Fun with math and a representative cross-section of weapons, compared at +1, +1 Keen, and +2.
Does “keen” pay?
For “cost” purposes, a Keen weapon is the moral equivalent of adding another +1 enhancement bonus to a magical weapon. A +1 Keen Longsword should therefore be worth about as much as a +2 Longsword. This is per the core DMG.
Let’s see to what degree this holds true. As an experiment, let’s take a lvl2 fighter with a strength of 14 (base attack bonus +2, strength bonus +2) and put a variety of weapons in his hand versus a variety of ACs and see how effective these weapons are over the course of 100 attack actions
Each round a lvl2 fighter with a 14 strength gets one attack at +4. As one would expect, the higher the AC of your opponent, the less damage you are likely to do to it over time. High ACs impact your ability to critical, as they reduce the chance of a threat succeeding (first you must threaten, then the confirmation roll must be adequate to hit). As a result, critical-intensive weapons such as the Scimitar did relatively poorly compared to the trusty Battle Axe and Longsword.
The following tables show the Longsword, Scimitar, Battle Axe, and Heavy Pick (all Medium martial weapons) in the hands of a lvl2 fighter with a 14 strength over the course of 100 attacks against opponents of AC10, AC15, and AC20. All of these numbers are based upon averages, so your results may vary.
Vs AC10
| Longsword | dmg | att | threat | hit | crits | dmg | critdmg | total |
|---|---|---|---|---|---|---|---|---|
| +1 | 1d8+3 | +5 | 10% | 75% | 7.5 | 506.25 | 112.5 | 618.75 |
| +2 | 1d8+4 | +6 | 10% | 80% | 8 | 612 | 136 | 748 |
| +1 Keen | 1d8+3 | +5 | 20% | 75% | 15 | 450 | 225 | 675 |
| Scimitar | ||||||||
| +1 | 1d6+3 | +5 | 15% | 75% | 11.25 | 414.375 | 146.25 | 560.625 |
| +2 | 1d6+4 | +6 | 15% | 80% | 12 | 510 | 180 | 690 |
| +1 Keen | 1d6+3 | +5 | 30% | 75% | 22.5 | 341.25 | 292.5 | 633.75 |
| Battleaxe | ||||||||
| +1 | 1d8+3 | +5 | 5% | 75% | 3.75 | 534.375 | 84.375 | 618.75 |
| +2 | 1d8+4 | +6 | 5% | 80% | 4 | 646 | 102 | 748 |
| +1 Keen | 1d8+3 | +5 | 10% | 75% | 7.5 | 506.25 | 168.75 | 675 |
| Heavy Pick | ||||||||
| +1 | 1d6+3 | +5 | 5% | 75% | 3.75 | 463.125 | 97.5 | 560.625 |
| +2 | 1d6+4 | +6 | 5% | 80% | 4 | 570 | 120 | 690 |
| +1 Keen | 1d6+3 | +5 | 10% | 75% | 7.5 | 438.75 | 195 | 633.75 |
Vs AC15
| Longsword | dmg | att | threat | hit | crits | dmg | critdmg | total |
|---|---|---|---|---|---|---|---|---|
| +1 | 1d8+3 | +5 | 10% | 55% | 5.5 | 371.25 | 82.5 | 453.75 |
| +2 | 1d8+4 | +6 | 10% | 60% | 6 | 459 | 102 | 561 |
| +1 Keen | 1d8+3 | +5 | 20% | 55% | 11 | 330 | 165 | 495 |
| Scimitar | ||||||||
| +1 | 1d6+3 | +5 | 15% | 55% | 8.25 | 303.875 | 107.25 | 411.125 |
| +2 | 1d6+4 | +6 | 15% | 60% | 9 | 382.5 | 135 | 517.5 |
| +1 Keen | 1d6+3 | +5 | 30% | 55% | 16.5 | 250.25 | 214.5 | 464.75 |
| Battleaxe | ||||||||
| +1 | 1d8+3 | +5 | 5% | 55% | 2.75 | 391.875 | 61.875 | 453.75 |
| +2 | 1d8+4 | +6 | 5% | 60% | 3 | 484.5 | 76.5 | 561 |
| +1 Keen | 1d8+3 | +5 | 10% | 55% | 5.5 | 371.25 | 123.75 | 495 |
| Heavy Pick | ||||||||
| +1 | 1d6+3 | +5 | 5% | 55% | 2.75 | 339.625 | 71.5 | 411.125 |
| +2 | 1d6+4 | +6 | 5% | 60% | 3 | 427.5 | 90 | 517.5 |
| +1 Keen | 1d6+3 | +5 | 10% | 55% | 5.5 | 321.75 | 143 | 464.75 |
Vs AC20
| Longsword | dmg | att | threat | hit | crits | dmg | critdmg | total |
|---|---|---|---|---|---|---|---|---|
| +1 | 1d8+3 | +5 | 10% | 30% | 3 | 202.5 | 45 | 247.5 |
| +2 | 1d8+4 | +6 | 10% | 35% | 3.5 | 267.75 | 59.5 | 327.25 |
| +1 Keen | 1d8+3 | +5 | 20% | 30% | 6 | 180 | 90 | 270 |
| Scimitar | ||||||||
| +1 | 1d6+3 | +5 | 15% | 30% | 4.5 | 165.75 | 58.5 | 224.25 |
| +2 | 1d6+4 | +6 | 15% | 35% | 5.25 | 223.125 | 78.75 | 298.875 |
| +1 Keen | 1d6+3 | +5 | 30% | 30% | 9 | 136.5 | 117 | 253.5 |
| Battleaxe | ||||||||
| +1 | 1d8+3 | +5 | 5% | 30% | 1.5 | 213.75 | 33.75 | 247.5 |
| +2 | 1d8+4 | +6 | 5% | 35% | 1.75 | 282.625 | 44.625 | 327.25 |
| +1 Keen | 1d8+3 | +5 | 10% | 30% | 3 | 202.5 | 67.5 | 270 |
| Heavy Pick | ||||||||
| +1 | 1d6+3 | +5 | 5% | 30% | 1.5 | 185.25 | 39 | 224.25 |
| +2 | 1d6+4 | +6 | 5% | 35% | 1.75 | 249.375 | 52.5 | 298.875 |
| +1 Keen | 1d6+3 | +5 | 10% | 30% | 3 | 175.5 | 78 | 253.5 |