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

CleverNickName

Limit Break Dancing
The YouTube channel Extra Credits posted an interesting video yesterday, on our perception of probability and reward in games. The episode speaks to game developers, particularly video games, but uses the critical hit mechanic of tabletop roleplaying games to illustrate an interesting point: critical hits really aren't as mathematically amazing as you think they are.



The episode spends a lot of time discussing the mechanics of the famous "Monty Hall" puzzle and how it works, and then at around the 3:50 mark asks "So why does this matter when we are designing games?" The answer given is "Well, because humans are both great, and terrible, at probability." To expand on this, Extra Credits talks at length about the critical hit mechanic, and how both the mechanics of probability and the perception of probability are very different. 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?
 
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payn

Legend
I suppose leaving crits in for PCs allows that feeling of awesome, while making the game more predictable on the NPC side. I dont think a better balanced mechanic is always better than one that feels right. I mean, we dont play this game to achieve mathematical satisfaction, we play it to role play fantasy characters.
 

CleverNickName

Limit Break Dancing
I suppose leaving crits in for PCs allows that feeling of awesome, while making the game more predictable on the NPC side. I dont think a better balanced mechanic is always better than one that feels right. I mean, we dont play this game to achieve mathematical satisfaction, we play it to role play fantasy characters.
Yep, agree. I'm not trying to under-value the importance of "feeling awesome," because that's kind of the point of playing this game! This video does help me put some of the recent math-heavy threads into perspective, though.

And I thought the conclusion was very helpful indeed: "Remember: clarity when you want your players to think, and obfuscation when you want your players to feel."
 

the Jester

Legend
I think that's fairly accurate unless you have critical hits do more than just deal more damage. For instance, in a lot of old school systems, a critical comes with a chart that lops off limbs, breaks bones, and removes eyeballs. That matters. I still use such a system, and it means crits matter- but in the interest of fairness, it also requires things like a way to fix small lost bits (a tooth, a finger, etc) that's lower level than regenerate, and a system for dealing with the effects of e.g. broken bones or twisted ankles that both makes them meaningful and yet allows them to be alleviated without forcing one pc to sit out three weeks of game time if magical healing isn't easily available.
 

Celebrim

Legend
Critical hits as a system almost entirely exist to punish the player.

Players perception of critical hits is that they exist almost entirely as a reward.

I am not a huge fan of critical hits but they have been wildly successful as a mechanic across multiple systems and as such they are almost impossible to get away from because players will demand them even when what they are really demanding is for the game to be more punishing.

There has been some amusing conversations really with players demanding critical hits but realizing that they are punishing so demanding that the can do critical hits but never receive them. This is mostly amusing because player critical hits rarely matter except as a thrill. As the video notes, they rarely add significant damage dealing capability in the long run unless your system deliberately gives ways to abuse them.

In my homebrew system I use critical hits in a couple of ways, because rooting them out of the system when players love them so much is just too much work.

a) I use critical hits to keep combats from being too predictable. One of the advantages of a hit point system is that you can very accurately gauge how challenging a combat is and very carefully weight the combat in the PC's favor. But when every combat is subtly weighted in the PC's favor, combats can get grindy and pointless. Critical hits provide random 'swinginess' where combats suddenly get tense that weren't tense before. I use a narrative currency system to mitigate against excessive 'swinginess' but even being forced to spend your narrative currency and losing your safety net is itself tension inducing.

b) I use critical hits to create verisimilitude of realism. One of the original design goals of critical hits was to explain serious maiming wounds which are otherwise impossible in an abstract damage system. The rules support that maiming wounds can exist all the way back to 1e, but without critical hits they were silo'ed off into special cases like Swords of Sharpness. In my homebrew, being dropped by a critical hit is one of the things that has a good chance of causing a traumatic injury. Dying and bleeding out is a common situation in most games I run because I run games that typically leave a large margin for saving a dying colleague. Critical hits create occasional color of brutality and critical injury most commonly to NPC's, but occasionally to PC's that are out of narrative currency as well.

Conversely, having a critical injury system described by the rules in concrete ways lets me handle those special cases in a straight forward manner in a way that they weren't handled even when mentioned. Think about it. In 1e, 2e, 3e, 4e, or 5e, where would you go to to quickly look up what it meant to have a PC's arm removed at the elbow? In 2e, I think you could turn to a sidebar on the Axe of the Dwarvish Lords in the module of the same name, but that's pretty obscure. Most of the time the rules just say, "DM, make up something." Well, I did, then I wrote it down.

c) I use critical hits as a mechanism for helping martials keep up with casters. I have a lot of ways for martials and especially fighters to gain advantages in the ability to deal critical hits and I typically do that instead of adding bonus damage.
 
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I suppose leaving crits in for PCs allows that feeling of awesome, while making the game more predictable on the NPC side. I dont think a better balanced mechanic is always better than one that feels right. I mean, we dont play this game to achieve mathematical satisfaction, we play it to role play fantasy characters.
The main issue is, if the rules on the net don't actually work toward the intended design goal (aka, poorly balanced), then you get an issue that...I guess you could call "insidious design." It's design that looks good, design that seems good when you use it, but which actually fights against you and you may not even realize it.

That's very much what happened to me with 3rd edition. I kept trying and trying and trying to get it to work the way I wanted. For easily 4-5 years, I thought the problem was bad specifics: a fault in Paladin, or in the spell list, or something of that nature. It took me sitting down and actually reading 4e (which I was only doing, at the time, in order to give someone an informed "take that" about how 4e was obviously horrible!) for me to realize exactly what I was missing from 3e. Because it's subtle! It's hard to see just by looking at it--superficially, 3e looks fine. It seems fine in play. But its underlying faults are so deep and so severe, they really do get in the way. WotC saw it, and eventually Paizo was forced to admit the same.

