Critical Hit Calculation variations.

[BGGCriticalMass]

Hi all. It seems like critical hit damage is calculated a number of different ways.

The most common approaches seem to be:
Roll damage dice then double the result - quicker in real life / needs less dice
Roll twice as many damage dice - more varied results but probability skews strongly towards the average result.

Some house rules exist for critical hits:
Roll damage dice then add the maximum for additional critical hit damage - triples the average damage of a critical hit compared to a normal hit (usually criticals have double the average using either above method) Minimum critical hit damage is just over double the average of a normal hit
Maximum damage dice instead of rolling but no additional dice used - predictable consistent result that is double the average damage of a normal attack (or very nearly) but half the maximum possible damage for a critical hit done in other ways.

It seems like homebrew rules for crits were mostly made to eliminate the critical hit that does less damage than an average hit because of low rolls or to make critical hits into epic badass moments.
What system do you use?
What are the advantages and disadvantages of the systems available?

[BurgerBeast]

I played in group with three DMs (I was one of them) and I realized that both of them the other DMs preferred to use max damage for the first di(c)e and roll the second di(c)e.

I had the same concern that you raised: this is a massive increase in damage (closer to triple instead of double, on average). But all three DMs held the other concern that you mentioned: we didn’t like critical hits to do less damage than some normal hits.

We eventually agreed that our solution would be to roll all dice, but that any critical hit would do minimum damage of (maximum normal hit) +1.

So if an attack does 2d6+3 damage, then on a crit you would roll 4d6+3, and treat any roll result less than 16 as 16.

[BGGCriticalMass]

Thanks for sharing that approach. I think it solves the disappointment of low roll crits but avoids the issue of massively dangerous inflated enemy crits.

[MrStabby]

A minor point 2*d6 damage has greater variance than d6+d6 damage.

I find the double the number of dice approach is good. It makes exceptional rolls unlikely, terrible rolls unlikely whilst still retaining the excitement of some uncertainty. As a DM I don't want an encounter ended by a lucky roll on either side.

[BloodSnake'sCha]

I played in group with three DMs (I was one of them) and I realized that both of them the other DMs preferred to use max damage for the first di(c)e and roll the second di(c)e.

I had the same concern that you raised: this is a massive increase in damage (closer to triple instead of double, on average). But all three DMs held the other concern that you mentioned: we didn’t like critical hits to do less damage than some normal hits.

We eventually agreed that our solution would be to roll all dice, but that any critical hit would do minimum damage of (maximum normal hit) +1.

So if an attack does 2d6+3 damage, then on a crit you would roll 4d6+3, and treat any roll result less than 16 as 16.
May I steal it?

[Imbalance]

Right now it's damage rolled x2 + mods, but I, too, am keen to overcome that sense of disappointment when the dice are weak. My last group favored a crit hit/miss deck of cards that would describe additional effects, which was often a lot of fun until your character was on the receiving end of something like three days of str damage or a fumble whilst fighting a wind elemental that sends your +2 dragon sword plummeting into a bottomless chasm. On the other hand, it was totally balanced when you've caused the dragon spinal damage that renders him unable to fly.

I've thought about the numbers, and I may use some of the approaches mentioned above to increase the resulting damage dealt, but I more want to take those cards as RP inspiration and make crits less about the numbers and more about something distinct happening during the course of actions. When they happen, it shouldn't only be exciting for the table, it should get the attention of the characters in the story. I'm not sure about fumbles, maybe for sparing use when it isn't detrimental, but a crit miss on either side while fighting orcs should result in a round of uproarious laughter and mockery, for example. An enemy should change tactics after receiving a doubly powerful strike, and may become more inclined to flee when below half hp. Crits on spells that use attack rolls should definitely do something extra, like the sudden knotting of the weave that is visible to all and causes distortions in the nearby environment, leaving a local patch of difficult terrain beneath the target's feet. I'm more inclined to improvise on the fly than just use the cards myself, because the random effects sometimes were inapplicable. While I strive for consistency, I also want to ensure that something always happens when the dice go to extremes.

These were just some ideas that were bouncing around, and I'm pretty sure they were inspired by other suggestions I have read from folks that have been doing this a long time. I feel like they are good tools to have on hand and employ to enhance the story as needed when crunching higher numbers is a less interesting option.

[PhantomSoul]

We use maximum damage on all dice + extra roll for the weapon/main damage dice, so if you're using a shortsword (1d6) with +3 from Dex and +2d6 from Sneak Attack, you maximise all of it (6+3+12) and then roll the weapon die (1d6), getting you 1d6+21. It's always higher than the best you could've rolled without a crit, but slightly tempered (smites, sneak attack, hex, and all other bonuses aren't being tripled, which also makes the difference between a flat bonus and a rolled bonus bigger)

[TurboGhast]

I've been using "Critical hits are double damage". The primary advantage this has over the other methods described here is that it's really simple and fast to apply, preventing gameplay from being slowed down by crit damage calculations. However, the only protection this system provides against a weak critical is doubled static damage.

