Sunday, 21 October 2012

Two Weapons or Sword and Board?

This is going to be a dull analytical post, so feel free to skip it. The question before the house is whether longsword and shield is better than longsword and hand axe (In AD&D, only daggers and hand axes are allowed for the "off-hand" weapon in two-weapon fighting and, since the AD&D dagger is almost worthless as a weapon, I'm going to use the axe as the most effective option).

The rules for two-weapon fighting (TWF) are fairly straight-forward: the combatant is treated like any monster with an attack routine and when it is their turn in the initiative scheme, they roll once for one weapon and then once more for the other weapon. Whether these attacks are both against the same target or not is never specified, but there is some reason to believe that they are and that's what I'll assume.

The primary weapon attacks at -2 to hit and the secondary at -4 if the character's dexterity is between 6 and 15. At dex 16 the modifiers are -1 and -3, at 17 they are ±0 and -2, and at 18 the secondary penalty goes to -1.

I'm going to start off with two fighters in platemail, one with a shield and longsword (sword and board as da kidz say) and the other with the longsword and hand axe. I've not calculated these effects ahead of typing this, so the conclusions will be new to me too and may or may not confirm my own feelings. Isn't science exciting?

1 Puny Veterans
We'll start off with no ability score bonuses and 1st level fighters. This is an easy win for sword and board; hardly worth calculating but it serves as a baseline. Calculating the average hit and damage rates gives this:

S&B: 0.9 hp per attack.
TWF: 0.625 per attack.

TWF is doing almost 70% of the damage rate, although in fact the repeating 20's of the combat chart have helped to level the field somewhat here. Let's try bumping the combat ability a bit.

2 Puny Heroes
Same as above but 4th level fighters.

S&B: 1.35 hp per attack.
TWF: 0.85 hp per attack.

The repeating 20's of the combat table are no longer important for these guys and so TWF falls further behind to 63% of the S&B damage.

3 Puny Superheroes
Moving up to 8th level on the "no bonuses" ladder, we find these values:

S&B: 2.25 hp per attack
TWF: 2.45 hp per attack

Now that armour itself is becoming less important, the TWF has overtaken the S&B fighter and is doing almost 9% more damage per attack. Both fighters are now also getting 3/2 attacks per round, but the effect of this cancels out so we don't need to worry about it.

4 Puny Lords
Final run without bonuses: 12th level:

S&B: 3.15 hp per attack.
TWF: 4.05 hp per attack.

TWF is now 28% more effective per attack routine.

This is all nice but unrealistic. Firstly, the fighters are unlikely to not have some bonuses, and secondly, the high level fighters are unlikely to not have magic armour, weapons, and shields.

Bonuses first.

5 Agile Veterans
We'll give both fighters 18 Dexerity and look at whether this has most effect on TWF or S&B.  The TWF now has no penalty for the longsword and only -1 to-hit on the axe. Back to first level:

S&B: 0.225 hp per attack.
TWF: 0.4hp per attack.

Essentially, the off-hand weapon is pure bonus here as everyone needs 20's to hit.

6 Agile Heroes
Moving up to 4th level with 18 Dex:

S&B: .45 hp per attack
TWF: .4 hp per attack

Simple enough: the TWF needs 20's with both weapons to do any damage while the S&B guy is hitting twice as often with his single weapon.

7 Agile Superheroes
8th level, 18 Dex:

S&B: 1.35 hp per attack
TWF: 1.825 hp per attack

TWF is now clearly superior, doing 35% more damage.

8 Agile Lords
Final run - 12th level 18 Dex:

S&B: 2.25 hp per round
TWF: 3.425 hp per round

52% better with two weapons.

Okay, at this point we've learnt something about the big value of 18 Dex as a two-weapon fighter. I'm not going to list every possible combination but I want to look at the possible effect of a magic shield. I'm going to assume that any magic armour and swords cancel out for to-hit purposes and see what a +3 shield does to the superhero and lord levels. I'm going to assume that the hand axe is not magical and that both longswords are +2 for damage.

