New Critical Hits
Traditional D&D combat is slow, and one of the causes is separate to-hit and damage rolls. We could eliminate to-hit rolls, but that’s a very different game. A common house rule is to make both rolls at once, but it’s hard to change ingrained habits. So what if there was motivation for players to remember?
Goofus makes everyone wait while he looks up a rule. Gallant has already rolled his to-hit and damage dice. Apologies to Marion Hull Hammel.
Instead of a critical hit occurring on a to-hit roll of 20, any roll of maximum damage hits automatically. This naturally incentivizes players to remember to roll both to-hit and damage at the same time. But does it really change the math that much?
The Math
Let’s assume a 5e baseline and take care of a few corner cases:
- Mauls and greatswords both deal 2d6 damage. Requiring boxcars for a critical hit makes these weapons immediately worse than their 1d12 counterparts, but requiring only one six is much more interesting.
- Blowguns don’t roll damage, so they’re excluded from this rule. If you want to hit with a blowgun, you’ll have to roll to hit.
- For simplicity, I have created “DC” as the difference of Armor Class and Attack Bonuses, rather than considering them separately.
- As a result of this flattening, it’s impractical to consider damage roll modifiers.
- I am disregarding “critical misses” in this analysis. I just don’t think they’re very exciting. So if you roll a 1 to-hit and maximum damage, then you still automatically hit.
- I’m also disregarding critical hit damage multipliers. You’re always going to roll the same number of dice and the value of a critical hit is that it bypasses AC.
The calculations here are relatively straightforward. The odds of a successful hit under this new regime are
where is the number of sides of the damage die. Similarly, the expected damage roll is
where is the expected value of a non-maximum damage roll. Working out these numbers give us the following table:
| Std | 1d4 | 1d6 | 1d8 | 1d10 | 1d12 | 2d6 | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| DC | Odds | Odds | Dmg | Odds | Dmg | Odds | Dmg | Odds | Dmg | Odds | Dmg | Odds | Dmg |
| 1 | 100% | 100% | 2.50 | 100% | 3.50 | 100% | 4.50 | 100% | 5.50 | 100% | 6.50 | 100% | 7.00 |
| 2 | 95% | 96% | 2.43 | 96% | 3.38 | 96% | 4.32 | 96% | 5.28 | 95% | 6.23 | 97% | 6.79 |
| 3 | 90% | 93% | 2.35 | 92% | 3.25 | 91% | 4.15 | 91% | 5.05 | 91% | 5.95 | 93% | 6.58 |
| 4 | 85% | 89% | 2.28 | 88% | 3.13 | 87% | 3.98 | 87% | 4.83 | 86% | 5.67 | 90% | 6.38 |
| 5 | 80% | 85% | 2.20 | 83% | 3.00 | 83% | 3.80 | 82% | 4.60 | 82% | 5.40 | 86% | 6.17 |
| 6 | 75% | 81% | 2.13 | 79% | 2.88 | 78% | 3.63 | 78% | 4.38 | 77% | 5.13 | 83% | 5.96 |
| 7 | 70% | 77% | 2.05 | 75% | 2.75 | 74% | 3.45 | 73% | 4.15 | 73% | 4.85 | 79% | 5.75 |
| 8 | 65% | 74% | 1.98 | 71% | 2.63 | 69% | 3.28 | 69% | 3.93 | 68% | 4.58 | 76% | 5.54 |
| 9 | 60% | 70% | 1.90 | 67% | 2.50 | 65% | 3.10 | 64% | 3.70 | 63% | 4.30 | 72% | 5.33 |
| 10 | 55% | 66% | 1.83 | 63% | 2.38 | 61% | 2.93 | 60% | 3.48 | 59% | 4.03 | 69% | 5.13 |
| 11 | 50% | 63% | 1.75 | 58% | 2.25 | 56% | 2.75 | 55% | 3.25 | 54% | 3.75 | 65% | 4.92 |
| 12 | 45% | 59% | 1.68 | 54% | 2.13 | 52% | 2.58 | 51% | 3.03 | 50% | 3.47 | 62% | 4.71 |
| 13 | 40% | 55% | 1.60 | 50% | 2.00 | 48% | 2.40 | 46% | 2.80 | 45% | 3.20 | 58% | 4.50 |
| 14 | 35% | 51% | 1.53 | 46% | 1.88 | 43% | 2.22 | 42% | 2.58 | 40% | 2.93 | 55% | 4.29 |
| 15 | 30% | 48% | 1.45 | 42% | 1.75 | 39% | 2.05 | 37% | 2.35 | 36% | 2.65 | 51% | 4.08 |
| 16 | 25% | 44% | 1.38 | 38% | 1.63 | 34% | 1.88 | 33% | 2.13 | 31% | 2.38 | 48% | 3.88 |
| 17 | 20% | 40% | 1.30 | 33% | 1.50 | 30% | 1.70 | 28% | 1.90 | 27% | 2.10 | 44% | 3.67 |
| 18 | 15% | 36% | 1.23 | 29% | 1.38 | 26% | 1.53 | 24% | 1.68 | 22% | 1.83 | 41% | 3.46 |
| 19 | 10% | 33% | 1.15 | 25% | 1.25 | 21% | 1.35 | 19% | 1.45 | 18% | 1.55 | 38% | 3.25 |
| 20 | 5% | 29% | 1.08 | 21% | 1.13 | 17% | 1.18 | 15% | 1.23 | 13% | 1.28 | 34% | 3.04 |
In this table, “Std” refers to the odds of a hit using the current (standard) scheme, and as indicated earlier, the average damage roll (“Dmg”) does not include additional bonuses. You can see that while odds to hit generally go up across the board, along with expected damage dice, not overwhelmingly, until a larger disconnect at higher AC.
This system has a couple interesting side-effects. It encourages less martial characters to use smaller weapons without any system of proficiencies or other penalties. And for higher-level monsters, it prioritizes HP over AC. I think this is promising and I’ll try it next time I get the chance.