Since gameplay calculation speed doesn't really matter to the flow of a play by post game, the primary advantage of this system doesn't exist there. I'm probably going to try out one of the other crit rules in this thread next time I DM a 5e PbP game to see if I like them enough to use them in an in-person game.

[Shabbazar]

I like the current critical hit system for regular normal critical hits in combat. What I don't like is the use of a critical hit as applied to unconscious/paralyzed/incapacitated/held creatures. I think creatures in those states are far more vulnerable than the critical hit system imposes on them.

I think there was something back in AD&D that said sleeping creatures could have their throats slit with instant death ensuing at the rate of one creature per round. I'm not sure where I got that from, but it must have been something formal since that rule seemed pretty widespread back in the day. That's kind of a rough rule when applied to the PCs, but most parties were pretty adept at rotating watch, etc.

I'm getting back into DMing and I will have to decide how to deal with this. Maybe something like triple max damage for creatures that can't move or defend themselves in any way. But that still doesn't address the fact that a crossbow bolt to the forehead from 3 feet away should kill just about every helpless humanoid.

[BloodSnake'sCha]

I like the current critical hit system for regular normal critical hits in combat. What I don't like is the use of a critical hit as applied to unconscious/paralyzed/incapacitated/held creatures. I think creatures in those states are far more vulnerable than the critical hit system imposes on them.

I think there was something back in AD&D that said sleeping creatures could have their throats slit with instant death ensuing at the rate of one creature per round. I'm not sure where I got that from, but it must have been something formal since that rule seemed pretty widespread back in the day. That's kind of a rough rule when applied to the PCs, but most parties were pretty adept at rotating watch, etc.

I'm getting back into DMing and I will have to decide how to deal with this. Maybe something like triple max damage for creatures that can't move or defend themselves in any way. But that still doesn't address the fact that a crossbow bolt to the forehead from 3 feet away should kill just about every helpless humanoid.

coup de grâce
Older editions did had rules for it. The one from 3.5e gave the creature a save based on a crit from the weapon that was use for the death blow.

[stoutstien]

I just use max damage of die or dice vs rolling any additional ones. 20d6 on a sneak attack crit seems like a pain to add up

[Shabbazar]

coup de grâce
Older editions did had rules for it. The one from 3.5e gave the creature a save based on a crit from the weapon that was use for the death blow.

I like the save idea. There was no save IIRC in AD&D and I am returning now to 5E not having experienced any of the systems in between.

Occasionally one reads about a guy shot in the forehead where the bullet skims around the skull underneath the skin and exiting out the back. Looks like the guy got his brains blown out, but only superficial damage has occurred. So stuff like that happens and a save seems a good way to represent that.

[BurgerBeast]

May I steal it?

Yes, of course.

[malachi]

My DM allows players (before they roll damage dice) to decide whether to roll 2x dice or to double the result of the dice. When my rogue gets sneak attack with booming blade, I just double the result of the dice (because it takes too long to count it up otherwise), but otherwise I'll roll twice the dice.

For exactly one session, he ran crits as "max dmg of normal roll + one additional roll + static mods". Then he critted too many times on the PCs and switched back. Which is exactly the result that I told him...


I'm thinking about DMing a game, and deciding to add special effects to each crit based on what type of damage was dealt (and allowing save effects to crit on a nat 1), but I'm struggling to figure out something that is roughly equal (and logical) for each damage type and that also scales.

For instance, it's easy to say that a crit with psychic dmg should cause disadvantage for attacks for one round. But it seems like slashing, piercing, and fire should deal some amount of extra damage - how much balances out with effects that are close to losing a turn? (This is mostly my thought process, not something I'm specifically asking for help with).

[Keravath]

Rules wise, RAW, criticals require rolling all the dice twice and adding static modifiers once. It requires rolling more dice but works pretty well in my experience.

Sometimes, there are good rolls, sometimes bad but in the end it all equals out. I've never played where a crit does max damage since if you do max damage on doubled dice then crits are very powerful - especially if you add smites or sneak attacks - while max damage on one set of dice just gives the average value of the rules way of calculating crits so there is no possibility of exceptional damage. It can be disappointing when a crit does less damage than a non-crit could have but I haven't found that to be much of an issue ... just luck of the die roll.

[PhoenixPhyre]

Rules wise, RAW, criticals require rolling all the dice twice and adding static modifiers once. It requires rolling more dice but works pretty well in my experience.