9 Magic, Agile Superheroes.
S&B now has an effective AC of -5 while TWF has an effective AC of -1.

S&B: 1.95 hp per attack.
TWF: 0.825 hp per attack.

TWF is back to doing only 42% of the damage rate of the sword and shield.

10 Magic, Agile Lords
12th level as previous example.

S&B: 3.25hp per attack.
TWF: 2.825hp per attack.

Improving back up to 87% of the opponent's score, the TWF is still clearly the less effective option here too.

Next, what happens if the S&B fighter decides to put their 18 into STR while the TWF keeps it in Dex? Assuming 18/50 and staying with the magic listed above, the S&B fighter's effective AC drops to -1, while the TWF's is reduced to 0 due to the +1 to-hit for 18/50 strength. How does the increased damage balance against this AC change?

11 Strong Vs Agile Magic Superheroes
Back to 8th level with +2 swords.

S&B: 3.325 hp per attack.
TWF: 2.825 hp per attack.

I have to admit to being surprised; I thought the TWF would win this one. Instead it scores 85%.

12 Strong Vs Agile Magic Lords
12th level as above:

S&B: 5.225hp per attack.
TWF: 4.825hp per attack.

TWF moves up to 92%.

I'm surprised enough by these results to briefly go back and look at the STR Vs Dex values without magic.

13 Strong Vs Agile Heroes

So we're back to no magic and 18 Str Vs 18 Dex. S&B guy has an AC of 2, while S&B is at 0 (again, because of the +1 to hit from Strength).

S&B: 1.425hp per attack.
TWF: 1.825hp per attack.

Advantage to the TWF guy; 28% better.

14 String Vs Agile Superheroes
When we move these two magically-impoverished fighters up to 8th level the pendulum swings again:

S&B: 2.85hp per attack
TWF: 2.625hp per attack.

Now TWF is back to being 92% as effective as S&B

Conclusions
As I suspected, the balance of power between TWF and S&B is quite delicate and it's not an easy thing to call which side it will settle on just by a casual glance over a character's stats and possessions. It's also true that these examples have been quite artificial and I don't expect every fighter to have an 18 in either Dex or Str.

Having said that, even a 16 Dex represents quite a step down for TWF and a quick calculation on some of the above situations suggests that it really isn't very viable.

To really dig into the implications of TWF you'd really need to construct a spreadsheet to allow changing of lots of factors so that more realistic situations could be examined. But "more realistic" equates to a huge number of possible combinations of magic swords, shields, dexterity, strength, weapons (and weapons Vs armour which I've ignored here) and numbers of opponents. Probably there are a lot more situations where TWF is at least marginally better than sword and shield but I'm pretty confident that a shield of the calibre of the +3 one in the examples here will more than negate the usefulness of TWF in any situation likely to arise in play.

Of course, "likely to arise" is of no consequence to the DM who has to handle the situation when it does arise and a fighter with 18 Str and 18 Dex would be mad not to take TWF and there's no value in the DM saying "well, that was really lucky rolling!". Of course it was. But rather than worrying too much about how such an unlikely thing might be "out of balance", I think it's more productive to say "this character could become one of the really memorable ones" and try to embrace it without allowing it to overshadow the other members of the party. All characters have weak points (usually the player behind them) and so long as the game doesn't become a long string of "well, Dexto the Barbarian handles it" then every one should still be able to have fun with such a fluky character in the party.

One other thing I've noticed while going through this process is that the two-handed sword is not as bad an option as I thought, if the character has 18/50 strength. With an average adjusted damage of 8.5 against a human and 13.5 against large creatures, it's probably worth consideration at low levels. At high levels, a magic shield is still a much better option, I think, especially as a magic longsword will probably have made an appearance by then.

As I've mentioned on Dragonsfoot, I charge a proficiency slot for fighting with two weapons over and above any used to learn how to use the weapons singly, although a character can learn, for example, "longsword and dagger" without taking either weapon on its own, and simply receives the non-proficiency penalty when forced to use one or the other alone. This is an additional factor in deciding whether to take two weapon combat or not, particularly for thieves who only start with two slots.

