D&D General Probability, Critical Hits, and the Illusion of Importance


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DND_Reborn

The High Aldwin
Personally, I am all for removing critical hits from D&D entirely.

The "20" means nothing more than success as attacks are binary: you hit or you miss. Damage is more important IMO.

With the assumed attack probability of 65%, doubling the damage dice on a natural 20 is less meaningful overall than a +1 to the attack roll. For example: assume you hit on an 8 or better (65%), dealing 1d8+5 damage:
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Your expected damage with a +1 to your attack roll and disregarding criticals on a natural 20 is better (6.65) than RAW double dice on a natural 20 (6.4).

With the double dice critical hit system, players feel disappointed when the roll low on the dice, since this was supposed to be "critical". So, many groups do max damage and a die roll, to keep players from getting the low critical damage rolls.

This is why I (and my group) moved the "critical" away from the hit and onto the damage. Now, if you roll maximum damage on a die, which happens more often of course, the die explodes and you roll another damage die, continuing the process until you don't roll maximum on a die.

This accomplishes a couple things which are beneficial IME:

1. It makes more sense in the narrative as you will not roll low damage on a critical.
2. It happens a bit more often (depending on your damage dice), but not so often it becomes routine. It is still exciting.
3. All sources of damage (spells, hazards, etc.) as well as damage from attacks.
4. While the increased damage is notable, the effect is actually less than if you used the next size die.

Finally, another thing that has always bothered me with criticals on a natural 20 is the case when you actually need a 20 to hit. Granted, this is very rarely the case in 5E, at least.
 

billd91

Not your screen monkey (he/him)
Personally, I am all for removing critical hits from D&D entirely.

The "20" means nothing more than success as attacks are binary: you hit or you miss. Damage is more important IMO.

With the assumed attack probability of 65%, doubling the damage dice on a natural 20 is less meaningful overall than a +1 to the attack roll. For example: assume you hit on an 8 or better (65%), dealing 1d8+5 damage:
View attachment 259880
The fun observation here is that the difference between the two comes entirely from the fact that the static bonus is not doubled for the crit. Otherwise, doubling the dice (and thus the expected value of a single hit) on a 20 yields the same expected damage as a +1 to hit and no crits. A character without a damage bonus at all (like with a strength 10-11) would have the same expected damage value using either table.
 

DND_Reborn

The High Aldwin
The fun observation here is that the difference between the two comes entirely from the fact that the static bonus is not doubled for the crit. Otherwise, doubling the dice (and thus the expected value of a single hit) on a 20 yields the same expected damage as a +1 to hit and no crits. A character without a damage bonus at all (like with a strength 10-11) would have the same expected damage value using either table.
Yep, that is precisely the case. :)
 

CleverNickName

Limit Break Dancing
Personally, I am all for removing critical hits from D&D entirely.

The "20" means nothing more than success as attacks are binary: you hit or you miss. Damage is more important IMO.

This accomplishes a couple things which are beneficial IME:
But there's more going on here in the game than just assigning damage to targets. There is tension and excitement that is created by The Unknown, and these things are a huge part (maybe even the biggest part) of playing a tabletop roleplaying game. Removing even a tiny bit of randomness from the game will remove an equal amount of that tension and suspense, and that would make the game less fun to me.
 

DND_Reborn

The High Aldwin
There is tension and excitement that is created by The Unknown, and these things are a huge part (maybe even the biggest part) of playing a tabletop roleplaying game.
The rolls are still unknown. My system just transfers the excitement from the attack roll to the damage roll.

Now, you could argue that since you are always making attack rolls, but only rolling for damage following the hit, you have fewer rolls that are thus "exciting", but I would challenge that because this makes ALL damage rolls potentially critical damage, including save-based damage spells, and hazards such as falling. It also has no cap.

It was pretty stellar when my PC did 21 points of damage using a torch as an improvised club (I rolled numerous 4's on the d4). IMO it was MUCH more exciting than if I had rolled a natural 20 for 2d4+STR damage. meh

Removing even a tiny bit of randomness from the game will remove an equal amount of that tension and suspense, and that would make the game less fun to me.
I can understand your concern, but all I can say is from my group's experience. NONE of us miss the critical hit on the natural 20. We all prefer the critical damage rules we use. I've shared them with other groups, and they sound better to them as well.

