching to THW for a bonus to hit. You are switching for a bonus your damage die. Couple this with the defenders ability to mark, and you will find that the question is still valid for defenders at least.

 

[Crashy75]

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.

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

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.)

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.

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. In a group that faces mostly minions, then sword and board is the best way to go. (and yes, definitely sword and board.) You will be attacked more and your higher damage means much less. However, if you face a lot of solo monsters (hopefully with a lot of rest in between!), you will be presumably unloading your high [w] attacks, making 2-handed weapons a reasonable choice.

Also, this varies widely depending on the powers, feats, equipment and class you choose.

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).