12 comments:

  1. I just skimmed over this, but are you comparing a long sword +2 and shield +3 versus a long sword +2? That seems a little lopsided to me!

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    1. I'm assuming that both sides have +2 platemail and +2 longswords too so the swords cancel out the armour. I wanted to mostly look at what the effect of the shield was but it seemed unreasonable to not have some other magic involved for high level combat. Like I said, the number of reasonable combinations at high level defies any exhaustive treatment but I think the point is still valid that the balance is finer than Don suggests.

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  2. I would say it is still a bit of a stretch to draw much in the way of conclusions based on three magical items versus two. At the least the fighter with two weapons should have a dagger +3.

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    1. I've never seen a dagger +3 in play; I've seen lots of +2 longswords and +3 shields. If I get time later this week I'll edit in another set with a magic dagger. Can't say fairer than that, gov.

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    2. I had not realised you were only counting one additional attack at higher levels either. I reckon the way attack routines work it has to be applied to both primary and secondary weapons. So, basically, this is the issue:

      Long Sword = 4.5 Damage
      Long Sword + Dagger = 4.5 + 2.5 = 8.0 Damage

      Add in a damage bonus of +4 (for example) and you end up with:

      Long Sword = 8.5 Damage
      Long Sword + Dagger = 8.5 + 6.5 = 15.0 Damage

      The trade off as presented in AD&D is the penalty to hit (−2/−4), which can be mitigated by dexterity and will eventually be outweighed by the damage adjustment, and the inability to use a shield (a potential 1-6 point advantage).

      What this results in is a very narrow context whereby the technique is balanced against weapon and shield or two-handed weapon and a large number of contexts where it is better or worse. Generally speaking, as characters advance in level and get access to better modifiers fighting with two weapons becomes increasingly better.

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    3. "I had not realised you were only counting one additional attack at higher levels either."

      I'm not. I've given values for damage per attack routine. The number of routines in a round makes no difference to which option does the most damage, providing, of course, that both combatants get the same number. Since I'm primarily thinking of the fighters here, I've assumed that to be the case so number of attacks per round is not significant.

      Also: 4.5+2.5=7 :) Leaving that aside, you can't really add the damages together in this context as one of them always has a lower chance to hit and the dagger's 2.5 is not as it were the same 2.5 as a dagger in the main hand.

      "What this results in is a very narrow context whereby the technique is balanced against weapon and shield or two-handed weapon and a large number of contexts where it is better or worse."

      That's fine - as long as there are common situations where one is better than the other and other common situations where the advantage is swapped then there's no problem. What would be a problem is if one option is clearly better all the time for every fighter.

      The more likely you are to hit, the more of an advantage two weapons are but off-hand weapons tend not to be magical or not as strongly magical as main weapons and high dex is needed to take advantage of two-weapon fighting.

      Again, if the situation is that high-level high-dex characters tend to be the ones that take TWF, then I don't see that as bad either.

      What I was worried about was the assertion that TWF is a no-brainer for any high-level fighter. I'm pretty satisfied that this is not in fact the case.

      Here's the example with +3 dagger I promised:

      Two 8th level fighters, 16 Dex, 17 Str. Both in +2 platemail and using +2 longswords. One has a +3 shield, the other a +3 dagger in the off-hand.

      S&B is AC -5; TWF is AC -1. Longswords are doing a base average of 7.5 including all damage bonuses, the dagger 6.5. Longswords are +3 to hit, dagger is +4.

      S&B does: 3.375 per attack.
      TWF does: 2.275 per attack routine.

      Add one level and things change a bit:
      S&B does: 4.125 per attack
      TWF does: 3.875 per attack

      Finally, at 11th level the TWF overtakes.
      S&B: 4.875 per attack
      TWF: 5.275 per attack

      I would perhaps point out, though, that the +3 dagger is not actually in the original DMG treasure tables so it's not going to be as common as a +3 shield.

      My purpose was not to show that TWF is no use but to show that the over-all choice between TWF and S&B was not broken and that there are plenty of use cases for both. 17+ dex definitely makes a case for it, and for any class that can't use shields it's more attractive as well.

