# How to determine if using the Great Weapon Master feat will increase DPR? [duplicate]

If I have the Great Weapon Master feat, how do I work out if using the -5 to hit and +10 damage gives more damage overall, given a certain AC, to hit, and damage bonus?

For example:

• I’m an Aasimar with Mounted Combatant feat for advantage and Great Weapon Master feat for -5 to hit and +10 to damage.
• My opponent has an AC of 16
• I have a normal “to hit” of +10 (thus +5 with GWM)
• My average damage bonus of +13 once the Aasimar racial hits (so +23 with GWM)

How do know what will do more damage overall? I know there is a way in Any-Dice to do this, but I’ve not found it.

Is it complicated by the fact that I get an entire extra attack (until Polearm Mastery) if I get a critical hit also?

• Hi Belfast. I edited your post to try to make it easier to read. If you dislike my changes feel free to roll them back or edit them further. – linksassin Jun 26 '19 at 1:38
• What does "damage bonus" here include and what is the Aasimar racial bonus? Also what damage dice does the weapon have, as the damage output of a crit varies by weapon. – Medix2 Jun 26 '19 at 4:34
• @Medix2 I assume they are referring to the 3rd level ability of each of the Aasimar subraces that add radiant/necrotic damage equal to your level 1/turn. – linksassin Jun 26 '19 at 5:11
• @Vigil Great Weapon Master offers you a bonus action extra attack if you critically hit or drop an enemy to 0 hp, which would have you one extra attack compared to your normal turn (until the character takes Polearm Master, at which point they will always be able to make a bonus action attack, though the one offered by GWF is better when available). – Carcer Jun 26 '19 at 11:20
• @Carcer that makes sense. Belfast Biker, do you have just a single attack per turn at the moment? That obviously affects whether your Aasimar damage bonus will apply to every attack or not. – Vigil Jun 26 '19 at 12:38

Here's an example anydice program which calculates the difference between the two styles of attack for a combatant using a glaive:

function: attack ATTACK:n AMOD:n AC:n DMG:d CRIT:d {
if ATTACK = 20 { result: DMG + CRIT }
if ATTACK + AMOD >= AC { result: DMG }
result: 0
}

output [attack 1@2d20 10 16 1d10+13 1d10] named "Glaive normal"
output [attack 1@2d20 5 16 1d10+23 1d10] named "Glaive GWF"
output [attack 1@2d20 5 16 1d10+23 1d10] - [attack 1@2d20 10 16 1d10+13 1d10] named "difference"


The way this works is that we define a function to calculate the results of an attack roll with the given parameters, and then invoke that function to compare the different scenarios. The function itself expects to be provided a d20 roll for attack, the attack's modifier, the target's AC, the damage done on a hit and the extra damage dealt by a crit.

Since you didn't specify which weapon you were using (but you mentioned polearm mastery), in this example I've chosen to use a glaive - you can obviously change those values as appropriate, and the choice of weapon is important, because the lower the base damage, the more significant the effect of GWF becomes. Your advantage is covered by rolling 2d20 and selecting the first die of the set using the 1@2d20 syntax, since anydice sorts rolled dice in descending order by default (this is functionally equivalent to using [highest 1 of 2d20] or [highest of 1d20 and 1d20]).

We can see from the resulting tables and graphs that the expected damage when using GWF in these circumstances is about 4 points better than not - but you're also significantly more likely to whiff completely when using GWF. For this hypothetical glaive wielder against the AC 16 foe, they're going to average better damage by using GWF than not.

GWF becomes less advantageous to use when you're doing more base damage, since as your base damage increases, the increased risk of missing entirely starts to offset the gain in expected damage. It also provides less benefit as your odds of hitting overall decrease, for the same reason - the turning point in this example is AC 19, at which point GWF style becomes a net negative. If you didn't have advantage on the attack, that drops to AC 17. Obviously, you can experiment with that by putting your own values in the script.

The other benefit of GWF, the bonus attack if you crit/drop an enemy to 0hp, doesn't influence whether or not you should use GWF if you have it, because you get that bonus attack regardless of whether you're currently using the damage bonus.

Once you've got Polearm Master, it might sometimes be the case that your optimal strategy is to make normal attacks with your Attack action but to use GWF on your bonus action Polearm Master attack, since it has a considerably lower base damage. The same might apply to additional attacks you get to make using Extra Attack or the GWF bonus attack, as some of your damage comes from features you can only use once a turn, so the calculation for those other attacks will be slightly different. Luckily you can choose whether or not to use the GWF bonus/penalty on each attack you make individually, rather than having to declare and then stick with it on all your attacks.

