D&D 5E Great Weapon Mastery - once more into the breach! (with math)

[Hillsy7]

Can you help me out with your math? I think I did not understand it. Let's say I have a D of 10 and H is 0.5. This results in a ratio of 20. If I take GWM and use it, D goes to 20 but H drops to 0.25, right? And in both cases, average damage would be 5. But taking the ABI would raise D to 11 and H to 0.55, also raising average damage to 6.05, and the conclusion I get is not aligned to yours.

Actually, by fixing D at 10 and varying H from 0.3 to 0.95 (so to avoid saturation) and checking the results for which GWM or ABI would be better, then fixing H at 0.75 and varying D from 5 to 20 and doing the same check, I was not able to define a single ratio to be the break even. In the first case, the tie would occur at a ratio around 16, while in the latter, it was 14.

Algebraically (?) He is correct - if you take the comparison between the two values of damage per Short Rest of D*A*R*C*H (where A=Attack per Round, D=Damage, R=Rounds per Combat, C=Combat per Short Rest, and H=Chance to Hit) and compare GWM vs +1 ASI - you get the following equation

GWM is Better......
Where D*A*R*C*H (GWM) > D*A*R*C*H(+1 ASI)
[A, R, & C are equal on both sides so remove and add modifiers for GWM and +1 ASI]
Where (D+10)*(H-0.25) > (D+1)*(H+0.05)
[Simplify]
Where (D+9)*(H-0.3) > D*H
[Simplify]
Where DH+9H-0.3D-0.27 > DH
[Subtract DH and Add 0.27 and Times 100]
Where 900H-30D > 27
[Divide Both Side by 30 And Round up, because ain't nobody got time for 27/30]
Where 30H-D>0
[Add D to both sides]
Where 30H>D

or to complete the full statement
GWM is better where your Damage per attack is 30 times greater than Your Chance to Hit (30H>D)

This of course assumes no advantage, trivial or impossible to hit requirements (Due to extremely high/low AC), and using GWM at all times

 

[Datalore]

This confuses me. How do we make those unique character choices if we drop the feats and multiclassing we used to make those unique character choices?

Two players of different classes using the same feat are less unique than two players of different classes relying on their own class abilities.

It's not about the uniqueness of a particular build but instead of a player within a larger party.

The more homogenized parties get (through shared abilities thanks to feats or multiclassing), the less unique they are. Again, look at a system like Savage Worlds. Totally classless. One would assume, wow, I can make such a unique character. In the end, though, characters feel pretty samey (especially as they advance) since party members often share various abilities.

Again, the strength of class based systems are the limits they impose.

If a wizard dips fighter to get heavy armor profiency, for example, that makes him very similar to the heavily armored folks. He is no longer the guy who relies on mage armor and defensive spells. He is more same. Sure, he pays for it a bit. I am not disputing that. But he is less unique than he used to be.

Other examples abound. What you call "unique", I call boring. It's a munchkinny hybridization of the game that goes against the strengths of a class based game and gives you a bunch of characters who play more similarly to each Other than differently from each Other. Similarly, if characters all go for similar feats that they "build around", that similarly homogenizes the game and makes characters play more the same than different. That, to me, is less dynamic and more ho-hum.

 

[FrogReaver]

I think his equation was to originally solve the issue of using gwm -5/+10 or not using it all other things being equal. I think he is misapplying his technique to this discussion..

Must have been a different equation before. I calculated his. It is correct. However he still needs a chart for his as his chance to hit varies based on monster ac. It also doesn't directly tell us how much better one method is than the other..

I'm really not seeing the benefits for analysis purposes..

i also wonder about about how his method could handle advantage..

 

[Hillsy7]

Must have been a different equation before. I calculated his. It is correct. However he still needs a chart for his as his chance to hit varies based on monster ac. It also doesn't directly tell us how much better one method is than the other..

I'm really not seeing the benefits for analysis purposes..

i also wonder about about how his method could handle advantage..

Well....It's sort of implied in the calculation when determining H and D

But yes, a chart would be easier to use (Or a handy graph) to locate the AC at which GWM and +1 ASI are equal.

Advantage gets a bit more ball-achey as the probability for rolling a specific value with advantage is (2n-1)*0.25%, so I think it might need factorals (!) which was never my strong suit......

 

[Satyrn]

Two players of different classes using the same feat are less unique than two players of different classes relying on their own class abilities.

Are you confusing me with someone else here? None of the characters at my table share the same feats.

 

[Barolo]

(...)

