Shield vs Great Weapon - Need a little math help

[Oramac]

Ok, so I actually need a lot of math help. This isn't my strong suit.

Background: I tend to play a lot of martial classes using a great weapon, which means I forgo the +2 AC of a shield, presumably in trade for more damage.

Now in my experience, it feels like I take significantly more damage due to the loss of AC than I deal due to the beefier weapon. But I want to try to prove/disprove that.

For purposes of discussion, let's ignore GWM for the time being, and just look at weapons and fighting styles (GWF or Dueling with SnB), versus the damage reduction of a +2 AC.

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Ok then. So we know that the average damage of a Greatsword is ~8.2 with GWF style (IIRC). Average for a longsword with Dueling is ~6.5 damage, or 4.5 without Dueling.

So an increase of 1.7 average damage w/ Dueling or 3.7 average damage without Dueling.

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What I'm fuzzy on is how to calculate the reduction to damage taken from adding a shield to the mix, all else being equal.

[Zman]

Well, that gets tough as there are a wide array of damaging effects, AC only helps against some and there are so many variables to considers.

Basically, +1AC lowers their to hit chance by 5% whit nets to around a 10%, assuming a 50% to hit chance, reduction of incoming damage, so +2AC yields about a +20% boost to survivability vs attacks targeting AC. Then we have to factor in that dealing more damage actually has defensive benefits as well, by killing something faster you take less incoming damage which means there is a ratio of damage dealing vs lessening damage received and that ratio is less than equal. We also have to examine how often we deal too much damage and that extra damage may not matter in many occasions just as damage taken doesn't matter so much either in many situations.

We can pick a certain situation vs a certain enemy type and see which is better, but across the whole game it becomes less so.

[Oramac]

Basically, +1AC lowers their to hit chance by 5% whit nets to around a 10%, assuming a 50% to hit chance, reduction of incoming damage, so +2AC yields about a +20% boost to survivability vs attacks targeting AC.

Even this helps a lot actually. With GWF the average damage (8.2) is about 26% higher than with Dueling (6.5), so given that the +2 AC is worth about a 20% boost to survivability, it seems they're actually pretty even on the face of it.

Very interesting.....

[Vorpalchicken]

Note that the higher your AC is before you add the shield, the more dramatically frequency of hits is reduced. Say your other party member is a paladin in splint armor with defense style and he habitually casts Shield of Faith in hairy fights. And you are fighting something with a +4 to hit, maybe a horde of goblins.

Well in that case, the goblins start with only a 25 per cent chance to hit and the paladin is lowering that to 15 per cent by equipping his shield. Here, the damage he takes is 40 per cent less. (Until he loses shield of faith)

I think this is why Great Weapon Master is important and shouldn't be discouraged. The bonus action attacks from critical and kills, and under the right circumstances (maybe reckless attack or zombie fighting ) the plus ten damage, really makes heavy weapons a competitive choice.

[Zman]

Note that the higher your AC is before you add the shield, the more dramatically frequency of hits is reduced. Say your other party member is a paladin in splint armor with defense style and he habitually casts Shield of Faith in hairy fights. And you are fighting something with a +4 to hit, maybe a horde of goblins.

Well in that case, the goblins start with only a 25 per cent chance to hit and the paladin is lowering that to 15 per cent by equipping his shield. Here, the damage he takes is 40 per cent less. (Until he loses shield of faith)

I think this is why Great Weapon Master is important and shouldn't be discouraged. The bonus action attacks from critical and kills, and under the right circumstances (maybe reckless attack or zombie fighting ) the plus ten damage, really makes heavy weapons a competitive choice.

It is absolutely true, the higher your AC the greater each additional AC is valued. So, against low to hit enemies a Shield is phenomenal, against high to hit Bruisers is underperforms.

GWM, as a feat, is too good. Against Low and Moderate AC enemies it drastically increases average damage output, especially when Advantage can be attained. GWM and PAM are two of the ways to achieve unparalleled damage output and are arguably too good.