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    4. Ha! Right, yes, apparently I am incapable of simple addition from time to time! :D

      Anyway, I was not adding the damage values together without taking into consideration the penalties to hit, I separated them out precisely because the penalties to hit vary by dexterity value.

      The contexts are all important, of course, because that is where the issues begin to appear. Sure, a dagger +3 is not on the random treasure type tables, but gauntlets of ogre power sure are, as are the various "belts of giant strength".

      You are quite right that hit probabilities affect the usefulness of fighting with two weapons, that is the basic interaction of damage. For example, if you are comparing +1 to hit versus +1 damage on 4.0:

      1.00 = 4.0 / 0.95 = 4.75
      0.95 = 3.8 / 0.90 = 4.50
      0.90 = 3.6 / 0.85 = 4.25

      You can see the gap closes by 0.05 damage for every 5% increment until at 0.03/0.25 both are doing the same average damage (1.00) and for probabilities less than that +1 to hit has the advantage [i.e. if you need a base 17+].

      Is it a "no brainer" for fighters to choose two weapons at high levels? Obviously not, it is context based, but [i]Gauntlets of Ogre Power[/i] or similar damage enhancements make a heck of a difference and are not particularly uncommon at high level.

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  3. I'm playing a low level fighter/MU in a DF chat game with dexterity of 17 & my only magic item acquired thus far is a magical dagger.

    The extra attack at -1 to hit & d4+1 damage is better than increasing my AC from 0 to -1; although right from the start I was intending to play a 2 weapon fighter character.

    High Str AND Dex indeed are the early "breakers", although high plus magic can replace either later on.

    Yes, if one has a +3 Shield & no magic off hand suitable weapons, one will use the shield. One might use the shield in certain situations even if they do have a +3 dagger.

    Your calculations, Nagora, on the L7+ fighters are off. Multiple attack routines are another "break point". Getting an extra 1.5 (or later 2) attacks per round, rather than one, will change your outcomes considerably. It's a common house rule to limit the off hand attack to only 1 per round, but it's by no means BTB in 1e AD&D. It is in 2e AD&D, but then, 2e has rules to allow for further reducing 2WF penalties & dual wielding bastard swords, etc.

    Another common house rule is expanding the potential off hand weapons usable. Gygax did this himself in his early published adventures, with horseman's mace, etc. It's difficult to justify allowing a hand axe but not a hammer (same weight, speed factor & length), for example. This doesn't have a great impact on damage (exception: short swords), but does make it easier to find a magical off hand weapon & allows clerics to fight with 2 weapons (as Gygax often presented in T1-4)

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    1. Well, things are complex enough without also trying to second guess what house rules are in play. If someone uses house rules and is worried about the effect, then they should start their own blog and post the calculations there. So, ha!

      "Multiple attack routines are another "break point"." Not if both sides are the same level, which was the situation I was looking at in order to get a comparison. If A is doing more damage per round than B when they have 1 attack per round, then A will still be doing more damage when they have 3/2 attacks or 2 attacks. The specific amount per round will change, sure, but the percentages (of effectiveness) won't. That's why I stated "per attack".

      I agree that the choice of dagger or hand-axe seems a strange limitation and a hammer is weaker than a hand axe so there's no game-balance issue. By all means expand the list but, as you have said yourself, the danger is that too-liberal a list will lead to the situation where there's no good reason to not take the option. But there are certainly several weapons that could be added safely, including as you say the horseman's mace.

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  4. OK, what makes you think that the off hand doesn't receive the extra attacks from high level fighting ability, haste or whatnot? I think it's a house rule to say off hand attacks are limited to ONE extra attack. A good rule, but...

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    1. I'm not saying that; I'm saying it *does* receive the extra attack for high level combat. The point is that if I attack you with a sword for 3 pts of damage and you attack me with sword and dagger for 2.5pts then when we BOTH get two attacks I'll hit you for 6 and you'll hit me for 5. The damage has gone up but it makes no difference to which of us does the most damage.

      Am I missing something here?

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  5. One of us is. Having done the math on several of these scenarios, I'd guess it's a case of the exact numbers you crunched then Nagora. No worries though.

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