DnD3 Attacks 2
another look at criticals
In D&D 3e, there are three possible results when swinging your weapon at a foe. You either miss, hit, or score a critical hit. Which result you get depends on one or two rolls of a d20, how high you need to roll, and the critical threat range of your weapon.
When crunching numbers, people often omit the critical hit part. I'm not sure whether that's done because people think it's insignificant or because they think it's hard to compute, or for some other reason. Regardless, I say it's both significant and easy to compute.
Significant
If you assume a 50% hit rate, then your average damage per round is half your average weapon damage. In other words, a damage factor of 0.5. However, this ignores the 2.5% crit rate that accompanies a 50% hit rate for a threat 20 weapon.Including the crit rate for a ×2 weapon yields a damage factor of 0.5 + 0.025 = 0.525. That's 5% more damage than without the critical hits. In case of a ×3 weapon, it would be 0.5 + 0.025 × 2 = 0.55. That's 10% more damage, nothing to ignore. For a 19–20/×2 weapon, it's 0.5 + 0.05 = 0.55, once again 10% more damage.
Easy
You have a 50% hit rate if you need to roll at least an 11 with your d20, regardless which modifiers get applied afterwards. But if you need at least a 12 instead, your hit rate becomes 45%. With each extra point needed to hit, the hit rate decreases by 5%, and vice versa. This is the fundamental math of a d20 roll.Critical hits are another d20 roll on top of that. The difference is that the starting point and steps have different odds. Which odds you need to use depends on the threat range of the wielded weapon.
Beyond that, there is one extra thing you need to keep in mind. A threat range only matters if the attack is a hit. For example, if you need to roll at least a 19 to hit, then any threat range greater than 19–20 functions like it was only 19–20.
| threat | 11 needed | step size | up to |
|---|---|---|---|
| 20 | 2.5% | 0.25% | 20 |
| 19–20 | 5.0% | 0.50% | 19 |
| 18–20 | 7.5% | 0.75% | 18 |
| 17–20 | 10.0% | 1.00% | 17 |
| 15–20 | 15.0% | 1.25% | 15 |
| 12–20 | 22.5% | 2.25% | 12 |
| needed | 20 | 19–20 | 18–20 | 17–20 | 15–20 | 12–20 |
|---|---|---|---|---|---|---|
| 2 | 4.75% | 9.50% | 14.25% | 19.00% | 28.50% | 42.75% |
| 3 | 4.50% | 9.00% | 13.50% | 18.00% | 27.00% | 40.50% |
| 4 | 4.25% | 8.50% | 12.75% | 17.00% | 25.50% | 38.25% |
| 5 | 4.00% | 8.00% | 12.00% | 16.00% | 24.00% | 36.00% |
| 6 | 3.75% | 7.50% | 11.25% | 15.00% | 22.50% | 33.75% |
| 7 | 3.50% | 7.00% | 10.50% | 14.00% | 21.00% | 31.50% |
| 8 | 3.25% | 6.50% | 9.75% | 13.00% | 19.50% | 29.25% |
| 9 | 3.00% | 6.00% | 9.00% | 12.00% | 18.00% | 27.00% |
| 10 | 2.75% | 5.50% | 8.25% | 11.00% | 16.50% | 24.75% |
| 11 | 2.50% | 5.00% | 7.50% | 10.00% | 15.00% | 22.50% |
| 12 | 2.25% | 4.50% | 6.75% | 9.00% | 13.50% | 20.25% |
| 13 | 2.00% | 4.00% | 6.00% | 8.00% | 12.00% | 16.00% |
| 14 | 1.75% | 3.50% | 5.25% | 7.00% | 10.50% | 12.25% |
| 15 | 1.50% | 3.00% | 4.50% | 6.00% | 9.00% | 9.00% |
| 16 | 1.25% | 2.50% | 3.75% | 5.00% | 6.25% | 6.25% |
| 17 | 1.00% | 2.00% | 3.00% | 4.00% | 4.00% | 4.00% |
| 18 | 0.75% | 1.50% | 2.25% | 2.25% | 2.25% | 2.25% |
| 19 | 0.50% | 1.00% | 1.00% | 1.00% | 1.00% | 1.00% |
| 20 | 0.25% | 0.25% | 0.25% | 0.25% | 0.25% | 0.25% |
Threat ranges
Using this AnyDice program – modified from a previous post – you can get a better look at the individual threat ranges. Horizontally we have the d20 result needed to hit, vertically the odds to get a miss (0), a normal hit (1), and a critical hit (2).Threat 20
Needing an 11 to hit corresponds with a 50% hit rate. In that case you crit 2.5% of the time, the remaining 47.5% will be normal hits. For each extra point you need to hit, the crit rate drops by 0.25%, and vice versa. So when needing a 16 (25% hit rate), your crit rate is 1.25%.
Threat 19–20
In this case a 50% hit rate corresponds with a 5% crit rate, adjusted 0.5% per step. So it's simply hit rate divided by ten. The exception is when you need a 20 to hit, in which case the crit rate drops to 0.25%. This is because an increased threat range is meaningless at that point.
Threat 18–20
A 50% hit rate means a 7.5% crit rate, adjusted 0.75% per step. The crit rate drops to 1% when you need a 19 to hit, as it effectively functions like threat 19–20 at that point. For the same reason it drops to 0.25% once you need a 20 to hit.
Threat 17–20
50% to-hit gives you 10% to-crit, adjusted 1% per step, so it's your hit rate divided by five. Once again crit rate deteriorates if you need to roll above the minimum threat to hit at all.
Ways to boost a 19–20 threat weapon to 17–20 include the Keen Edge spell, the Keen weapon enhancement, and the Improved Critical feat.
Threat 15–20
At this point 50% to-hit gets you 15% to-crit, adjusted 1.25% per step. Threat decline sets in once you need a 16 or higher to hit.
This is the domain of threat-enhanced falchions, kukris, rapiers, and scimitars. Possibly "double-keened" swords too, if that is allowed.
Threat 12–20
By now a 50% hit rate gives you a 22.5% crit rate, adjusted 2.25% per step up to requiring a 12 to hit. Lots of your hits are crits at this point, but as soon as you need a 15 or higher to hit, it's no better than threat 15–20.
You can only get here with "double-keened" rapiers and the like, which is usually not allowed.
Other treat ranges
The above threat ranges are the most common. You can use the previously mentioned AnyDice program to compute any other treat range you like. Just for fun, here's the graph for threat 2–20.
You can't get a better threat range than this!