So, my advice is the same with every thing else when it comes to alternative systems: give it a try. If you don't like it, no harm done. :)

EDIT: I will add just so people know healing is critical as well. If you roll maximum on a die for healing, including spending HD, the die explodes.
 

billd91

Not your screen monkey (he/him)
It was pretty stellar when my PC did 21 points of damage using a torch as an improvised club (I rolled numerous 4's on the d4). IMO it was MUCH more exciting than if I had rolled a natural 20 for 2d4+STR damage. meh
I can imagine a number of tables where the exploding dice resolution wouldn't fly too well, though. Rolling 2d4+Str may be occasionally disappointing compared to d4+d4+d4+d4 etc. But it doesn't come with an open-ended resolution time. And there's something to be said for knowing how many dice you're picking up to roll at the outset.

There's also the idea that dice with the fewest faces are the ones most likely to explode. While that may tend to keep damage down overall since a d4 that explodes is, well, it's still just a d4, it kind of sucks that hitting someone with a torch is more likely to explode than hitting them with a great axe.

So definitely a different aesthetic going on.
 

CleverNickName

Limit Break Dancing
The rolls are still unknown. My system just transfers the excitement from the attack roll to the damage roll.

Now, you could argue that since you are always making attack rolls, but only rolling for damage following the hit, you have fewer rolls that are thus "exciting", but I would challenge that because this makes ALL damage rolls potentially critical damage, including save-based damage spells, and hazards such as falling. It also has no cap.
Yes, that is exactly what I would argue. Fewer rolls = more predictable, and that can often mean less excitement. I like rolling max damage when I barely hit the target, outshining the crit-fishing Lucky Rogue if only for a moment. And I like it when an enemy's nat-20 ends up dealing less damage than his regular attack did. To my mind, the swingy, unpredictable nature of combat is best modeled by rolling attacks and damage separately.

I can understand your concern, but all I can say is from my group's experience. NONE of us miss the critical hit on the natural 20. We all prefer the critical damage rules we use. I've shared them with other groups, and they sound better to them as well.

So, my advice is the same with every thing else when it comes to alternative systems: give it a try. If you don't like it, no harm done. :)
My players dearly love the critical hit rules. I think they would sooner give up D&D altogether, than give them up. So I found that the best way to handle the Critical Hit ConnundrumTM is to add options to it. When a player rolls a nat-20, they can choose to deal double damage as per the PHB, or they can choose to do a cinematic stunt.

Here's an excerpt from my house rules. Bear in mind that this is a swashbuckling, cinematic-style campaign with pirates and Musketeers and swinging from the chandeliers.
Critical Hits: Double the Damage, or Double the Fun?
When you score a critical hit on an opponent, you can deal extra damage per the rules in the Player’s Handbook. Or you can choose to do regular damage and perform some kind of stunt or trick instead! Maybe you want to knock the weapon out of your enemy’s hand, or you want to knock them prone, or you want to snatch their coin pouch from their belt.

If you want to do one of these stunts, just describe it to me in-character. I’ll maybe ask you to roll something, but for the most part, it’s really up to you to decide what happens. In all cases, these stunts and trick shots are all part of the attack action, so they don’t cost you your reaction or any extra movement.

  • Blind: instead of dealing extra damage, your critical hit knocks sand or dust into your opponent’s eyes, blinding them until the end of their next turn.
  • Disarm: instead of dealing extra damage, your critical hit deals damage as normal and also knocks one item out of your opponent’s hand. The object lands at your opponent’s feet at the end of your turn, occupying the same space as your opponent.
  • Distract: instead of dealing extra damage, you pull your opponent’s focus toward you and away from its surroundings. One ally of your choice gains Advantage on their next attack roll against that same opponent.
  • Escape: instead of dealing extra damage, you Disengage at the end of your turn.
  • Improved Grab: instead of dealing extra damage, you grapple your opponent at the end of your turn.
  • Knockback: instead of dealing extra damage, you knock your opponent back 10 feet at the end of your turn.
  • Knockdown: instead of dealing extra damage, you knock your opponent off his feet. Your opponent falls prone in his space at the end of your turn.
  • Snatch: instead of dealing extra damage, your critical hit causes your opponent to lower their guard, allowing you an opportunity to snatch an unattended, visible item from their person (such as an amulet or pouch).
  • Trade Places: instead of dealing extra damage on your critical hit, you trade places with your opponent at the end of your turn. Obviously this applies only to melee.)
  • Something else: get creative!
Again, these are just examples, feel free to come up with your own. Jump onto its back and konk it on the head? Handcuff the creature to a fence? Kick them into the well, This-Is-Sparta style? Go wild! Whenever you score a crit, ask yourself: “Do I want extra damage? Or do I want extra flair?”