[Oramac]

So if I'm understanding this correctly, using a great weapon is strictly worse than using a shield unless you make liberal use of Great Weapon Master?

[Giant2005]

So if I'm understanding this correctly, using a great weapon is strictly worse than using a shield unless you make liberal use of Great Weapon Master?

Not strictly worse as it depends entirely on how much AC you have with and without the shield (and whether your AC is even being targeted in the first place), vs the enemy's attack bonus.
It is certainly better in most situations though.

[Oramac]

It is certainly better in most situations though.

That's more or less what I expected to be the case. Which is unfortunate.

Thanks!

[Zman]

So if I'm understanding this correctly, using a great weapon is strictly worse than using a shield unless you make liberal use of Great Weapon Master?

Not necessarily true. My post earlier pointed out how complicated and conditional the benefit of each is. Offense generally is more important than defense and ranked higher, ie if someone offered to let you deal 10% more damage or take 10% less damage you'd choose the more damage every time.

[Cybren]

Not necessarily true. My post earlier pointed out how complicated and conditional the benefit of each is. Offense generally is more important than defense and ranked higher, ie if someone offered to let you deal 10% more damage or 10% less damage you'd choose the more damage every time.

Well yeah, because you didn't provide a benefit to accommodate the downside. You just said "Do you want +1 or -1?"

[Zman]

Well yeah, because you didn't provide a benefit to accommodate the downside. You just said "Do you want +1 or -1?"

What are you talking about? Fairly certain I've said nothing of the sort.

[Oramac]

Not necessarily true. My post earlier pointed out how complicated and conditional the benefit of each is. Offense generally is more important than defense and ranked higher, ie if someone offered to let you deal 10% more damage or 10% less damage you'd choose the more damage every time.

I understand this insofar as a dead enemy doesn't deal any damage.

My concern is that the extra damage from a great weapon (even with GWM) isn't high enough to offset the extra damage taken from a -2AC due to losing the shield. Especially since you can combine the shield with Dueling and only be a point or two damage behind the great weapon (albeit without GWM).

Sadly, I'm not good enough with the math to know how to prove it one way or the other.

[Cybren]

What are you talking about? Fairly certain I've said nothing of the sort.
Your question was "would you Iike to deal 10% more or 10% less damage". It's a non-choice. You don't give any benefit to accepting less damage, so of course people will choose the extra damage. If someone said "would you like to deal 10% more damage or have 50% more HP" the trade off seems more acceptable

[Oramac]

Your question was "would you Iike to deal 10% more or 10% less damage". It's a non-choice. You don't give any benefit to accepting less damage, so of course people will choose the extra damage. If someone said "would you like to deal 10% more damage or have 50% more HP" the trade off seems more acceptable

True. I think he meant to ask "would you rather deal 10% more damage or take 10% less damage".

[Cybren]

True. I think he meant to ask "would you rather deal 10% more damage or TAKE 10% less damage".

Yeah, I think so?

[WereRabbitz]

This calculation gets hairy quick.

Look at your role here as well.

In our group my Paladin is the tankiest person and one of 2 melee out of a group of 6. My companions can wrought far more destruction then I can without burning away all my smites, but by controlling the field and preventing monsters from getting too or killing the allies with little hp and ac i'm improving our damage.

My AC Plate(19) + Ring(1) + Shield(2) + Shield of Faith(2) = 24AC

A Monster with a +4 attack only has a 5% (Crit) of hitting me. So monsters have a option they can try to get past me facing: shield Master, Sentinel, Command, Ensnaring Strikes, ect... or they have to kill me and to kill me they need a +14 to hit to have a 50% chance of landing a hit.

I'm increasing our damage output by controlling the field and keeping the spellslingers in a worry free burn everything mood.

You also have to consider that if you go 2handed Greatsword for instance you have something like Great Weapon Master to increase the damage

You also have a feat called Shield Mastery which does a very different kind of help. Shoving someone prone as a bonus action gives you a really good chance of consistently landing both your attacks every round and that too increases your damage output.

