D&D 5E Removing the Critical Hit, Using Exploding Dice

[Ovinomancer]

@dnd4vr

I can't follow your d20 averaging math above -- what did you do?

And, as a point you might want to consider, while the averages for switching to exploding damage from critical 20's is very small (usually a few tenths of a point of damage), the standard deviation is almost twice as large. In short, this will make damage output very swingy and hard to predict.

d6 average is 3.5, SD of 1.7, meaning 65% of all outcomes will be between 1.8 and 5.2 damage.

d6 exploding average is 4.18, SD 3.16, meaning 65% of outcomes will be between 1.02 and 7.34 damage.

That's a big shift.

 

[DND_Reborn]

@Ovinomancer

What I mean about averaging over the range of the d20 is that if you needed a 5 to hit, 1-4 would be 0's, and 5-20 would be the average of the die type.

This is different from nat 20, where 1-4 would be 0, 5-19 would be the average of the die type, and a 20 would be twice that.

If you sum up those values and divide by 20, you get the average over the entire range based on a 5 or higher is a successful hit.

Yeah, damage becomes much more variable with exploding dice, but that is a feature IMO, not a bug. It is something I like. Of course, that might not appeal to everyone, but I like the idea that d4 and d6 weapons can be more lethal and with an exploding die, theoretically a level 1 character with a dart could kill the tarrasque. That is less likely than winning the lottery LOL, but it could happen with exploding dice. Under the nat 20 crit, it is impossible.

 

[Ovinomancer]

@Ovinomancer

What I mean about averaging over the range of the d20 is that if you needed a 5 to hit, 1-4 would be 0's, and 5-20 would be the average of the die type.

This is different from nat 20, where 1-4 would be 0, 5-19 would be the average of the die type, and a 20 would be twice that.

If you sum up those values and divide by 20, you get the average over the entire range based on a 5 or higher is a successful hit.

Yeah, damage becomes much more variable with exploding dice, but that is a feature IMO, not a bug. It is something I like. Of course, that might not appeal to everyone, but I like the idea that d4 and d6 weapons can be more lethal and with an exploding die, theoretically a level 1 character with a dart could kill the tarrasque. That is less likely than winning the lottery LOL, but it could happen with exploding dice. Under the nat 20 crit, it is impossible.

I see, you figured for each needed to hit value on d20, summed, and averaged. You made a mistake at 1, though, as that's not 0 damage, it's the same as needing a 2 or better. Slightly changes your numbers.

That said, this is a weird metric that doesn't tell you much of anything useful at all.

As for the shift, yes, it means that a dart might take out a big creature (not the tarrasque, who's immune to non-magical weapons, ) but this will hurt the players far more than the normal crit mechanic. Especially with monsters with multiple die damage. It also vastly privileges multi-die spells. 8d6 fireball goes from a 28 damage mean with 4.83 SD to 33.44 mean with a 8.93 SD. That means they have the same rough bottom of the 65% distribution (25.17 vs 24.51) but the top end the normal fireball doesn't even get to the exploded's mean in a single SD (tops are 32.83 vs 42.37).

 

[DND_Reborn]

I see, you figured for each needed to hit value on d20, summed, and averaged. You made a mistake at 1, though, as that's not 0 damage, it's the same as needing a 2 or better. Slightly changes your numbers.

That said, this is a weird metric that doesn't tell you much of anything useful at all.

As for the shift, yes, it means that a dart might take out a big creature (not the tarrasque, who's immune to non-magical weapons, ) but this will hurt the players far more than the normal crit mechanic. Especially with monsters with multiple die damage. It also vastly privileges multi-die spells. 8d6 fireball goes from a 28 damage mean with 4.83 SD to 33.44 mean with a 8.93 SD. That means they have the same rough bottom of the 65% distribution (25.17 vs 24.51) but the top end the normal fireball doesn't even get to the exploded's mean in a single SD (tops are 32.83 vs 42.37).