Sometimes, there are good rolls, sometimes bad but in the end it all equals out. I've never played where a crit does max damage since if you do max damage on doubled dice then crits are very powerful - especially if you add smites or sneak attacks - while max damage on one set of dice just gives the average value of the rules way of calculating crits so there is no possibility of exceptional damage. It can be disappointing when a crit does less damage than a non-crit could have but I haven't found that to be much of an issue ... just luck of the die roll.

I agree with this, although one pedantic note:

Max of dice is actually lower than the average of doubled dice. Take for example, a shortsword with no modifier.
Normal: 1d6, average 3.5
Max: 6
Doubled dice: 2d6, average 7

A greatsword (2d6):
Normal: 2d6, average 7
Max: 12
Doubled dice: 4d6, average 14

It comes down to 1 point of damage less for every die in the original damage roll. That's equivalent to losing an entire dice size (1d8 -> 1d6).

[J-H]

The houserule generally used at the FLGS, which I go by, is that you roll for damage, and then add your maximum possible damage on top of that. I guess that's about 33% more than you'd get if you just rolled for damage, but nobody seems to mind. Crits should be fun.

[Imbalance]

Another reason I'm somewhat hesitant to blow the damage number up is because a crit also represents, to me, the chance to turn impossible odds into a guaranteed hit or miss in dramatic fashion. Even if the target's AC is astronomical (as much as it can be, bounded and all), and the attacker, for some reason, cannot mathematically hit, the crit hit means there is still a chance and removes impossible from the factoring. Reciprocally, a crit miss is that lingering possibility that even when all the stars are aligned, the mods are stacked, and every advantage taken, as the dust settles the attacker finds their weapon plunged deep into the plank just shy of its mark. Yeah, longshots and outliers, but coming from other games, I dig it.

[El_Jairo]

I like the current critical hit system for regular normal critical hits in combat. What I don't like is the use of a critical hit as applied to unconscious/paralyzed/incapacitated/held creatures. I think creatures in those states are far more vulnerable than the critical hit system imposes on them.

I think there was something back in AD&D that said sleeping creatures could have their throats slit with instant death ensuing at the rate of one creature per round. I'm not sure where I got that from, but it must have been something formal since that rule seemed pretty widespread back in the day. That's kind of a rough rule when applied to the PCs, but most parties were pretty adept at rotating watch, etc.

I'm getting back into DMing and I will have to decide how to deal with this. Maybe something like triple max damage for creatures that can't move or defend themselves in any way. But that still doesn't address the fact that a crossbow bolt to the forehead from 3 feet away should kill just about every helpless humanoid.
I would avise to use the 3.5 Coup de Grace rules for killing off helpless creatures.

Link to Helpless Defenders in 3.5 (https://www.dandwiki.com/wiki/SRD:Helpless_Defenders)
TLDR: Coup de Grace is a full turn action and grants an auto Critical Hit. If the target didn't die from the damage it needs to pass a DC (10+ damage dealt) Constitution Save to avoid dying. Maybe base DC should be brought down to 8 because of the hard capping on saves and the likes.
Sneak Attack bonus does apply.

Yet if we consider d8 to be an average weapon to be used with a +3 dmg mod, the average DC would be 17 with base 10 and 15 with base 8.
So it is clear that characters who have bigger damage potential will be able to make that DC almost impossible to pass.

I like this rule because it leaves room for epic creatures to survive a Coup de Grace while most minor creatures will die on the spot.

[El_Jairo]

Rules wise, RAW, criticals require rolling all the dice twice and adding static modifiers once. It requires rolling more dice but works pretty well in my experience.

Sometimes, there are good rolls, sometimes bad but in the end it all equals out. I've never played where a crit does max damage since if you do max damage on doubled dice then crits are very powerful - especially if you add smites or sneak attacks - while max damage on one set of dice just gives the average value of the rules way of calculating crits so there is no possibility of exceptional damage. It can be disappointing when a crit does less damage than a non-crit could have but I haven't found that to be much of an issue ... just luck of the die roll.

I also quite like the critical hit ruling as it is. People complain when they roll low but that's just some good RNGezus which makes for great story telling opportunities.
You can critically hit your foe, but with the blunt side of your sword, that unlucky and lucky at the same time. These things are rare and if your character has this happen more than once, it could become a defining description of the character.

In regards of extra effects on a crit, based on the damage type: I would avise to go look at the critical hit tables in Mordheim, or the 40k RPG's which had a stacking critical hit total. Which started to accumulate when dropped below 0 HP or when a critical hit was scored. Fire is like energy damage, that burns of limbs. Slashing weapons, dismember and let you bleed out. Piercing weapons can go through one target and damage the next in line, or ricochet on missile weapons.
Bludgeoning can push creatures back, thunder will stun and/or deafen the target,...