[Zman]

I understand this insofar as a dead enemy doesn't deal any damage.

My concern is that the extra damage from a great weapon (even with GWM) isn't high enough to offset the extra damage taken from a -2AC due to losing the shield. Especially since you can combine the shield with Dueling and only be a point or two damage behind the great weapon (albeit without GWM).

Sadly, I'm not good enough with the math to know how to prove it one way or the other.


Well, it is probably impossible to "prove", but you can take a look at individual situations and gauge for yourself. I'll break down a lvl 1 Fighter with a Longsword vs Greatsword when pitted up against an Orc. Trying to account for all of these factors even in a single simple situation is incredibly complicated.

Orc HP15 AC13 +5(D12+3)

Lvl 1 Fighter 12HP AC18 Chainmail(AC 16) with Longsword(+5 for D8+3) and Shield
Hit chance: 60%
Crit chance: 5%
Damage Range: 4-11(7.5) Average
Minimum Hits to Kill(No Critical): 2
Maximum Hits to Kill(No Critical): 4
1 Hit chance to Kill(No Critical): 0%
2 Hit chance to Kill(No Critical): 56%
3 Hit chance to Kill(No Critical): 98%
Critical Chance to Kill: 23%

Orc vs Sword and Board/Greatsword
Hit chance: 40%(50%)
Crit chance: 5%
Damage Range: 4-15(9.5) Average
Minimum Hits to Kill(No Critical): 1
Maximum Hits to Kill(No Critical): 4
1 Hit chance to Kill(No Critical): 8%
2 Hit chance to Kill(No Critical): 81%
3 Hit chance to Kill(No Critical): 99%
Critical Chance to Kill: 62%


Lvl1 Fighter 12HP AC16 Chainmail(AC 16) with Greatsword(+5 for 2d6+3)
Hit chance: 60%
Crit chance: 5%
Damage Range: 5-15(10) Average
Minimum Hits to Kill(No Critical): 1
Maximum Hits to Kill(No Critical): 3
1 Hit chance to Kill(No Critical): 3%
2 Hit chance to Kill(No Critical): 95%
3 Hit chance to Kill(No Critical): 100%
Critical Chance to Kill: 76%


Now, we don't need to figure out exactly the liklihood of each scenario happening, but we can see that a stock Longsword user is going to need 2-3 hits on average to kill an Orc, and will need on average 3-4 swings to accomplish that task and has a very small likelihood of killing it in one round(1.1%) and an incredible small chance of it taking more than three hits(<2%). When compared to the Greatsword that really will only need two hits or three attacks most of the time to kill the Orc.

When looking at return damage sans Crits the Sword and Board has a 13% chance of being dropped in two attacks with a 20% chance of dropping the Orcs in those two attacks.
When looking at return damage sans Crits the Greatsword Fighter has a 20% chance of being dropped in two attacks with a 34% chance of dropping the Orc in two attacks.
The Sword and Board Fighter is ~35% less likely to be dropped in two rounds of combat but is 41% less likely to drop the Orc in those first two rounds.

When expanded out to rounds three the Sword and Board Fighter has a reasonable chance of ending the fight, with very good chance of surviving three attacks in return.
When expanded out to rounds three the Greatsword Fighter has a very good chance of ending the fight, with a good chance of surviving three attack in return.

Without creating a nice complicated spreadsheet to try and figure out the exact likelihoods of each scenario and aggregating them it feels like the Greatsword is superior here pound for pound in this singular 1st level example against an Orc, but not by that much. When you expand this with Fighting Styles ie Dueling and GWF the Fighter's chances in each gets better and more likely to kill, but the Duelist gets significantly better and increases the likelihood of two hit killing an Orc to 91% from 56% which makes it much more likely that it won't require a third hit or more than three swings to fell an Orc which puts it in the same relative category as the Greatsword with additional survivability, in this particular scenario the GWF Fighter is slightly more likely to one hit or crit kill the Orc, but doesn't see much of the benefit of almost guaranteeing that it two hits kills, with the Fighting styles factored in I'd give it to the Duelist vs an Orc at lvl 1.