Even so, my players still choose the extra damage 90% of the time. But the times they have taken the "extra flair" have been memorable: breaking an enemy's grapple on an ally, for example, or knocking the wizard's arcane focus (an orb) out of his hand while they were standing on the stairs...those tiny decisions by the player were WAY more interesting than just dealing extra damage. :)
 
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DND_Reborn

The High Aldwin
The time factor is negligible, honestly, IME, and worth the excitement it generates. I could easily understand how others might not find it so, however.

There's also the idea that dice with the fewest faces are the ones most likely to explode. While that may tend to keep damage down overall since a d4 that explodes is, well, it's still just a d4, it kind of sucks that hitting someone with a torch is more likely to explode than hitting them with a great axe.
While lower facet dice are more likely to explode, their expected value is always less than the next higher die.

So, a single d6 (not exploding) averaging 3.5 is always better than an exploded d4 averaging 3.33.

Another thing to consider: your chance of scoring a critical hit RAW is 1 in 20 or 5%. Compare this to my system with a greataxe. If you hit 65% (the assumed typical value) and roll maximum damage on 1 in 12, the cumulative chance of rolling critical damage is actually 5.4%, better than the RAW 1 in 20!! So, while you might not get critical damage with a greataxe as often as a dagger, it is better than RAW and your damage is better as well.

Finally, it encourages the play of smaller die weapons, which otherwise get largely ignored IME.

My players dearly love the critical hit rules. I think they would sooner give up D&D altogether, than give them up.
That's cool. To each their own, of course! We love critical damage so much it has become one of our Golden House Rules for D&D.
 

OB1

Jedi Master
My players dearly love the critical hit rules. I think they would sooner give up D&D altogether, than give them up. So I found that the best way to handle the Critical Hit ConnundrumTM is to add options to it. When a player rolls a nat-20, they can choose to deal double damage as per the PHB, or they can choose to do a cinematic stunt.
Just thought of a way to get your players to try out the new rules, just have them all play Fighters or Barbarians! :D Those are the big winners with the change, as they both get inspiration and get their regular CritHit!

Edited to add: Oh, and Monks as well. And probably clerics, I don't think they really lose much with the new rules. Do they have an attack roll spell?
 
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Isn't it just simpler to do "max damage plus some extra"? That's quick, painless, should feel amazing ("wow, that attack did 28 damage?! It usually does 12!"), and makes +1 crit range a solid but not insanely strong benefit. (Better for multiple big dice, worse for singular small dice, as one would expect.)

Which is sort of what I meant earlier. Sometimes there are easier ways that don't require any "obfuscation" at all, which still produce exactly the intended design experience. I would 100% say that that pithy bit of advice should be amended. "Clarity in general, but especially if you want your players to think; obfuscation only if you need to when wanting to make them feel."

Obscurantism doesn't help anyone.
 

Debating the probability of critical hits seems to me a little like not seeing the trees for the wood (cliche deliberately inverted)

The impact of critical hits on the game isn't one that's intended to have a major game-balance effect over time (there are exceptions, like a Champion fighters' increased crit range etc, but I'm talking in general). It's intended to have an impact on the very tactical level of individual combats. The paladin gets a big critical smite off against the orc warlord and gets a moment of awesome, or the frost giant lands a crit on a PC and all of a sudden a previously routine random encounter turns desperate and tense in a hurry.

Averaging and the statistical analysis of damage over time smooths out these peaks and troughs by definition, and by design. That seems to me to be missing the point. Critical hit mechanics exist to bring the peaks and troughs into the game, because they're the sort of thing that creates in-game moments that you'll remember. Nobody looks back on a game rhapsodising about how their fighter averaged 0.5 hp more damage per hit over the course of the campaign by using a greatsword instead of a greataxe. They talk about the time the cleric was down to 2hp, out of healing and getting savaged by the remorhaz, when the ranger crit it in the eye with an arrow from across the map.
 