Typically you can set up a d6 table with incremental bonus to the critical hit damage.

You can make it as complex as you want, yet what I like about 5e the most is that the mechanics are quite simply, almost never punishing and leave most up to the cooperative story telling of the players and DM.
So I would advice to roll for an extra effect but don't have the effect to pre-determined, so you can adapt to each situation.

[El_Jairo]

The houserule generally used at the FLGS, which I go by, is that you roll for damage, and then add your maximum possible damage on top of that. I guess that's about 33% more than you'd get if you just rolled for damage, but nobody seems to mind. Crits should be fun.

Let's calculate the bonus actually for a d6 weapon.

So normal rule is 2d6 rolled, with an median of 7, with expected min at 4 and max at 10.
If you have 6 + d6: median becomes 9,5, with min and max expected 8-11.

So median increases by 35% minimum by 100% and max by 10%. Which makes critical hits far more reliably to do more damage than normal hits and still not increase the maximum damage potential.

[NNescio]

Let's calculate the bonus actually for a d6 weapon.

So normal rule is 2d6 rolled, with an median of 7, with expected min at 4 and max at 10.
If you have 6 + d6: median becomes 9,5, with min and max expected 8-11.

So median increases by 35% minimum by 100% and max by 10%. Which makes critical hits far more reliably to do more damage than normal hits and still not increase the maximum damage potential.

You don't want to calculate the median. You want to calculate the mean, i.e., the expected value because it gives you the average value of repetitive dice rolls over the long run (which is how you calculate average damage). Median (and quartiles and percentiles) is for things with a binary outcome like Sleep. Or percentages of things that get 1HKO by an attack or other source of damage (again, binary).

For symmetric discrete distributions the median(s) is usually close to the mean, but there can be subtle differences.

(The results of damage dice in isolation follow symmetric discrete distributions, assuming fair dice. But they are no longer symmetric once you factor things that modify the roll, like Elemental Adept. Things like AC (misses deal effectively zero damage) and crits also 'modify' the damage roll, in a way.)

2d6 has a mean (i.e. expected value) of 7, a minimum of 2 and a maximum of 12. There is no such thing as an "expected minimum". The standard deviation is approximately 2.42. The median, in this case, is also 7, identical to the mean.

1d6 + 6 has a mean of 9.5, a minimum of 7 and a maximum of 12. The standard deviation is approximately 1.71. (that is, there is less variation compared to the 2d6 distribution). The medians, in this case, are 9 and 10, not 9.5.

(Because P(X ≤ 9) ≥ 50% and P(X ≥ 9) ≥ 50% , and also P(X ≤ 10) ≥ 50% and P(X ≥ 10) ≥ 50%, which is exactly how the median is defined for discrete random variables. The median is not necessarily unique, especially for discrete distributions.)

(Edit: The high school math definition of a median is different, because it uses the definition of the median of a set of numbers, not the median of a probability distribution. Dice rolls are probability distributions, so we use the latter.)

[Darkstar952]

I would avise to use the 3.5 Coup de Grace rules for killing off helpless creatures.

Link to Helpless Defenders in 3.5 (https://www.dandwiki.com/wiki/SRD:Helpless_Defenders)
TLDR: Coup de Grace is a full turn action and grants an auto Critical Hit. If the target didn't die from the damage it needs to pass a DC (10+ damage dealt) Constitution Save to avoid dying. Maybe base DC should be brought down to 8 because of the hard capping on saves and the likes.
Sneak Attack bonus does apply.

Yet if we consider d8 to be an average weapon to be used with a +3 dmg mod, the average DC would be 17 with base 10 and 15 with base 8.
So it is clear that characters who have bigger damage potential will be able to make that DC almost impossible to pass.

I like this rule because it leaves room for epic creatures to survive a Coup de Grace while most minor creatures will die on the spot.

All of that may sound OK from the point of view of players doing it, but how would it feel if they got totally TPK'd on the first round of a combat by the BBEG upcasting hold person and then the minions rushing in and Coup de Grace all of the held characters.

Paralysis and the current autocrits are often punishing enough given multi-attack, adding in an autokill would just blow everything else out of the water.

[Keravath]

The houserule generally used at the FLGS, which I go by, is that you roll for damage, and then add your maximum possible damage on top of that. I guess that's about 33% more than you'd get if you just rolled for damage, but nobody seems to mind. Crits should be fun.

The FLGS's I play at usually just use RAW since they are often running Adventurer's League games. I'm guessing your FLGS doesn't run AL then?

[J-H]

Nobody there has ever uttered the phrase "Adventurer's League" in my hearing.