Now, as characters level up and Monsters have more HP we get a movement towards average and it becomes more predictable how long it will take to kill an enemy and the valuation of each of those buffs gets a bit more prevalent. The 1st level example I chose is actually quite lethal and really shows us just how dangerous Orcs are even for a fully armored and shielded Fighter at early levels. Without Fighting Styles the extra damage from the Greatsword really resulted in a one on one fight ending a round or so earlier which outweighted the defensive boost. But, when Dueling hits the table in this particular scenario is closes the Greatsword's damage gap quickly and the GWF doesn't really benefit from his added damage nearly as much as the Duelist does making it the superior style in this one particular scenarior.

Wow, that is a bit of txt...

[Zman]

Your question was "would you Iike to deal 10% more or 10% less damage". It's a non-choice. You don't give any benefit to accepting less damage, so of course people will choose the extra damage. If someone said "would you like to deal 10% more damage or have 50% more HP" the trade off seems more acceptable

Ahh, it's called context and a typo, not sure how you didn't figure that one out. It has been fixed.

[WereRabbitz]

Good post!

I do think it's only fair to factor in the Styles though.
GWF kicks in from time to time to help reduce the bottom end, but Dueling +2 static bonus helps a bunch.

That takes the Longsword up to a nice 9.5dmg Average vs the GWF gets a +1.33 average damage so 10.83


so 9.5dmg/+2 AC VS 10.83dmg

This means both can kill the Orc in 1-3 turns accounting for a chance to miss.

The problem with this questions is it gets out of hand quickly.

What if the person is using Great Weapon Master to increase damage? Now you got to account for missing

But the Sword and Board guy could be using PAM with Quarterstaff & Shield getting the bonus 1d4 without an attack penalty.


I stand by my earlier post it depends on what your role in the group is going to be.

[Zman]

Good post!

I do think it's only fair to factor in the Styles though.
GWF kicks in from time to time to help reduce the bottom end, but Dueling +2 static bonus helps a bunch.

That takes the Longsword up to a nice 9.5dmg Average vs the GWF gets a +1.33 average damage so 10.83


so 9.5dmg/+2 AC VS 10.33dmg

This means both can kill the Orc in 1-3 turns accounting for a chance to miss.

Thanks!

Yep, when you factor in the Fighting styles against a 15HP enemy the Duelist wins out. Had we picked an enemy with say 14HP the GWF would have gained over the Duelist, or if we had picked something with say 20HP or 10HP the GWF would have again been on top again. Depending on the exact number of Hit Points etc the valuation of each of the Fighting styles fluctuates.

This is likely showing that either Duelist is a bit strong, or GWF is a bit weak, it is one of the reasons that in my Tweaks located in my signature, I changed GWF to being able to reroll any die instead of just 1s and 2s, that brings the Greatsword from 8.33 to 8.5 and gives them a bit more flexibility when in situations where a better roll could result in a kill, but that change to GWF does wonders for a Greataxe bringing its damage up to 8.0 instead of 7.33.


Edit: To your edits it becomes 9.5 Average for the Dueling Longsword vs 11.33 for the GWF Greatsword.

[WereRabbitz]

Thanks!

Yep, when you factor in the Fighting styles against a 15HP enemy the Duelist wins out. Had we picked an enemy with say 14HP the GWF would have gained over the Duelist, or if we had picked something with say 20HP or 10HP the GWF would have again been on top again. Depending on the exact number of Hit Points etc the valuation of each of the Fighting styles fluctuates.

This is likely showing that either Duelist is a bit strong, or GWF is a bit weak, it is one of the reasons that in my Tweaks located in my signature, I changed GWF to being able to reroll any die instead of just 1s and 2s, that brings the Greatsword from 8.33 to 8.5 and gives them a bit more flexibility when in situations where a better roll could result in a kill, but that change to GWF does wonders for a Greataxe bringing its damage up to 8.0 instead of 7.33.

