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

[DND_Reborn]

Again, I'm not offering this as a criticism of the approach, since, particularly at higher levels, the game can get too easy. I think the biggest difference would be on save effects, if you're applying it there too. Enemy spellcasters become a lot scarier.

Yeah, I see the game losing some of the risk present at lower levels myself. It is no wonder many games don't make it past 10th level from what I hear.

As for casters, it helps PCs as well as hurts them. Consider even a sleep spell. 5d8 normally is 22.5 hp, exploding it is 25.7. That isn't huge jump, but as you know with the skew towards higher totals, makes the spell more useful to PC casters.

As I said in the OP, I am not sold on the idea of exploding things that don't require an attack roll. In some ways, I would love adding it, but in other ways it is daunting.

 

[Esker]

As for casters, it helps PCs as well as hurts them. Consider even a sleep spell. 5d8 normally is 22.5 hp, exploding it is 25.7. That isn't huge jump, but as you know with the skew towards higher totals, makes the spell more useful to PC casters.

Yes, it helps PCs too, but because encounters aren't balanced as symmetric contests where each side has an equal chance of prevailing (if they were, campaigns would be really short), boosting the severity of monsters' lucky rolls does more than boosting the severity of PCs' lucky rolls. Basically, if the PCs get lucky, they turn an encounter that favored them anyway into a cakewalk. By making good luck more powerful, it just becomes a super-cakewalk. But if the monsters get lucky, they turn what was a favorable situation for the PCs into potentially an unfavorable one. And by making monsters' good luck more potent, you might be making unfavorable into deadly.

As a party, you're more likely to die after one really easy and one really deadly encounter than you are after two medium encounters, even if the average difficulty is the same.

 

[Ovinomancer]

Another way to look at it: the exploding fireball has a standard deviation of 9.2 (not sure where you got the 8.9 you cited; maybe assuming some Normal approximation?). If it were a Normal, then the middle 2/3 of the distribution would be 33.6 +/- 9.2, or 24.4 to 42.8. But in reality the middle 2/3 of the distribution is 23 to 33. Pretty big difference on that high end.

Where'd you get 9.2? Bad form to question how someone else got their numbers while asserting you have the right ones without evidence. I used Anydice, because it does mean/SD pretty darn well.

Secondly, if the mean value for exploding is 33, how'd you get that 33 is the top of the middle 2/3rds? I mean, looking at the distribution graph you put above it's pretty clear that the upper bounds of the middle 2/3rd is east of 33. It looks like 43 is a much better candidate.

In fact, the middle 2/3rds of the exploding fireball, marked as between 16% and 84%, is 25 and 41. The SD calculation comes in at 24.51 and 42.37 (using my SD, natch) which is pretty doggone close, which is what I said -- it's normal enough for 1st approximations.

 

[Esker]

Where'd you get 9.2? Bad form to question how someone else got their numbers while asserting you have the right ones without evidence. I used Anydice, because it does mean/SD pretty darn well.

I simulated it 1M times and took the SD.

Secondly, if the mean value for exploding is 33, how'd you get that 33 is the top of the middle 2/3rds? I mean, looking at the distribution graph you put above it's pretty clear that the upper bounds of the middle 2/3rd is east of 33. It looks like 43 is a much better candidate.

Yeah, I screwed this one up; I accidentally put in the middle 2/3 of the non-exploding fireball. Should be 25 to 42 for the exploding one. I retract my earlier statement about the high end of the middle 2/3 being off; it's only off by 0.5. Mea culpa.

The asymmetry in the high and low percentiles relative to the median though still stands: The mean is at about the 55th percentile.

 

[Esker]

Oh, I see the problem, @Ovinomancer ; looking at the AnyDice documentation, it caps the number of times a die can explode at 2. So that will result in underestimating the SD (as well as the mean; I get 33.6).

If you set "explode depth" to 10 first, you get my numbers.

 

[jmartkdr2]

Another class feature to consider is brutal critical (half-orcs, barbarians).

I'm not sure how to deal with this, but it's something to think about.

 

[Esker]

By the way, you can work out the results analytically as well: The number of rerolls, r, of an exploding k-sided die, r, has a Geometric distribution with termination probability (k-1)/k. The actual damage result is

r*k + t

where r ~ Geometric((k-1)/k), and t is the last roll (which didn't explode, and so it is DiscreteUniform(1,k-1)).

These two variables are independent --- the value of the last roll is independent of how many times we re-rolled --- so the variance of the sum is the sum of the variances.

A Geometric(p) distribution (parameterized as above) has mean (1-p)/p, and variance (1-p)/p^2. In this case that works out to be mean (1/k) / ((k-1)/k) = 1/(k-1), and variance (1/k) / ((k-1)/k))^2 = k/(k-1)^2.

A DiscreteUniform(1,n) (in other words an n-sided die) has mean (n+1)/2, and variance (n^2-1)/12; for n = k-1, this is mean k/2 and variance ((k-1)^2 - 1)/12.

So, r*k + t (the exploding 1dk) has:

mean k/(k-1) + k/2, or [(k+1)/2] * [k/(k-1)], and

variance k^2 * (k/(k-1)^2) + ((k-1)^2-1)/12 = [k^3 / (k-1)^2] + [(k-1)^2 / 12].

In the case of a fireball, we have 8 of these with k=6. Means and variances add, so we have

Mean = 8 * ((6+1)/2) * (6/5) = 33.60
Variance = 8 * ((6^3 / 5^2) + (5^2 / 12)) = 85.79
Std. Dev = sqrt(8 * ((6^3 / 5^2) + (5^2 / 12))) = 9.26

 

[DND_Reborn]

Another class feature to consider is brutal critical (half-orcs, barbarians).

I'm not sure how to deal with this, but it's something to think about.

Yeah, I noted Champion and Savage Attacks for Half-Orc in the OP, but there are definitely more.

As much as I like a lot of the idea, I have a couple weeks to really think about all the tweaks needed to make it function. Ultimately, I don't know if it is worth it... but we'll see.