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General Tabletop Discussion
*Pathfinder & Starfinder
Weapon Balance - A Statistical Analysis
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<blockquote data-quote="Alex319" data-source="post: 4447960" data-attributes="member: 45678"><p>First of all, the highest AC you can get at 30th level is far more than 35. At 30th level you can have +6 godplate armor (total AC bonus 14+6=20), combined with the 10 base and 15 from level gives 45, and that's not even counting a shield or feats like Armor Specialization and Two-Weapon Defense. But this is a secondary point of relatively minor concern to the overall analysis.</p><p> </p><p>First of all, I explained a couple posts up about why offensive bonuses are in general better than defensive bonuses, which is why an extra +1 to attack is worth about 1.2 points of [W] while an extra +2 to AC/Reflex is worth far less than 2.4 points of [W]. (And don't forget that an extra +2 to AC/Reflex is worth nothing if an enemy targets your Fortitude or Will defense.) But in order to address the relationship between attack rolls and damage rolls, let's compare the effectiveness of a longsword (+3 prof, 1d8 damage) and warhammer (+2 prof, 1d10 damage). </p><p></p><p>A good way to think of this is in terms of "expected damage per round." This is the probability the attack will hit times the expected damage if it does hit. Also note that the expected damage includes both the damage from the weapon and any damage bonuses (from attributes, magic weapons, feats, powers, etc.)</p><p></p><p>So our formula is:</p><p></p><p><strong>Expected Damage = H*(XW+B)</strong></p><p><strong></strong></p><p><strong></strong>where H is the hit probability, X is the number of [W] the power has, and B is any bonuses to damage or additional damage other than the [W].</p><p></p><p>So suppose that the probability of hitting is 0.5 with the warhammer, and so it is 0.55 with the longsword. We want to see under what conditions the longsword and warhammer will have an equal amount of damage per round.</p><p></p><p><strong>Expected Damage from Warhammer = 0.5*(5.5X + B)</strong></p><p><strong>Expected Damage from Longsword = 0.55*(4.5X + B)</strong></p><p><strong></strong></p><p><strong></strong>Setting these equal we get:</p><p></p><p><strong>0.5*(5.5X+B) = 0.55*(4.5X+B)</strong></p><p><strong>2.75X + 0.5B = 2.475X + 0.55B</strong></p><p><strong>0.275X = 0.05B</strong></p><p><strong>5.5X = B</strong></p><p><strong></strong></p><p><strong></strong>A higher value of B in comparison to X makes the longsword a better choice, while a lower value of B in comparison to X makes the warhammer a better choice.</p><p></p><p>Consider the case of a paladin attacking a marked target with Holy Strike (damage is 1[W] + Str + Wis). Assuming a 1st-level paladin with 18 Str and 16 Wis, this gives B=7 and X=1, making the longsword the better choice. Now suppose the paladin is now 30th level. He will have added 8 points to both Str and Wis, giving him a 26 Str (+8) and 24 Wis (+7), and will probably have a +6 weapon and an additional +3 from Weapon Focus, giving him B=24. Even though X is now 2, the very high value of B means that the longsword is still the better choice.</p><p></p><p>This is not always true, however. Consider a 30th level fighter using No Mercy (7[W] + Str damage), and also with a 26 Str, +6 weapon, and weapon focus. He now has X=7 and B=17, making the warhammer by far the better choice. (Additionally, No Mercy is Reliable, so that even if the difference in proficiency bonuses makes the attack miss instead of hit, the fighter can try again next round.)</p><p></p><p>And back to the topic of two-handed weapons: another very good reason to take a two-handed weapon is Reaping Strike, which does more damage on a miss if the weapon is two-handed. If Reaping Strike is one of your primary at-wills this is a very good benefit. Another benefit is that if you have a Warlord in your party with Commander's Strike, the Warlord can go sword-and-shield and use your melee basic attack (plus the Warlord's Int modifier to damage), so the Warlord can get the additional damage from the two-handed weapon as well as the shield bonus to his own AC and Reflex!</p></blockquote><p></p>
[QUOTE="Alex319, post: 4447960, member: 45678"] First of all, the highest AC you can get at 30th level is far more than 35. At 30th level you can have +6 godplate armor (total AC bonus 14+6=20), combined with the 10 base and 15 from level gives 45, and that's not even counting a shield or feats like Armor Specialization and Two-Weapon Defense. But this is a secondary point of relatively minor concern to the overall analysis. First of all, I explained a couple posts up about why offensive bonuses are in general better than defensive bonuses, which is why an extra +1 to attack is worth about 1.2 points of [W] while an extra +2 to AC/Reflex is worth far less than 2.4 points of [W]. (And don't forget that an extra +2 to AC/Reflex is worth nothing if an enemy targets your Fortitude or Will defense.) But in order to address the relationship between attack rolls and damage rolls, let's compare the effectiveness of a longsword (+3 prof, 1d8 damage) and warhammer (+2 prof, 1d10 damage). A good way to think of this is in terms of "expected damage per round." This is the probability the attack will hit times the expected damage if it does hit. Also note that the expected damage includes both the damage from the weapon and any damage bonuses (from attributes, magic weapons, feats, powers, etc.) So our formula is: [B]Expected Damage = H*(XW+B) [/B]where H is the hit probability, X is the number of [W] the power has, and B is any bonuses to damage or additional damage other than the [W]. So suppose that the probability of hitting is 0.5 with the warhammer, and so it is 0.55 with the longsword. We want to see under what conditions the longsword and warhammer will have an equal amount of damage per round. [B]Expected Damage from Warhammer = 0.5*(5.5X + B) Expected Damage from Longsword = 0.55*(4.5X + B) [/B]Setting these equal we get: [B]0.5*(5.5X+B) = 0.55*(4.5X+B) 2.75X + 0.5B = 2.475X + 0.55B 0.275X = 0.05B 5.5X = B [/B]A higher value of B in comparison to X makes the longsword a better choice, while a lower value of B in comparison to X makes the warhammer a better choice. Consider the case of a paladin attacking a marked target with Holy Strike (damage is 1[W] + Str + Wis). Assuming a 1st-level paladin with 18 Str and 16 Wis, this gives B=7 and X=1, making the longsword the better choice. Now suppose the paladin is now 30th level. He will have added 8 points to both Str and Wis, giving him a 26 Str (+8) and 24 Wis (+7), and will probably have a +6 weapon and an additional +3 from Weapon Focus, giving him B=24. Even though X is now 2, the very high value of B means that the longsword is still the better choice. This is not always true, however. Consider a 30th level fighter using No Mercy (7[W] + Str damage), and also with a 26 Str, +6 weapon, and weapon focus. He now has X=7 and B=17, making the warhammer by far the better choice. (Additionally, No Mercy is Reliable, so that even if the difference in proficiency bonuses makes the attack miss instead of hit, the fighter can try again next round.) And back to the topic of two-handed weapons: another very good reason to take a two-handed weapon is Reaping Strike, which does more damage on a miss if the weapon is two-handed. If Reaping Strike is one of your primary at-wills this is a very good benefit. Another benefit is that if you have a Warlord in your party with Commander's Strike, the Warlord can go sword-and-shield and use your melee basic attack (plus the Warlord's Int modifier to damage), so the Warlord can get the additional damage from the two-handed weapon as well as the shield bonus to his own AC and Reflex! [/QUOTE]
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Weapon Balance - A Statistical Analysis
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