LOL good catch! I was just thinking of a 1 being a miss and plopped a 0 there on the spreadsheet. I'll update the OP with the new numbers later.

That metric is what allows me to determine for what values exploding dice outperform in average damage the nat 20 crit. So, for a particular die type, if someone is very likely to hit, exploding dice are better, but if they have a relatively small range to hit, such as 18-20, nat 20 crits are better.

This means that people who are not likely to hit are penalized even more with exploding dice. Granted, it isn't a LOT, but it would be worse.

 

[DND_Reborn]

I see, you figured for each needed to hit value on d20, summed, and averaged. You made a mistake at 1, though, as that's not 0 damage, it's the same as needing a 2 or better. Slightly changes your numbers.

That said, this is a weird metric that doesn't tell you much of anything useful at all.

I updated the table. Let me know if it looks off to you but I think it is correct now. Thanks again!

As for the shift, yes, it means that a dart might take out a big creature (not the tarrasque, who's immune to non-magical weapons, ) but this will hurt the players far more than the normal crit mechanic. Especially with monsters with multiple die damage. It also vastly privileges multi-die spells. 8d6 fireball goes from a 28 damage mean with 4.83 SD to 33.44 mean with a 8.93 SD. That means they have the same rough bottom of the 65% distribution (25.17 vs 24.51) but the top end the normal fireball doesn't even get to the exploded's mean in a single SD (tops are 32.83 vs 42.37).

Well, it was a magic dart!

Yeah, it makes stronger monsters stronger, but also I see 5E as not very lethal and this helps to make it more deadly.

All that being said, we might try it for a session or two, or the others might not want to try it at all. We won't play again until after Thanksgiving so it will be a while.

 

[Ovinomancer]

LOL good catch! I was just thinking of a 1 being a miss and plopped a 0 there on the spreadsheet. I'll update the OP with the new numbers later.

That metric is what allows me to determine for what values exploding dice outperform in average damage the nat 20 crit. So, for a particular die type, if someone is very likely to hit, exploding dice are better, but if they have a relatively small range to hit, such as 18-20, nat 20 crits are better.

This means that people who are not likely to hit are penalized even more with exploding dice. Granted, it isn't a LOT, but it would be worse.

The ranges you're talking about don't usually exist in game, though, so, as I said, not a terribly useful metric.

Also, I used SD above for a single die, I shouldn't have as the distribution of exploded dice is not normal. It holds pretty well for multiple dice, though, as that distribution approaches normal quickly. Actually doing stats on single die is, well, lost in the recesses of my education. I vaguely remember something about dealing with skewed distributions using log functions to get a normal distribution, but that was for skewed normals, which the single d6 roll is a stepped function... meh, it's ugly. Long and short, though, is that you should be very careful when comparing mean of a d6 to the mean of the exploding d6 -- they're not in the same family of things.

 

[DND_Reborn]

The ranges you're talking about don't usually exist in game, though, so, as I said, not a terribly useful metric.

Also, I used SD above for a single die, I shouldn't have as the distribution of exploded dice is not normal. It holds pretty well for multiple dice, though, as that distribution approaches normal quickly. Actually doing stats on single die is, well, lost in the recesses of my education. I vaguely remember something about dealing with skewed distributions using log functions to get a normal distribution, but that was for skewed normals, which the single d6 roll is a stepped function... meh, it's ugly. Long and short, though, is that you should be very careful when comparing mean of a d6 to the mean of the exploding d6 -- they're not in the same family of things.

I don't see how those ranges don't usually exist. They are the number needed on a d20 to hit (after bonuses, of course). If you have a +5 bonus to attack rolls, and you are attacking a target with AC 17, you need a 12 or higher. So, if the player was using a d8 weapon, his expected damage per attack would be 2.314 points (remember, 11 or lower would be 0 damage here ). So, it tells me exploding dice would result in greater damage. If the character used a d12 weapon, nat 20 crits would result in better damage in this case.

Yeah, it is not normal, so I was never very concerned with the SD, but the expected damage is still useful to know. This can be true even if the distribution types differ.

