Choosing Between Two Similar Weapons
Aaedyn1987
Member Posts: 41
Does anyone know of a formula or good way to choose between two similar weapons that factors in THAC0, Damage Range, and Attacks Per Round? I have 2 crossbows that one is 3 attacks per round and one that is two. The 3 per round does 4 - 12 with THAC0 of 7 and the 2 per round does 5-12 with THAC0 of 3. Neither grants any additional bonuses. I would think you could add up the least amount of damage either could do per hit, then factor for To Hit percentage. But, I am a language person, NOT a math person. Thanks in advance.
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I have no math equation for this, but my logic is that with the 7 THAC0 one even though you have more attacks per round you'll also be missing more.
Avg. damage (4+12)/2=8 *3=24 DMG per round vs. Avg. damage (5+12)/2=8.5 *2=17
On AC0 it would be 16,8 damage/round vs. 15,3 damage/round. So the lower the enemies AC, the more useful is better THAC0.
But generally speaking, the extra attack is more useful.
With those stats, you almost have an equilibrium, if the enemy has AC-4. (12dmg/r vs 11,9 dmg/r). And there are not that many enemies out there with such an AC. In BG/SoD at least.
(Hit probability) * (Expected damage per hit) * (Attacks per round)
The hit probability is (21 + AC - THAC0)/20, except that it's always at least 0.05 and at most 0.95 (because of critical hits and misses). The expected damage per hit for a crossbow bolt is (1+8)/2 = 4.5, plus any bonuses you have. In this case you have +2 from proficiencies and +1 from the Light Crossbow of Speed or +2 from the Heavy Crossbow of accuracy, so the expected damage per hit is 7.5 and 8.5, respectively.
Now let's apply this formula to compare fighting a Hobgoblin, Taurgosz Khosann, and Drizz't with these two weapons.
Hobgoblin (AC 7 vs. missiles):
Light Crossbow of Speed - Hit probability is 0.95, so we expect 0.95 * 7.5 * 3 = 21.375 damage per round.
Heavy Crossbow of Accuracy - Hit probability is 0.95. Expect 16.15 damage per round.
Taurgosz (AC -4 vs. missiles):
Light Crossbow of Speed - Hit probability is 0.50. Expect 11.25 damage per round.
Heavy Crossbow of Accuracy - Hit probability is 0.70. Expect 11.9 damage per round.
Drizz't (AC -16 vs. missiles)
Light Crossbow of Speed - Hit probability is 0.05. Expect 1.125 damage per round.
Heavy Crossbow of Accuracy - Hit probability is 0.10. Expect 1.7 damage per round.
As you can see, THAC0 tends to matter more as AC goes down. There are also two other factors to consider here. The first is variance: according to your playing style, you might want a weapon that is more consistent in the amount of damage it does in each round, or you might want one that varies a lot, occasionally doing much more damage. This is more relevant in BG2. The other is that higher APR can be useful in itself, especially against spellcasters; if you're just trying to interrupt casting or get through Mirror Image/Stoneskin/Iron Skins, then the damage per hit doesn't really matter.
TL;DR: Prioritize THAC0 against high-level warriors. Prioritize APR against everyone else.
Generally speaking I would go for THACO over APR any day of the week, except when going up a against Mages when spell interruption is more important than damage infliction (imho) - but you can easily bump up APR with Haste spells or potions.
If in doubt, keep both?