Debating the probability of critical hits seems to me a little like not seeing the trees for the wood (cliche deliberately inverted)

The impact of critical hits on the game isn't one that's intended to have a major game-balance effect over time (there are exceptions, like a Champion fighters' increased crit range etc, but I'm talking in general). It's intended to have an impact on the very tactical level of individual combats. The paladin gets a big critical smite off against the orc warlord and gets a moment of awesome, or the frost giant lands a crit on a PC and all of a sudden a previously routine random encounter turns desperate and tense in a hurry.

Averaging and the statistical analysis of damage over time smooths out these peaks and troughs by definition, and by design. That seems to me to be missing the point. Critical hit mechanics exist to bring the peaks and troughs into the game, because they're the sort of thing that creates in-game moments that you'll remember. Nobody looks back on a game rhapsodising about how their fighter averaged 0.5 hp more damage per hit over the course of the campaign by using a greatsword instead of a greataxe. They talk about the time the cleric was down to 2hp, out of healing and getting savaged by the remorhaz, when the ranger crit it in the eye with an arrow from across the map.
This isn't an either-or.

We can have crits that are (a) easy to use, (b) give that rush of "something awesome just happened," and (c) are actually a real benefit on a macro/statistical scale.

There is a false dichotomy here, as though making sure that beneficial actions are actually beneficial is somehow incompatible with those events also being exciting and memorable.
 

GMMichael

Guide of Modos
. . . In conclusion, it posits that the critical hit mechanic only exists to make you feel awesome and powerful, even though that is almost never the case numbers-wise.

With critical hits in D&D gaining traction in certain discussions, I'm curious what other folks might think. What are your thoughts?
Rolling a critical is awesome...if your opponent is 1st level. Otherwise, it doesn't (formerly?) even feel exciting. Wasn't the 3e war axe a 3x critical weapon? Those were the days, back when a critical hit would do some decent damage.

Want to talk about obfuscation? I use a rule that allows defenders to roll to reduce damage or stick with half of the die's top value. Taking half means you don't roll a 1 (or some other low roll). Rolling means that on average, you'll do better than taking half. There's the additional problem that if you're rolling to reduce damage, your opponent is guaranteed to do at least one damage (otherwise her attack was a little short of successful). So you can roll to beat your average protection, but rolling higher doesn't always mean taking less damage because there will always be one point of damage you can't avoid.

Decisions, decisions. And which is the right one?
 


James Gasik

Legend
Supporter
This is precisely how and why I can get away with implementing the critical hit mechanic that I use in OD&D and OAD&D, systems which emphatically predicate the balance of their combats on not having critical hits (a mechanic that Gygax appears to have despised, as he never missed a chance to ridicule it mercilessly).

Since players love and expect critical hits, I give them a mechanic that looks powerful — on a natural 20 attack roll, they get to roll "corrected-exploding" damage dice. That is, they roll damage normally, and if they roll max damage, they subtract 1 point and roll again, repeating as often as they continue to roll maximum. The actual impact of this mechanic? No matter the die-size (it can be as small as d2 or as large as d-any-finite-integer), it increases the expectation value by +½ hp. So if a d6 damage weapon can be expected to deal 3.5 damage on a hit, a critical hit means an expected 4 damage. It's pure mathematical sleight of hand… and yet my players still love scoring critical hits on enemies, and they still cringe and sit on the edge of their seats whenever they suffer a critical hit at the hands of a foe.

I never explain the rationale behind the critical hit rules I use, and I have never once seen a player suss it out either.
And when the master of complicated subsystems says he doesn't like a complicated subsystem, that's kind of telling!
 

Jack Daniel

Never give up! Never surrender!
And when the master of complicated subsystems says he doesn't like a complicated subsystem, that's kind of telling!

Well when you design a game predicated on managing risk vs. reward, managing resources (like hit points), and deciding just how deep you want to risk delving down into a dungeon during each adventure, a certain degree of measured predictability is desirable. That, I think, lies at the heart of Gygax's recorded attitude toward critical hits.

crit1.jpg

(—From Dragon #16)

critical2.jpg

(—From Dragon #39)
 
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