So I was min-maxing my new character as I usually do and stumbled upon a question - is Great Weapon Master feat worth it?
Assumptions Just for the sake of simplicity, we will assume that we don't use feat's bonus attack actions when critical hitting and killing monsters. We will also assume we use every action to attack with -5 penalty for +10 damage with a normal attack without advantage or disadvantage.
Formula I derived a quick formula for calculating the ratio of damage with -5 penalty attack and normal attack. The formula also takes into account critical rolls:
c -> chance of a hit. For example, Monster has AC 15, and you have +8 to attack. That means you will hit a monster on a 7+ roll, which translates to 14/20 chance to hit. d -> average die roll. For example, d10 has an average roll of 5.5. m -> damage modifier
Graph I used an online graph calculator (https://www.symbolab.com/) to check how damage is scaling depending on the hit chance. To get some reference points, I made 2 scenarios. For both, I used Glaive weapon with d10 die (I have taken into account Great Weapon Fighting style for average die roll). I also took a +5 damage modifier for the first scenario (light line), and +0 modifier for the second scenario (dark line).
By reading a graph we can see that in order to increase damage on Glaive with +5 damage modifier (light line), we will need to have more than a 55% chance of hitting the target (before we apply -5 penalty). To put it this way: every attack would need to be able to hit a target with a d20 roll of 10+ or else we would actually deal less damage than without using it. From there on it scales quite nicely. If you would hit with a roll of 8+ it would increase your damage output by 15%, on 6+ it would increase by 25%. It maxes out on a 40% damage if every roll is a hit.
The second scenario, with Glaive and +0 modifier (dark line), shows how damage output changes with a decrease of damage dice modifier (due to some possible in-game effects), but it assumes attack die modifier remains the same. In that example, we can see that damage scales even faster the lower damage modifier is.
How does it scale with monsters Assuming a player has a +5 modifier on damage rolls from an early level, and by comparing average monster's AC per player's average attack modifier at certain levels, I have roughly estimated that constantly using a -5 penalty and +10 damage from Great Weapon Master feat can increase average damage output by 5%-15% while fighting level appropriate bosses, and 15-25% while fighting level appropriate normal monsters. Having an advantage on those attacks can rise damage up to 20-30% for both bosses and normal monsters. Constant use of feat when having a disadvantage on attack or when fighting abnormally strong AC monsters, can, on the other hand, cause loss of damage.
Conclusion Generally, even though it sounds counter-intuitive, if you could hit a monster by rolling 10 or more on your d20 dice, you might be better of taking -5 penalty and +10 damage. This does fluctuate depending on your damage modifier, bigger damage modifier your attack has, the more room for the hit you want and vice versa (e.g. at low level you might want to use it even when you have to roll 11+, while in higher levels you might be better of with 9+).
Also, I have to repeat that calculations do not include a bonus attack from the feat. If you don't have any other bonus action that deals damage, then taking a bonus attack from this feat every time you score critical hit also increases your average damage output by another 5%.
So to answer the question, I would recommend taking this feat if you are looking for a way to maximize damage output with basic attacks. You should be able to get an increase of damage just by activating the -5 penalty on your every attack (unless you have a disadvantage). There are exceptions when monsters will have so high AC that the use of -5 penalty will have negative consequences on your damage, but such instances are rare.
GWM and Sharpshooter are certainly great! But Sharpshooter is better, simply because 1) the other features of Sharpshooter all help you have a higher to-hit bonus, which feeds directly into the payoff of this feat, while GWM's other features are more situational, compete with other class features, and likely to trigger without a valid target; and 2) Archery Fighting style feeds into and enhances your break even point of where the feat pays out with its +2 to hit, while Great Weapon Fighting style doesn't help the feat's math in any way.
But both feats are excellent and "must have's" for a character built to use that weapon. Which has always kind of bugged me, because by and large dropping "feat tax" was a major design element of 5E, and its odd to see a feat that really doesn't do much cool other than making your math better.
