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

[OB1]

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 Connundrum^TM 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! 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?

 

[FrogReaver]

we dont play this game to achieve mathematical satisfaction, we play it to role play fantasy characters.

...speak for yourself

 

[EzekielRaiden]

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.

 

[humble minion]

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.

 

[EzekielRaiden]

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]

. . . 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?

 

[HaroldTheHobbit]

Critical hits are fun. Probability be damned.

This. Even though my games aren't combat focused, the whole party still goes into cheering mode when the paladin gets a crit smite on the bbeg. And the opposite - when a big baddie slams a fat crit on the fragile cleric/rogue multi the party holds their breath while the damage dice clatter.

 

[James Gasik]

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]

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.

Spoiler: Courtesy of the 'Grognardia' Blog:

(—From Dragon #16)

(—From Dragon #39)

 

[Umbran]

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.

The point being that, on long average, it isn't actually that much more random.