How Often Do Critical Hits Underperform?

Critical Hits are often the subject of homebrew rules. Driven by the perception that critical hits frequently underperform, these homebrew rules juice up the damage of critical hits to a more impressive level. They’re often implemented after a player waits 20 rolls (on average) to score a critical hit that lands with a thud. But, is this underperformance a reflection of perception or reality?

Critical Hit Homebrews

Whereas a normal critical hit deals twice the damage dice, these homebrew rules can improve it as follows:

  • Roll one damage die. Add the maximum face value instead of rolling again.
  • Roll one damage die. You can choose to double that die or roll a second die.
  • Roll two damage die. Take the higher of the result or the maximum face value.

Since all these homebrew suggestions increase the damage output of critical hits, we can infer that players making these changes feel that critical hits are underpowered.

The Numbers

Do these perceptions jive with reality? In order to determine the origin of this perception, let’s run some numbers and see how often it really happens.

Critical Odds

How often does a critical hit fail to outperform a normal hit?

In order to determine how often a critical hit fails to outperform a normal hit, we need to know how often it deals equal or less damage. So, for each face of the regular die roll, we need to know how often the critical hit has an equal or smaller result. Then we add all those together and get the total odds.

As it turns out, the odds of a normal die roll being equal or better than a critical hit lies somewhere between 6% and 17%. While not impossible, this does seem to be too seldom an occurrence to spur a rules change at the table. While we shouldn’t discount human’s notoriously poor ability to judge randomness, there must be a different factor at play.

How often does a critical hit do less damage than a max roll?

It seems this perception truly arises from rolling critical hits that are worth less than the face value of the damage die. Psychologically, we think that the critical hit should do more damage than a normal hit could possibly do. In order to satisfy this perception, we need at least an average roll for critical damage. Yet, we can only roll more than the face value of the damage less than half the time, with some variance depending on the size of die we’re rolling.

Indeed, the odds of a critical roll being equal or less than the max value of a regular roll is quite frequent: between 33% and 46% of the time. It seems much more likely that players would feel compelled to homebrew a rule that was leaving them dissatisfied between 1/3 to 1/2 the time.

Perception vs. Reality

Unfortunately, perception can be reality. Often in TTRPGs, the feel of a design matters much more than how the numbers really shake out. So, telling your players just to “get over it” because their critical hits are only really underperforming about 1/6 of the time probably isn’t going to leave them satisfied. Their expectations are based on the face value of the dice, not the actual odds of a critical hit underperforming. If that’s the case, try out one of the homebrew rules above.

4 thoughts on “How Often Do Critical Hits Underperform?

  1. Thank you for the great article. I think most of the players having issue with weak critical hints in 5E are due to the perception that a crtiical hint must deliver more damage than maximum normal attack. I believe that this perception issue is legit and there has to be way to satisfy these players.

    The homebrew rules are interesting approaches and are completely new to me, never heard of them before. They seem to have many problems with player optimization of loading critical hints with abilities that add attack damage and this would be broken if all dice added their face value etc. A fourth proposal I am playing with is.

    Roll all of the attack’s damage dice twice and add them together.Then you may reroll each weapon die and choose between the old or the new result. Extra damage dice cannot be rerolled.

    This seems to make a subtle improvement targeted at weapons dice, doesn’t affect loaded extra damage, and the more weapon dice the attack has the more likely to deliver doubled above average, which is more than a maximum attack – the golden zone for most players.

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  2. I’m curious to know how the average damage output of a RAW critical hit compares to that of each of the above homebrew options. A table like the above with those numbers would be a great addition to this article

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  3. I’ve always maximized one of the dice of a critical just to ensure they don’t end up doing less than a normal hit. Natural 20s should feel good, especially in combat. However, that means that the monsters’ crits hurt worse as well.

    Also, to balance this out, I make exact hits on a target’s AC “glancing blows” that deal half damage.

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