Asisreo
Patron Badass
(This is about the 2024 version of GWF)
I'm sure many immediate reactions to the title would be "What is this poster talking about? The calculations have been done ad nauseam and its clear that GWF doesn't hold up to snuff." And while I too was under the impression that the math was solid and undeniable, I recently wondered about the assumptions behind the theory that was used to come up with this conclusion.
To start, let's review how averages work in probability when you have dice rolls. In order to calculate a dice roll, we can use the formula A = k+1/2 where A is the dice average and k is the highest possible roll on that dice. This average is also referred to as the "Expected Value" because we expect all of the values to equal this number given a large enough number of samples in a population. None of this is new under the sun, and if you were ever interested in the math behind D&D, this is one of the first concepts you encounter. Using this concept, we can easily visualize the difference between, say, a 1d4 and a 1d6, that being a +1 average expected value. The same is seen if you were to compare a 1d4 to 1d4+1. But I want to highlight that these two things are not the same. And to highlight it more greatly, let's say there's one warrior with a regular greatsword that does 2d6, then we'll say there's a warrior with a magic greatsword that does 2d6+1 damage (no accuracy bonus, in order to keep it neglible). The magic warrior obviously does +1 average damage, again, that's to be expected. But let's say he trades it in and for a greatsword that does 2d8 damage. The damage difference is not +1, rather it's +2. We can easily calculate this: The regular greatsword is 2 * (6+1/2) = 7, where the magic greatsword is 2 * (8+1/2) = 9.
Now, clearly the difference from 1d6 to 1d8 is 1 damage, yet that difference was doubled because we have two dice. These averages actually add up, which might be counterintuitive because we expect rolling more dice only to reinforce the original expected value. But we do not actually care about expected value, we care about damage. And because we're totaling the result, the expected value of each die is totaled as well. To frame it a different way, think about the +1 greatsword. In the total dice rolled, you see a +1 bonus, but if you actually calculate the bonus for each die you get a +.5 bonus each. Now, you may have just noticed, but the same thing happens when you use GWF. The dice itself changes to have an average similar to if you simply added +0.5 to expected value.
In essence, GWF actually gives you the equivalent of +1 damage per attack when you take it. It's just a roundabout way to give it. Now, I do want to clear up that GWF is still worse on 1d10 and 1d12 weapons, and it still is worse than the 2014 version which does +1.32 extra damage per attack. But it is not merely a +0.5 average increase on a greatsword, its a +1 increase. And +1 damage tends to be more respected among players and, in my opinion, can actually be a worthwhile feature for those wanting to maxmize damage as you'd already want to use a great sword if you're going for optimal damage as a martial.
I'm sure many immediate reactions to the title would be "What is this poster talking about? The calculations have been done ad nauseam and its clear that GWF doesn't hold up to snuff." And while I too was under the impression that the math was solid and undeniable, I recently wondered about the assumptions behind the theory that was used to come up with this conclusion.
To start, let's review how averages work in probability when you have dice rolls. In order to calculate a dice roll, we can use the formula A = k+1/2 where A is the dice average and k is the highest possible roll on that dice. This average is also referred to as the "Expected Value" because we expect all of the values to equal this number given a large enough number of samples in a population. None of this is new under the sun, and if you were ever interested in the math behind D&D, this is one of the first concepts you encounter. Using this concept, we can easily visualize the difference between, say, a 1d4 and a 1d6, that being a +1 average expected value. The same is seen if you were to compare a 1d4 to 1d4+1. But I want to highlight that these two things are not the same. And to highlight it more greatly, let's say there's one warrior with a regular greatsword that does 2d6, then we'll say there's a warrior with a magic greatsword that does 2d6+1 damage (no accuracy bonus, in order to keep it neglible). The magic warrior obviously does +1 average damage, again, that's to be expected. But let's say he trades it in and for a greatsword that does 2d8 damage. The damage difference is not +1, rather it's +2. We can easily calculate this: The regular greatsword is 2 * (6+1/2) = 7, where the magic greatsword is 2 * (8+1/2) = 9.
Now, clearly the difference from 1d6 to 1d8 is 1 damage, yet that difference was doubled because we have two dice. These averages actually add up, which might be counterintuitive because we expect rolling more dice only to reinforce the original expected value. But we do not actually care about expected value, we care about damage. And because we're totaling the result, the expected value of each die is totaled as well. To frame it a different way, think about the +1 greatsword. In the total dice rolled, you see a +1 bonus, but if you actually calculate the bonus for each die you get a +.5 bonus each. Now, you may have just noticed, but the same thing happens when you use GWF. The dice itself changes to have an average similar to if you simply added +0.5 to expected value.
In essence, GWF actually gives you the equivalent of +1 damage per attack when you take it. It's just a roundabout way to give it. Now, I do want to clear up that GWF is still worse on 1d10 and 1d12 weapons, and it still is worse than the 2014 version which does +1.32 extra damage per attack. But it is not merely a +0.5 average increase on a greatsword, its a +1 increase. And +1 damage tends to be more respected among players and, in my opinion, can actually be a worthwhile feature for those wanting to maxmize damage as you'd already want to use a great sword if you're going for optimal damage as a martial.
