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

[Esker]

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.

The distribution doesn't approach normal that quickly. Here are the probability distributions for a fireball (8d6):

Still a fair amount of skew there. Comparing percentiles:

            5% 10% 25% 50% 75% 90% 95%
Normal     20  22  25  28  31  34  36
Exploding  21  23  27  32  39  46  50

So unlike just increasing the standard deviation, which lowers the low end in addition to raising the high end, this change keeps the low end pretty much the same, raises the middle a little bit, and raises the high end a lot.

 

[Fenris-77]

I might look at handling the Champion and other examples of crit range extension by upping the damage dice instead. So a short sword in the hands of an increased crit range character (19-20) does a d8. The dice change could either apply generally or just on the appropriate roll. At the top end something like a great axe changes from a d12 to 2d8 (exactly like the greatsword). A caveat with this whole idea is looking at the impact of the reroll on damage granted by GWM. Maybe you did that above, but I don't remember reading it.

Alternatively for expanded crit rang, you could split damage X into multiple dice to give a greater chance to explode. So a d8 changes to 2d4, a d10 to d6/d4 or whatever. I like the first idea more but they both have some juice.

You could also limit the number of dice that can explode in a given roll. If you limit it to two dice regardless of dice rolled it doesn't change the effect on melee but it does scale back stuff like fireball.

 

[Ovinomancer]

The distribution doesn't approach normal that quickly. Here are the probability distributions for a fireball (8d6):

Still a fair amount of skew there. Comparing percentiles:

            5% 10% 25% 50% 75% 90% 95%
Normal     20  22  25  28  31  34  36
Exploding  21  23  27  32  39  46  50

So unlike just increasing the standard deviation, which lowers the low end in addition to raising the high end, this change keeps the low end pretty much the same, raises the middle a little bit, and raises the high end a lot.

Which is what applying the SDs to the means in those distributions shows, because while, yes, it is skewed, it's not badly so.

 

[Esker]

Which is what applying the SDs to the means in those distributions shows, because while, yes, it is skewed, it's not badly so.

I guess "badly so" is subjective, but I would disagree: the gap between the 90th percentile and the median is 50% larger than the gap between the 10th percentile and the median, for example.

 

[Esker]

Which is one reason why this method would make the game tougher for the PCs. Typically the average outcome is calibrated to favor them; Leroy Jenkins / poor play moments aside, TPKs tend to happen when you wind up in the tails of distributions. By using exploding dice, you're making those tail outcomes more devastating, so you need fewer unlucky happenings for the tide to turn against the PCs. On the flip side, lucky rolls merely turn an encounter that already favored them into even more of a cakewalk than they otherwise would have. That's not as big a benefit as the other side is a cost.

Not citing this as a criticism, since @dnd4vr specifically mentioned more deadly games as a goal. Just connecting it to the probabilities.

 

[Esker]

Which is what applying the SDs to the means in those distributions shows, because while, yes, it is skewed, it's not badly so.

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.

 

[DND_Reborn]

Not citing this as a criticism, since @dnd4vr specifically mentioned more deadly games as a goal. Just connecting it to the probabilities.

While this makes for a more deadly game, it applies to the monsters as well, which is why I don't mind. Now, since many monsters do damage with multiple dice, and PCs don't with notable exceptions, in that sense it will make things more difficult for PCs more than for others--but hey, I like a challenge!

 

[Esker]

While this makes for a more deadly game, it applies to the monsters as well, which is why I don't mind. Now, since many monsters do damage with multiple dice, and PCs don't with notable exceptions, in that sense it will make things more difficult for PCs more than for others--but hey, I like a challenge!

That's what I'm saying. This works against the PCs on balance.

 

[DND_Reborn]

That's what I'm saying. This works against the PCs on balance.

But, honestly, how much?

I mean, sure a lot of monsters get 2 or more dice for an attack, but at that point many PCs will either have Extra Attack (in essence, gaining multiple dice), use Sneak Attack, Divine Smite, or be casting multiple dice damaging spells (even as early as Magic Missiles and later Fireballs) against the monsters as well.

Over all, I think instinctively, and edge against the PCs won't be huge. It might make them a bit more cautious, but again I don't see that as a bad thing.

Either way, nice analysis and thanks for the contributions!

 

[Esker]

But, honestly, how much?

I mean, sure a lot of monsters get 2 or more dice for an attack, but at that point many PCs will either have Extra Attack (in essence, gaining multiple dice), use Sneak Attack, Divine Smite, or be casting multiple dice damaging spells (even as early as Magic Missiles and later Fireballs) against the monsters as well.

Over all, I think instinctively, and edge against the PCs won't be huge. It might make them a bit more cautious, but again I don't see that as a bad thing.

Either way, nice analysis and thanks for the contributions!

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.