Impact of Critical Hits

A little while back, in response to a critical hit rolling snake eyes, my group adopted a house rule as follows:

Instead of rolling dice for damage twice, roll them only once and add the maximum result possible from those dice, example on a critical hit: a d8+2 attack, does 8 + 2 + the result of rolling one eight sided die. This assures that critical hits are impactful, always resulting in more damage than is typically possible. Note: As per RAW, spells that roll a d20 to hit, can critically hit. (Added 11/6/19)

Some things about that rule change are in my mind excellent.  It eliminates the snake eye critical, or more generally all critically that hit for less than a good normal hit.  It also speeds things up by eliminating the need to make extra rolls or borrow dice (though that can be fun too).

While this change has been working fine at our table, I’ve done some web surfing and run across situations where this rule goes wonky and rewards high crit classes/builds at the expense of others, bending the game in unintended ways.

To understand how things go off the rails, first take a reread of the RAW critical hits rule:

When you score a critical hit, you get to roll extra dice for the attack's damage against the target. Roll all of the attack's damage dice twice and add them together. Then add any relevant modifiers as normal.  

Please notice that RAW says to roll ALL of the attacks dice a second time.  It doesn’t allow a normal roll and double the result (which tremendously ups the variance).  But it doubles ALL the dice.  Why is that ALL, which I seem to insist on bolding, important in this context? Because it interacts with this change significantly.

Consider a combatant making a mundane swing with a longsword which might be set to do 1d8+2 (10 max, 6.5 avg, 3 min).  The paladin comes up with a nat 20, a critical hit.  Under RAW, she now does 2d8+2 (18 max, 11 avg, 4 min).  That’s a better shot, but there is a fair chance it’s going to be a disappointment.  My house rule changes the result to 1d8+10 (18 max, 14.5 avg, 9 min).  My change eliminated the chance of a borrowing critical without causing a wild swing in results!

 

Paladin Attacker

Now, what if that combatant was paladin?  After they roll that critical, they add a smite.  Say they burn a 2nd level slot, which will add 3d8 to the attack, which doubles on a critical (smite is part of the attack).

The damage roll will now be 2d8 + 6d8 + 2 (66 max, 38 avg, 10 min). Rolling that many dice strongly favors average results, so it’s reasonable (80%) to anticipate between 30 and 45 damage. 

With my rule the damage becomes 1d8 + 3d8 + 34 (66 max, 52 avg, 38 min). Rolling half as many dice less strongly strongly favors the average, 80% of the time this hit will land for between 46 and 57 damage. 
The rule I am using buffs this Paladin Smite from an average of 38 to 57/  Adding 19 average damage to a critical in this case really increases its damage.

This also highlights the arguably broken nature of smite.  Especially when it can be added to a rolled critical to make it guaranteed damage.

Rogue Attacker

A rogue sneak attack has a similar but not as dramatic effect from sneak attack which adds extra dice to an attack. A sixth level rogue, attacking with a short sword does 4d6 instead of 1d6 of damage.  When that attack critical hits, damage explodes.  With my rule it becomes 4d6 + 24, averaging 38 instead of the 28 by RAW. Adding more that 35% damage on an already devastating attack just gets to be silly.  

Conclusions

Putting a floor under critical hits, especially through a mechanism that eliminates the need to roll extra dice remains attractive to me, but the effect it has on rolls of bunches of dice is just extreme and flies in the face of the theme of bounded accuracy. 

I think my house rule as written is just broken when it approaches corner cases like this. Changing it to max a single die out of the dice rolled for a critical hit would retain the effect my group has seen to date (no rogues or paladins) while reining in the piles of dice that would otherwise be rolled.

Maximizing a single die is a slight to Greatsword and Maul (2d6) and a larger benefit to Great Axe (1d12) than others, so that’s not perfect.  This makes maxing the basic attack dice tempting, but then there are spells like Guiding Bolt that are “to hit” spells and can crit.  Guiding Bolt does 4d6 damage, which quickly heads into the silly range when the first four dice are maximized. 

On balance, I think maximizing one die out of the pile on a critical is preferable as it eliminates the truly awful snake eye critical without making critical damage on average explode.  My proposed rule:

On a critical hit, roll one less die than prescribed by RAW, add the resulting numbers and the maximum from the die not rolled. Example, on a critical hit for a d8+2 attack, 8 + 2 + the result of rolling one eight sided die. Note: As per RAW, spells that roll a d20 to hit, can critically hit.

 

Digression into Probabilities

As more dice are rolled, the odds of getting an extreme result drop sharply.  A single eight sided die comes up with it’s minimum value 12.5%, the same as any other result.  Two d8 have  a 4.75% chance of coming up as 2 or 3 their lowest two about two and a half times less than a 9, their average.  A fist full of d8, define that as 8d8, has a 2.6% chance of totally 8 through 23 and an 18% chance of totally 35 through 36.  The probability curve very strongly favors average results with larger number of dice. 

I found a nifty web page, the Troll dice roller and probability calculator that automatically calculates the probabilities associated with various die distributions.

Digression into Paladin Smite

I used Paladin smite in this post because it is one of the most die heavy attacks that I know of.  It is in fact, seemingly broken, being able to add a smite on a certain critical hit at the cost of a spell slot is a bit absurd.  It doesn’t even cost a bonus action.  The change to my house rule removes my unintended nerf to this damage train wreck, but it remains a huge source of free damage, seemingly well out of bounds of the remainder of the game. 

I came across an article on Hispters & Dragons, Paladins’ Divine Smite Overpowered? The author of that article discusses the topic at length and proposes what seems like a reasonable fix, making smite a spell as follows:

Divine Smite
1st-level evocation

Casting Time: 1 bonus action

Range: Self

Components: V

Duration: Concentration, up to 1 minute

Appealing to your god’s anger, you channel their divine wrath into your weapon. The first time you hit a creature with a melee weapon attack during this spell’s duration your attack deals an extra 2d8 radiant damage to the target. The damage increases by 1d8 if the target is an undead or a fiend.
At Higher Levels. When you cast this spell using a spell slot of 2nd level or higher, the extra damage dealt by the attack increases by 1d8 for each slot above 1st level.

The topic is currently largely moot in my campaign, but it is something to think about.