That is a great analysis. As soon as I get someone to explain the math to me I am sure it will be even cooler and more impressive.
I am a little confused and do have a question.
When you say ". . . bigger damage modifier your attack has, the more room for the hit you want. . ." by "hit you want" are you referring to the total damage you want or hitting/critting the opponent vs missing them?
GWM is super great against mooks (weak monsters). The bonus action hit on a kill or crit really pumps it up as well. If you are playing a barb and have reckless it's especially handy as you won't be getting more attacks after 5th lvl. As almost all monsters are suspiciously low AC compared to the PCs it really is a superpowerful feat, same goes for sharpshooter.
However.
You know what DOES have a high AC? Big bads. Whether they're dragons or liches they just don't seem to like having an AC below 20 (the lich has shield). Which isn't weird considering any idiot with a str of 15 can do it with plate and a shield. So against them you won't be using it much. That said, they usually come with a ton of minions and if you're fine being the one who runs around squishing them, well, somebody's gotta do it. Builds with a higher to-hit definitely get more dmg than people think due to the fact that they don't miss all the time. Personally having done both gwm and ss I'm really into finding other ways to bring the dmg now. Another important consideration is your brawler's real job isn't actually damage (the mage and rogue do that), your job is control. Specifically the kind of control that comes from sitting right in front of the big bad so they have to hit your high AC or rage hp. Also grabbing anyone with a low grapple escape and dragging them into the mage's AOE. Or proning them so everybody else can pile on. Or proning and grappling them so they can't get up. All of these are super important brawler jobs and gwm gets in the way of them all. Just sayin'. OK except for shoving them prone with your first attack so you can GWM them with the second everybody else loves that.
I think I am missing something, but how does GWM interfere with shoving or grappling? You have to decide to use GWM before every attack. Plus, shove isn't a valid target for GWM.
***EDIT*** I can see the argument for a grapple being a legal target for GWM, but can't think of a single case where you would ever want to target your grapple attack with GWM since your grapple doesn't deal any damage. ***END EDIT***
Shoving works great with two handed weapons. Nobody seems to remember that you can hold a two handed weapon in one hand while you use the other hand to do stuff. Grappling is a different story. If you grapple a troll to hold it in somebody's aoe spell, you now have to drop your two hander on the ground (free action), draw your one handed backup weapon (object interract), and then attack with no GWM. Which means spending that ASI on str or con would have been better. If you don't like to grapple monsters GWM is great, and good grapple and drag opportunities don't come along so often that GWM is a problem if you do want to grapple, you just don't get to use it that turn.
It's just that lately I'm noticing that battlefield control is very underestimated in DND compared to DPR, and the battlefield's power is even bigger now that everybody is using virtual tabletops. Even a theater of the mind DM lays out each fight a certain way and with specific big spells or terrain effects going off. Move the monsters and players around and their whole battle plan goes out the window. Drag a mook one space forward then run to where they were standing (still grappling!) - now the villain who dropped their big bad aoe spell on you last round has to recast it or kill their own guy. Who are we kidding they don't care;) Did the DM download a cool map with a neat magic swirl in the middle of it? Good thing I'm a rune knight. Lemme just grow to Large then you cast enlarge on me and let's see happens when I drag the dragon over then shove em in. PS - you DON'T need a free hand to make an unarmed attack (kicks, bites etc). This is useful if grappling and using the shield master feat (for dragons) to knock people down. Prone grappled people hit you with disadvantage and can't get up, but you can drag em around the same so prone BEFORE you grapple because you need a free hand for the shove, unless you have a sneaky trick like shield master.
So I was min-maxing my new character as I usually do and stumbled upon a question - is Great Weapon Master feat worth it?
Assumptions
Just for the sake of simplicity, we will assume that we don't use feat's bonus attack actions when critical hitting and killing monsters.