Now, this DOES NOT mean that a balanced mechanic is automatically better! It just means that a "feels right" mechanic isn't automatically better either.
 
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payn

Legend
The main issue is, if the rules on the net don't actually work toward the intended design goal (aka, poorly balanced), then you get an issue that...I guess you could call "insidious design." It's design that looks good, design that seems good when you use it, but which actually fights against you and you may not even realize it.

That's very much what happened to me with 3rd edition. I kept trying and trying and trying to get it to work the way I wanted. For easily 4-5 years, I thought the problem was bad specifics: a fault in Paladin, or in the spell list, or something of that nature. It took me sitting down and actually reading 4e (which I was only doing, at the time, in order to give someone an informed "take that" about how 4e was obviously horrible!) for me to realize exactly what I was missing from 3e. Because it's subtle! It's hard to see just by looking at it--superficially, 3e looks fine. It seems fine in play. But its underlying faults are so deep and so severe, they really do get in the way. WotC saw it, and eventually Paizo was forced to admit the same.
Oh this broken record again? Funny how both times the reaction design sucked most of the fun right out of the game. Every version has its issues there is no perfect game. Well, for most folks anyways.
 


billd91

Not your screen monkey (he/him)
Critical hits as a system almost entirely exist to punish the player.

Players perception of critical hits is that they exist almost entirely as a reward.

I am not a huge fan of critical hits but they have been wildly successful as a mechanic across multiple systems and as such they are almost impossible to get away from because players will demand them even when what they are really demanding is for the game to be more punishing.

There has been some amusing conversations really with players demanding critical hits but realizing that they are punishing so demanding that the can do critical hits but never receive them. This is mostly amusing because player critical hits rarely matter except as a thrill. As the video notes, they rarely add significant damage dealing capability in the long run unless your system deliberately gives ways to abuse them.

In my homebrew system I use critical hits in a couple of ways, because rooting them out of the system when players love them so much is just too much work.
Honestly, if the players don't perceive it as punishment, but as a thrill, something they love so much, and will demand... then I think seeing critical hits as a punishment just means you're out of step with your players.
If you persist in considering it punishment, then pull on your metaphorical B&D gear, and flog away! They're clearly consenting to it. Just be sure to mind your safe words...
 

Oh this broken record again? Funny how both times the reaction design sucked most of the fun right out of the game. Every version has its issues there is no perfect game. Well, for most folks anyways.
I mean, the designers at Paizo straight-up said "yeah, we tried, we really did, we can't keep using this engine. Give us a chance to drill down and fix the issues, please?"

So...yeah. And I don't at all grant that either "sucked most of the fun right out of the game." I've had a blast every single time I've played 4e, and PF2e looks like it scratches a similar itch.
 

payn

Legend
I mean, the designers at Paizo straight-up said "yeah, we tried, we really did, we can't keep using this engine. Give us a chance to drill down and fix the issues, please?"

So...yeah. And I don't at all grant that either "sucked most of the fun right out of the game." I've had a blast every single time I've played 4e, and PF2e looks like it scratches a similar itch.
Cool. Maybe, we don't have to hear about it in every single thread that isn't about editions; like this one?
 

Celebrim

Legend
Honestly, if the players don't perceive it as punishment, but as a thrill, something they love so much, and will demand... then I think seeing critical hits as a punishment just means you're out of step with your players.

No, I think that as Extra Credits note, humans are just bad at math. A humans objective understanding ("This is bad for me") frequently conflicts with their instinctive desires ("But I like it."). This is not a novel or controversial take.

I have left critical hits in, because I know that the players will demand it and because they are often difficulty to take out of a system that has them written into its assumptions. But the monsters get more joy out of critical hits than the players ever will, to the extent that I explicitly had to create narrative currency and had to make one of things that narrative currency does is transform a critical hit to a non-critical hit to avoid a situation where Raise Dead is the only solution to the problems in the combat system created by the damage spikes of critical hits.

Other solutions to that would be make critical hits basically meaningless (maximum weapon damage, +1d8 damage, etc.), make NPCs and PCs use separate rules, etc.
 

Stormonu

Legend
For me, critical hits are neither reward nor punishment. They’re a tool for drama, in that they shake up the ho-hummedness of predictable odds. A lot of players evaluate their odds on not only the chance of being hit, but how many hits they can take. A critical system messes with that calculation. You can’t plan for it, it happens, and when it happens it tends to swing the encounter in a dramatic fashion.
 

Jack Daniel

dice-universe.blogspot.com
The answer given is "Well, because humans are both great, and terrible, at probability." To expand on this, Extra Credits talks at length about the critical hit mechanic, and how both the mechanics of probability and the perception of probability are very different. 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.

And I thought the conclusion was very helpful indeed: "Remember: clarity when you want your players to think, and obfuscation when you want your players to feel."

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.
 
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Blue

Ravenous Bugblatter Beast of Traal
One point posters here have gotten is that the reward for critical hitting is a critical hit. It doesn't need to have a huge game effect. It feels like a winning lottery ticket. And since player enjoyment is the goal of the game, that's a direct win. The extra damage it does is just an indirect bonus that it does for the character, who winning a combat may or may not also increase player enjoyment.

In other words, if you are measuring the damage of a critical hit, you aren't actually looking at the benefit as players of a game, you are looking at the benefit within the game, which can indirectly also add but that is secondary to the real benefit.
 




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