I really should have explained it better: D and H don't represent the values as if the feat/ASI don't exist. They represent the values that D and H have in common before the feat/ASI differentiate them.

Oh, thanks, that clarifies the point. So you actually have to do one step with the values you have prior to applying either ABI or feat, in order to calculate the ratio. And this step includes adding the +1 dmg from ABI to your base damage (which becomes the D in your formula) and subtracting the -5 (0.25) penalty to hit from GWM to your assumed accuracy (which becomes the H in the formula).

Algebraically (?) He is correct - if you take the comparison between the two values of damage per Short Rest of D*A*R*C*H (where A=Attack per Round, D=Damage, R=Rounds per Combat, C=Combat per Short Rest, and H=Chance to Hit) and compare GWM vs +1 ASI - you get the following equation

GWM is Better......
Where D*A*R*C*H (GWM) > D*A*R*C*H(+1 ASI)
[A, R, & C are equal on both sides so remove and add modifiers for GWM and +1 ASI]
Where (D+10)*(H-0.25) > (D+1)*(H+0.05)
[Simplify]
Where (D+9)*(H-0.3) > D*H
[Simplify]
Where DH+9H-0.3D-0.27 > DH
[Subtract DH and Add 0.27 and Times 100]
Where 900H-30D > 27
[Divide Both Side by 30 And Round up, because ain't nobody got time for 27/30]
Where 30H-D>0
[Add D to both sides]
Where 30H>D

or to complete the full statement
GWM is better where your Damage per attack is 30 times greater than Your Chance to Hit (30H>D)

This of course assumes no advantage, trivial or impossible to hit requirements (Due to extremely high/low AC), and using GWM at all times

Well, yes, Ganymede81's algebra is correct. Yours, on the other hand, does not seem so. At least not on the step I marked red. Ganymede81's result does not need rounding.

 

[Yunru]

It's not about the uniqueness of a particular build but instead of a player within a larger party.

A Tempest Cleric and a Dragon Sorcerer both take Elemental Affinity (Adept?), and yet they play completely different.

A Death Cleric takes Magic Initiate (Cleric), and plays very differently from the Fighter who did the same.

A two-weapon Ranger takes Dual Wielder, and is different from the dagger-throwing Rogue that does likewise.

The Shield Master stabby Rogue is a different beast from the Shield Master swishy Fighter.

Hell, the Great Weapon Master Battle Master who calculates every attack is different to the Great Weapon Master Barbarian who roars and recklessly charges forth.

I could go on?

 

[Datalore]

Are you confusing me with someone else here? None of the characters at my table share the same feats.

I don't pretend to know your table. I am speaking to the overarching effect of allowing characters to define their characters with a either a fix set of poorly balanced feats or by overhybridizing their character with class dips.

Again, not all of us feel the need to use the OPTIONAL rules included with 5e to define our characters. While you seem to believe they make your characters unique, I see these options as making characters more vanilla. That's all my post is meant to convey. If you disagree, so be it.

Ultimately, I have played the game with and without these options. I can only say that characters and campaigns have been both more memorable and enjoyable without these optional rules in play.

 

[Yunru]

Well, yes, Ganymede81's algebra is correct. Yours, on the other hand, does not seem so. At least not on the step I marked red. Ganymede81's result does not need rounding.

Damn you for pointing that out! It makes my inner mathematician cringe. You can't just cancel out a +1 inside a brackets with a -1 on the other side of the equation! D:
[MENTION=6689191]Hillsy7[/MENTION]
Before you simplify I advise you expand your damn brackets.

(D+10)*(H-0.25) > (D+1)*(H+0.05)
Goes to:
DH-0.25D+10H-2.5 > DH+0.05D+H+0.05

Which then you can simplify.

DH-0.25D+10H-2.5 > DH+0.05D+H+0.05
Goes to:
9H-0.2D-2.55 > 0

 

[Hillsy7]

Damn you for pointing that out! It makes my inner mathematician cringe. You can't just cancel out a +1 inside a brackets with a -1 on the other side of the equation! D:
[MENTION=6689191]Hillsy7[/MENTION]
Before you simplify I advise you expand your damn brackets.

(D+10)*(H-0.25) > (D+1)*(H+0.05)
Goes to:
DH-0.25D+10H-2.5 > DH+0.05D+H+0.05

Which then you can simplify.

DH-0.25D+10H-2.5 > DH+0.05D+H+0.05
Goes to:
9H-0.2D-2.55 > 0

Aye....spotted that waaaay too late. Awful schoolboy error

I'll happily eat 3d10 algebra damage....