We will also assume we use every action to attack with -5 penalty for +10 damage with a normal attack without advantage or disadvantage.
Formula
I derived a quick formula for calculating the ratio of damage with -5 penalty attack and normal attack. The formula also takes into account critical rolls:
c -> chance of a hit. For example, Monster has AC 15, and you have +8 to attack. That means you will hit a monster on a 7+ roll, which translates to 14/20 chance to hit.
d -> average die roll. For example, d10 has an average roll of 5.5.
m -> damage modifier
Graph
I used an online graph calculator (https://www.symbolab.com/) to check how damage is scaling depending on the hit chance.
To get some reference points, I made 2 scenarios. For both, I used Glaive weapon with d10 die (I have taken into account Great Weapon Fighting style for average die roll). I also took a +5 damage modifier for the first scenario (light line), and +0 modifier for the second scenario (dark line).
By reading a graph we can see that in order to increase damage on Glaive with +5 damage modifier (light line), we will need to have more than a 55% chance of hitting the target (before we apply -5 penalty). To put it this way: every attack would need to be able to hit a target with a d20 roll of 10+ or else we would actually deal less damage than without using it. From there on it scales quite nicely. If you would hit with a roll of 8+ it would increase your damage output by 15%, on 6+ it would increase by 25%. It maxes out on a 40% damage if every roll is a hit.
The second scenario, with Glaive and +0 modifier (dark line), shows how damage output changes with a decrease of damage dice modifier (due to some possible in-game effects), but it assumes attack die modifier remains the same. In that example, we can see that damage scales even faster the lower damage modifier is.
How does it scale with monsters
Assuming a player has a +5 modifier on damage rolls from an early level, and by comparing average monster's AC per player's average attack modifier at certain levels, I have roughly estimated that constantly using a -5 penalty and +10 damage from Great Weapon Master feat can increase average damage output by 5%-15% while fighting level appropriate bosses, and 15-25% while fighting level appropriate normal monsters. Having an advantage on those attacks can rise damage up to 20-30% for both bosses and normal monsters. Constant use of feat when having a disadvantage on attack or when fighting abnormally strong AC monsters, can, on the other hand, cause loss of damage.
Conclusion
Generally, even though it sounds counter-intuitive, if you could hit a monster by rolling 10 or more on your d20 dice, you might be better of taking -5 penalty and +10 damage. This does fluctuate depending on your damage modifier, bigger damage modifier your attack has, the more room for the hit you want and vice versa (e.g. at low level you might want to use it even when you have to roll 11+, while in higher levels you might be better of with 9+).
Also, I have to repeat that calculations do not include a bonus attack from the feat. If you don't have any other bonus action that deals damage, then taking a bonus attack from this feat every time you score critical hit also increases your average damage output by another 5%.
So to answer the question, I would recommend taking this feat if you are looking for a way to maximize damage output with basic attacks. You should be able to get an increase of damage just by activating the -5 penalty on your every attack (unless you have a disadvantage). There are exceptions when monsters will have so high AC that the use of -5 penalty will have negative consequences on your damage, but such instances are rare.
Printable stuff: Equipment Sheet, Battle Grid
Honourable posts: Great Weapon Master - is it worth it?
So... Yes?
I draw the line at using any math that requires a graphing or scientific calculator. Once it gets that far, too much of the fun is lost.
I'm very impressed by your analysis! Nice work!
Partway through the quest for absolute truth.
For you. I personally find maths extremely interesting and fun so I like things like this.
I mean - I'll ignore the results and just choose whatever fits my character thematically - but still.
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GWM and Sharpshooter are certainly great! But Sharpshooter is better, simply because 1) the other features of Sharpshooter all help you have a higher to-hit bonus, which feeds directly into the payoff of this feat, while GWM's other features are more situational, compete with other class features, and likely to trigger without a valid target; and 2) Archery Fighting style feeds into and enhances your break even point of where the feat pays out with its +2 to hit, while Great Weapon Fighting style doesn't help the feat's math in any way.