# Based on the specific parameters you've given, you're better off with the -5/+10 attack, period.

Since the -5/+10 attack option given by the Great Weapon Master feat requires the use of a heavy weapon, I ran the numbers with the highest-damaging and lowest-damaging heavy weapons as boundary conditions (greatsword/maul and glaive/halberd/pike, respectively).

With the conditions you're provided (net to-hit bonuses of +10 without power attack/+5 with power attack, average damage bonuses of +13 and +23, attacking with advantage, attacking against AC 16), I generated the following tables to calculate the expected value for each attack mode:

## Glaive/Halberd/Pike (expected damage on hit: 18.5 (crit 24) with regular, 28.5 (crit 34) with -5/+10)

$$\begin{array} {|r|r|r|r|} \hline d20 Result &Probability &Reg Attack Partial &Pow Attack Partial \\ \hline 1 &0.0025 &0 &0 \\ \hline 2 &0.0075 &0 &0 \\ \hline 3 &0.0125 &0 &0 \\ \hline 4 &0.0175 &0 &0 \\ \hline 5 &0.0225 &0 &0 \\ \hline 6 &0.0275 &0.50875 &0 \\ \hline 7 &0.0325 &0.60125 &0 \\ \hline 8 &0.0375 &0.69375 &0 \\ \hline 9 &0.0425 &0.78625 &0 \\ \hline 10 &0.0475 &0.87875 &0 \\ \hline 11 &0.0525 &0.97125 &1.49625 \\ \hline 12 &0.0575 &1.06375 &1.63875 \\ \hline 13 &0.0625 &1.15625 &1.78125 \\ \hline 14 &0.0675 &1.24875 &1.92375 \\ \hline 15 &0.0725 &1.34125 &2.06625 \\ \hline 16 &0.0775 &1.43375 &2.20875 \\ \hline 17 &0.0825 &1.52625 &2.35125 \\ \hline 18 &0.0875 &1.61875 &2.49375 \\ \hline 19 &0.0925 &1.71125 &2.63625 \\ \hline 20 &0.0975 &2.34 &3.315 \\ \hline Total Expected & &17.88 &21.91125 \\ \hline \end{array}$$

## Greatsword/Maul (expected damage on hit: 20 (crit 27) with regular, 30 (crit 37) with -5/+10)

$$\begin{array} {|r|r|r|r|} \hline d20 Result &Probability &Reg Attack Partial &Pow Attack Partial \\ \hline 1 &0.0025 &0 &0 \\ \hline 2 &0.0075 &0 &0 \\ \hline 3 &0.0125 &0 &0 \\ \hline 4 &0.0175 &0 &0 \\ \hline 5 &0.0225 &0 &0 \\ \hline 6 &0.0275 &0.55 &0 \\ \hline 7 &0.0325 &0.65 &0 \\ \hline 8 &0.0375 &0.75 &0 \\ \hline 9 &0.0425 &0.85 &0 \\ \hline 10 &0.0475 &0.95 &0 \\ \hline 11 &0.0525 &1.05 &1.575 \\ \hline 12 &0.0575 &1.15 &1.725 \\ \hline 13 &0.0625 &1.25 &1.875 \\ \hline 14 &0.0675 &1.35 &2.025 \\ \hline 15 &0.0725 &1.45 &2.175 \\ \hline 16 &0.0775 &1.55 &2.325 \\ \hline 17 &0.0825 &1.65 &2.475 \\ \hline 18 &0.0875 &1.75 &2.625 \\ \hline 19 &0.0925 &1.85 &2.775 \\ \hline 20 &0.0975 &2.6325 &3.6075 \\ \hline Total Expected & &19.4325 &23.1825 \\ \hline \end{array}$$

In both cases, you're better off using your -5/+10 power attack.

# Extrapolating to other AC values

Since I initially generated the tables in Excel, I was able to handle this with formulas and also look into the question of at what enemy AC values you're better off with regular attacks versus power attacks. With the business end of the weapon, you're better off with regular attacks against AC values from 20 to 29 inclusive. At AC 30 you'll only hit on a 20 with both types of attack, so you're better off with power attack, and below AC 20, you're hitting reliably enough that power attack is the better call. With the Polearm Master bonus action attack (glaive/halberd), you're better off with regular bonus action attacks against AC values from 21 to 29 inclusive. Once again, at AC 30 you'll only hit on a 20 with both types of attack, so you're better off with power attack.