I agree, you did a wonderful job with your post and laying the information out clearly though /applause

[Oramac]

Truncated

Wow, that is a bit of txt...

Indeed it is! But quite the useful bit of text as well. Thank you!

Obviously, the answer to the question is far too complex to solve without a pretty large spreadsheet and a lot of time, which most of us probably don't have. But at the very least you've given a solid place to extrapolate from.

Overall, this [mostly] confirms my suspicions that the great weapon is slightly worse in the damage dealt vs damage taken trade-off (situation dependent, of course). Which isn't unexpected, but it's nice to have at least a ballpark idea of where it stands.

Thank you both, again!

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EDIT: slightly off topic, but it doesn't seem a big enough deal to start a new thread. Does anyone know the output string in AnyDice to get the odds of at least one 20 out of 4d20? I've read pretty much the whole site and can't seem to get it to work. :(

[Foxhound438]

Even this helps a lot actually. With GWF the average damage (8.2) is about 26% higher than with Dueling (6.5), so given that the +2 AC is worth about a 20% boost to survivability, it seems they're actually pretty even on the face of it.

Very interesting.....

not quite; add your mod to damage, GS will be something like 12.33 (you didn't recall quite right), and longsword will be 10.5. you get about 17% better damage.

That said, it may still be worth it to go for the better damage from your end, as killing things a bit faster means the enemies get fewer actions.

also note that not everything targets AC, so in some cases you get 17% better damage without taking any more in return.

[Oramac]

not quite; add your mod to damage, GS will be something like 12.33 (you didn't recall quite right), and longsword will be 10.5. you get about 17% better damage.

True enough. I was just looking at weapon damage because you add the modifier regardless of type. But it does indeed make a difference.

[WereRabbitz]

not quite; add your mod to damage, GS will be something like 12.33 (you didn't recall quite right), and longsword will be 10.5. you get about 17% better damage.

That said, it may still be worth it to go for the better damage from your end, as killing things a bit faster means the enemies get fewer actions.

also note that not everything targets AC, so in some cases you get 17% better damage without taking any more in return.

D8 Averages 4.5 + Duel 2.00 = 6.5 +4 Str = 10.5 x2 Crit = 21
2d6 Averages 7.0 + GWF 1.33 = 8.33 +4 Str = 12.33 x2 Crit = 24.66

Now that you got the base line you can throw things in like Great Weapon Master & Shield Mastery bless ect.. and get into the really awful gritty stuff :)


Although I like the idea of a Longsword With Dueling, Great Weapon Master & Shield Mastery.

Off set the -5 penalty you get by using your Shield on your turn as a bonus to knock them prone so you get advantage on your attacks with +10 dmg.

: )

[Zman]

D8 Averages 4.5 + Duel 2.00 = 6.5 +4 Str = 10.5 x2 Crit = 21
2d6 Averages 7.0 + GWF 1.33 = 8.33 +4 Str = 12.33 x2 Crit = 24.66

Now that you got the base line you can throw things in like Great Weapon Master & Shield Mastery bless ect.. and get into the really awful gritty stuff :)


Although I like the idea of a Longsword With Dueling, Great Weapon Master & Shield Mastery.

Off set the -5 penalty you get by using your Shield on your turn as a bonus to knock them prone so you get advantage on your attacks with +10 dmg.

: )

Ok, +4 Str is only really going to happen after an ASI at 4th level.

Your Crits don't double the Dueling Damage or the Str Damage, just the dice so Crits are only an additional 4.5 Damage for a Longsword and an additional +8.33 Damage for a Greatsword.

You can't use Great Weapon Mastery with a Longsword or with Shield Mastery. GWM requires a heavy two handed weapon, a longsword is not Heavy, and when using a shield it isn't even two handed.

[famousringo]

One thing I haven't seen mentioned is that combat isn't warrior vs monster, it's team versus team. And usually, most of the enemy team's damage is focused on that frontline warrior.

