D&D 5E Quick Great Weapon Style math question

[Mouseferatu]

Given that a number of people feel the "reroll if you roll a 1 or 2 on a damage die" bit can slow things down, is there any solid mathematical reason not to change that to "treat any rolls of 1 or 2 on your damage die as if you'd rolled the average for that die"?

I know it's not going to average exactly the same, but am I correct in thinking it ought to be near enough for most practical purposes? Do you see any hidden downsides? (I'm foolishly posting this after 4 AM, so if I'm overlooking anything blatantly obvious, I blame sleep deprivation.)

(And yes, I realize that this leads to a situation where it's better--for instance--for certain characters to roll a 2 than it is a 5 on a greataxe. But I'm not necessarily opposed to that, given that the die roll is an abstraction.)

 

[fewilcox]

Whenever I used a brutal weapon in 4e I simply changed the math to remove the reroll. Once again my chronic pain issues ruled my life. I remember having something that was 1d10 brutal 2, so the GM let me roll 1d8+2 instead. Heck of a lot easier.

 

[Staffan]

Well, one issue is that the average of a single even-sided die is something.5 - 6.5 for a greataxe for example. That could complicate things, depending on how you interpret the rule. One method would be to have 1s be average round down, and 2s round up - so a 1 on a greataxe would be a 6, and a 2 a 5. The other would of course be to just say "half max" or "half max+1", and be done with it.

The other issue would be: is that really faster? In the regular rules, you go "Oh, a 1 - I reroll". In these, you go "Oh, a 1, and I'm using a d10 weapon, which is 5.5 on average, so 5 rounded down."

 

[Shiroiken]

Given that a number of people feel the "reroll if you roll a 1 or 2 on a damage die" bit can slow things down,

If this is actually an issue, I'd suggest you roll all weapon dice twice (with different colors, of course), so that you don't have to fiddle with re-rolling. This assumes you always choose to re-roll (which everyone I've seen with the feature has chosen to do). It could get a bit out of hand if you have lots of additional dice (2d6 weapon with smite and divine favor for example), but in those cases just counting the dice is going to slow things down...

 

[Sword of Spirit]

The major problem that I have with the feature is that it doesn't play nice with the digital dice cups I'm using in my VTT. Re-rolls are just annoying all around. Whenever a crit is rolled, I have them roll twice and add just the roll result from one of the rolls (since the results tell us both the die roll and the sum with modifiers). Doing the mental math for that is annoying enough as-is. Needing to have an extra "Great Weapon Style Re-roll" dice cup with a couple d6s in it, and then have the player have to click that and then figure out which of the numbers get used based on the rules in the PHB is going to be a pain when it comes up.

 

[nomotog]

Use a smaller die and then just add 2 directly to it. From 1d8 to 1d6+2. That would get you about the same?

 

[Quickleaf]

Given that a number of people feel the "reroll if you roll a 1 or 2 on a damage die" bit can slow things down, is there any solid mathematical reason not to change that to "treat any rolls of 1 or 2 on your damage die as if you'd rolled the average for that die"?

I know it's not going to average exactly the same, but am I correct in thinking it ought to be near enough for most practical purposes? Do you see any hidden downsides? (I'm foolishly posting this after 4 AM, so if I'm overlooking anything blatantly obvious, I blame sleep deprivation.)

I think you're on sound math doing this. I mean if you were running the probabilities, you would assume a statistical average for the re-rolled damage dice anyhow, wouldn't you? I think the maths are more complex than I'm making them, but I’ll do my best. Note: I am not a professional statistician.

The only question is if this gives an unfair advantage to certain weapons. I'm thinking greatsword/greataxe (2d6 damage, avg 7, so rolling a '1' isn't possible) vs. a reach/versatile weapon (1d10 damage, avg 5.5).

According to my dirty maths:

Great Weapon Expert with greatsword/greataxe gives you a net +0.2777 damage bonus per round.

[SBLOCK=Greatsword/greataxe Maths]
Let’s say your average PC taking the Great Weapon Expertise feat is likely to use a greatsword or greataxe which deals 2d6 damage.

The odds of rolling a 2 (1, of course, is impossible) on 2d6 is 2.77% each time you roll.

Usually we do DPR (damage-per-round) calculations for monsters over 3 rounds, so let’s do the same here. Also, let’s assume that the character with this feat is making two attacks per round, so either they are 5th level with Extra Attack, make an opportunity attack, or have haste cast on them; I think that’s a pretty reasonable assumption.

So two attacks per round, over the course of 3 rounds - what are the odds of rolling a 2?

2.77% * 6 = 16.62%

This means that in about 1 out of every 6 combats (which we’re assuming last 3 rounds each) you’re going to see a 2 rolled on 2d6 (statistically speaking).

And we’re going to assume that when you re-roll your 2d6 you get a statistically average result of 7.

Which works out to getting a +5 bonus to damage (from a 2 to a 7) once every 6 combats, or once every 18 rounds.

And that works out to getting a +0.27777 bonus to damage each round.[/SBLOCK]

Great Weapon Expert with a reach/versatile weapon gives you a net +0.26666 damage bonus each round.

[SBLOCK=Reach/versatile weapon Maths]
Now the same situation, but they’re wielding a reach weapon or a versatile weapon in two hands which deals 1d10 damage.

The odds of rolling a 1 or 2 on 1d10 is 20%.

So two attacks per round, over the course of 3 rounds - what are the odds of rolling a 1 or 2?

20% * 6 = 120%

This means that in 1 out of every 5 combats (which we’re assuming last 3 rounds each) you’re going to see a 1 or 2 rolled on 1d10 (statistically speaking).

And we’re going to assume that when you re-roll your 1d10 you get a statistically average result of 5.5.

Which works out to getting a +4 bonus to damage (from a 1.5 to a 5.5) once every 5 combats, or once every 15 rounds.

And that works out to getting a +0.2666 bonus to damage each round.[/SBLOCK]

 

[Rune]

Using a smaller die and adding 2 worked in 4e because 1s and/or 2s for brutal weapons could be rolled over and over again until they were something else.

In 5e, you're stuck with the result. The math isn't the same.

 

[The Human Target]

Its fun for the players who choose it.

5e combat is already blazingly fast.

Its important to remember- they can only reroll once. That second roll stays, even if it is a 1 or 2. Its not like brutal in 4e.

Changing a d10 great weapon to a d8+2 increases its power.

Leave as is.

 

[Staffan]

I think you're on sound math doing this. I mean if you were running the probabilities, you would assume a statistical average for the re-rolled damage dice anyhow, wouldn't you? I think the maths are more complex than I'm making them, but I’ll do my best. Note: I am not a professional statistician.

The only question is if this gives an unfair advantage to certain weapons. I'm thinking greatsword/greataxe (2d6 damage, avg 7, so rolling a '1' isn't possible) vs. a reach/versatile weapon (1d10 damage, avg 5.5).

Great Weapon fighting style works on a per-die basis, not per-roll. So a greatsword-user would reroll any 1s and 2s on either die, not just dice that sum to 1 (which is of course impossible) or 2. So the greatsword has an average increase of 1 1/3 (each die goes from 3 1/2 to 4 1/6 which is a 2/3 increase).