But both feats are excellent and "must have's" for a character built to use that weapon. Which has always kind of bugged me, because by and large dropping "feat tax" was a major design element of 5E, and its odd to see a feat that really doesn't do much cool other than making your math better.
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I'm going to make this way harder than it needs to be.
That is a great analysis. As soon as I get someone to explain the math to me I am sure it will be even cooler and more impressive.
I am a little confused and do have a question.
When you say ". . . bigger damage modifier your attack has, the more room for the hit you want. . ." by "hit you want" are you referring to the total damage you want or hitting/critting the opponent vs missing them?
GWM is super great against mooks (weak monsters). The bonus action hit on a kill or crit really pumps it up as well. If you are playing a barb and have reckless it's especially handy as you won't be getting more attacks after 5th lvl. As almost all monsters are suspiciously low AC compared to the PCs it really is a superpowerful feat, same goes for sharpshooter.
However.
You know what DOES have a high AC? Big bads. Whether they're dragons or liches they just don't seem to like having an AC below 20 (the lich has shield). Which isn't weird considering any idiot with a str of 15 can do it with plate and a shield. So against them you won't be using it much. That said, they usually come with a ton of minions and if you're fine being the one who runs around squishing them, well, somebody's gotta do it. Builds with a higher to-hit definitely get more dmg than people think due to the fact that they don't miss all the time. Personally having done both gwm and ss I'm really into finding other ways to bring the dmg now. Another important consideration is your brawler's real job isn't actually damage (the mage and rogue do that), your job is control. Specifically the kind of control that comes from sitting right in front of the big bad so they have to hit your high AC or rage hp. Also grabbing anyone with a low grapple escape and dragging them into the mage's AOE. Or proning them so everybody else can pile on. Or proning and grappling them so they can't get up. All of these are super important brawler jobs and gwm gets in the way of them all. Just sayin'.
OK except for shoving them prone with your first attack so you can GWM them with the second everybody else loves that.
I think I am missing something, but how does GWM interfere with shoving or grappling? You have to decide to use GWM before every attack. Plus, shove isn't a valid target for GWM.
***EDIT*** I can see the argument for a grapple being a legal target for GWM, but can't think of a single case where you would ever want to target your grapple attack with GWM since your grapple doesn't deal any damage. ***END EDIT***
Shoving works great with two handed weapons. Nobody seems to remember that you can hold a two handed weapon in one hand while you use the other hand to do stuff. Grappling is a different story. If you grapple a troll to hold it in somebody's aoe spell, you now have to drop your two hander on the ground (free action), draw your one handed backup weapon (object interract), and then attack with no GWM. Which means spending that ASI on str or con would have been better. If you don't like to grapple monsters GWM is great, and good grapple and drag opportunities don't come along so often that GWM is a problem if you do want to grapple, you just don't get to use it that turn.
It's just that lately I'm noticing that battlefield control is very underestimated in DND compared to DPR, and the battlefield's power is even bigger now that everybody is using virtual tabletops. Even a theater of the mind DM lays out each fight a certain way and with specific big spells or terrain effects going off. Move the monsters and players around and their whole battle plan goes out the window. Drag a mook one space forward then run to where they were standing (still grappling!) - now the villain who dropped their big bad aoe spell on you last round has to recast it or kill their own guy. Who are we kidding they don't care;) Did the DM download a cool map with a neat magic swirl in the middle of it? Good thing I'm a rune knight. Lemme just grow to Large then you cast enlarge on me and let's see happens when I drag the dragon over then shove em in.
PS - you DON'T need a free hand to make an unarmed attack (kicks, bites etc). This is useful if grappling and using the shield master feat (for dragons) to knock people down. Prone grappled people hit you with disadvantage and can't get up, but you can drag em around the same so prone BEFORE you grapple because you need a free hand for the shove, unless you have a sneaky trick like shield master.