So if your warrior represents 25% of your teams damage and you boost his damage output by 10%, the team's total damage only goes up 2.5%.

But if that warrior is taking 50% of the enemy's attacks and you reduce his incoming damage by 10%, the team's incoming damage falls by 5%.

This depends on the tactics of your team, the tendency of your DM to target the weak, and so forth, but it's worth keeping in mind when you're deciding to optimize for defense or offense.

[WereRabbitz]

One thing I haven't seen mentioned is that combat isn't warrior vs monster, it's team versus team. And usually, most of the enemy team's damage is focused on that frontline warrior.

So if your warrior represents 25% of your teams damage and you boost his damage output by 10%, the team's total damage only goes up 2.5%.

But if that warrior is taking 50% of the enemy's attacks and you reduce his incoming damage by 10%, the team's incoming damage falls by 5%.

This depends on the tactics of your team, the tendency of your DM to target the weak, and so forth, but it's worth keeping in mind when you're deciding to optimize for defense or offense.

This is like my earlier post it really depends on your role. Are you damage Dealer or Damage Soaker? or both?

[Mandragola]

It also depends on who you are hitting. If you're hitting the wizard then your AC isn't relevant, only how much damage you deal is. A fair number of things you'll meet come under the category of casters (whether or not they actually cast spells) rather than melee brutes, and against all of them you want the greatsword.

Your character's mobility will influence whether you get to decide who you are hitting of course. A vengeance paladin with misty step can easily get to the wizard at the back but a fighter might struggle to.

I do think that GWM is what makes two-handers worth having though. Otherwise the damage increase really is kind of trivial, especially compared to duelist.

Another thing to remember with shields is that magic ones exist. Some of these just boost your AC more and others do cool things, like give you advantage on perception. So it's not only the 2 AC you should factor in - it's a "slot" for an interesting magic item.

[MeeposFire]

Ok, +4 Str is only really going to happen after an ASI at 4th level.

Your Crits don't double the Dueling Damage or the Str Damage, just the dice so Crits are only an additional 4.5 Damage for a Longsword and an additional +8.33 Damage for a Greatsword.

You can't use Great Weapon Mastery with a Longsword or with Shield Mastery. GWM requires a heavy two handed weapon, a longsword is not Heavy, and when using a shield it isn't even two handed.

Well not exactly the +10 damage requires a heavy weapon but the bonus action on a crit or drop does not. I will admit though that it would be unlikely that we are actually talking about the bonus action attack on crits and drops.

[the secret fire]

EDIT: slightly off topic, but it doesn't seem a big enough deal to start a new thread. Does anyone know the output string in AnyDice to get the odds of at least one 20 out of 4d20? I've read pretty much the whole site and can't seem to get it to work. :(

I'm not an expert in AnyDice commands, but that is a trivial percentage to calculate. Simply multiply the odds of a 20 not occurring to the 4th power. .95^4 = .8145. You have approximately an 81% chance of not rolling any 20s in any given set of four d20 rolls, or a 19% of rolling at least one.

[bid]

Ok then. So we know that the average damage of a Greatsword is ~8.2 with GWF style (IIRC). Average for a longsword with Dueling is ~6.5 damage, or 4.5 without Dueling.

So an increase of 1.7 average damage w/ Dueling or 3.7 average damage without Dueling.

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What I'm fuzzy on is how to calculate the reduction to damage taken from adding a shield to the mix, all else being equal.
You should compare the ratio.

greatsword = 2d6+3+4/3 = 11.3
longsword = 1d8+3+2 = 9.5
ratio = 1.189

Now, here's the trick: you want that +2 AC to give the same to-hit ratio as your damage ratio.

(hit+2/20)/hit = 1.189
hit + .1 = 1.189hit
.1 = .189hit
hit = .1 / .189 = 0.529
validating: 0.629 / 0.529 = 1.189

If you are hit 9+ and shield would bring it to 11+, both are close enough.


Now, you should get hit way less than that, making dueling much better. OTOH, you'd rather have them attack you than your squishy friends since you have more hp.