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.

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.