 

[Blue]

Don't heed the undeserved skepticism. You will want to tweak, but it's not a big deal really; in fact it has some nice effects and can become a useful kit in your toolbox if you want to rework the game's damage values.

D4s are now now scrappier but not by enough to make them ever better than a d6. A d4's average damage goes up by about 0.63 damage per roll, while a d6 only goes up by 0.58. That's only a 0.05 damage relative increase, and the gap between then was already 1 full average damage.

I think that you may be minimizing the issue of differences between one and two handed weapons. Two handed weapons give up a lot for their damage dominance. They aren't finesse, don't allow a shield/casting hand/two weapon/grappling, and are expected to do more damage for that difference.

Let's take the dagger vs. the great axe. For ease of math I'm going to assume a 55% chance to hit - that's a 50% change for a hit and a 5% chance for a crit the old way.

Taking a look at just the dice part of damage, since that's all that's affected by crits. An abilty score bonus is static and the same on either.

PHB way:
Dagger: 50% * d4 (2.5) + 5% * 2d4(5) = 1.5 average damage per attack.
Great Axe: 50% * d12 (6.5) + 5% * 2d12(13) = 3.9 average damage per attack.
Dagger does 38% of the Great Axe on an attack.

Exploding Dice way:
Dagger: 55% * d4 Exploding (3.333) = 1.833 average damage per attack.
Great Axe: 55% * d12 Exploding (7.091) = 3.900 average damage per attack.
Dagger does 47% of the Great Axe on an attack.

Relative to each other, the dagger improved by more than 23% (47/38). That is a "big deal really".

Changing the balance to favor one handed over two handed also give DEX characters a boost, since they get more out of this than the two handed weapon wielders going for damage. It would be yet another reason STR loses out to DEX.

 

[DND_Reborn]

I think that you may be minimizing the issue of differences between one and two handed weapons. Two handed weapons give up a lot for their damage dominance. They aren't finesse, don't allow a shield/casting hand/two weapon/grappling, and are expected to do more damage for that difference.

Let's take the dagger vs. the great axe. For ease of math I'm going to assume a 55% chance to hit - that's a 50% change for a hit and a 5% chance for a crit the old way.

Taking a look at just the dice part of damage, since that's all that's affected by crits. An abilty score bonus is static and the same on either.

PHB way:
Dagger: 50% * d4 (2.5) + 5% * 2d4(5) = 1.5 average damage per attack.
Great Axe: 50% * d12 (6.5) + 5% * 2d12(13) = 3.9 average damage per attack.
Dagger does 38% of the Great Axe on an attack.

Exploding Dice way:
Dagger: 55% * d4 Exploding (3.333) = 1.833 average damage per attack.
Great Axe: 55% * d12 Exploding (7.091) = 3.900 average damage per attack.
Dagger does 47% of the Great Axe on an attack.

Relative to each other, the dagger improved by more than 23% (47/38). That is a "big deal really".

Changing the balance to favor one handed over two handed also give DEX characters a boost, since they get more out of this than the two handed weapon wielders going for damage. It would be yet another reason STR loses out to DEX.

LOL you happened to pick a d12 weapon at the exact point where the exploding die and nat 20 crits yield the exact same damage?

Percentages often seem big, but you are overlooking the raw damage. You are really looking at a 0.33 hp increase for a dagger from d20 crit to exploding. Not a big deal.

Do the same comparison with the greatsword:
PHB: 4.2 vs. ExDice: 4.62

That is 0.42 hp increase in damage, greater than the 0.33 of the dagger, even if the percentage is only 10% vs. 22.2%.

So, the point is exploding dice, overall, will yield better weapon damage but not so much over d20 nat crit as to make it too powerful. Now, exploding dice on spells, sneak attacks, and other sources can be much more powerful, but as I have stated before I don't have any issue with that personally.

 

[Esker]

You could just make d10s explode on a 9 or 10 and d12s explode on an 11 or 12.