clearstream
(He, Him)
In another thread I wanted to understand a revision I'm making to Sharpshooter, adding "Once per turn" to the power-attack. An obvious question is "If this is good, why not apply it to Great Weapon Master, too?" The answer lies in our tendency to fix no firm value on ranged. We know that dealing damage at range is better, but we generally don't convert that into a commensurable. Here I want to suggest a firm value for ranged, based on the concepts of up-time and damage mitigation.
First background numbers. At 11th level against an expected AC 17
We expect our GWM fighter to deal about 43 damage/turn from 5' while our SS archer ("once per turn" revision) deals about 32* damage/turn from up to 600'. My thesis is that range makes up the difference, i.e about one-third of effective damage. *With PHB Sharpshooter and Crossbow Expert (losing one Dex increase), using Hand Crossbow, our SS archer deals instead about 40 damage/turn from up to 120'.
Up-time
Up-time means over an average 5-round combat (and over many such combats) how often can I expect to be able to deal my damage? I'm going to assert that the melee fighter gains about 90% up-time. On average, at least every other combat, one attack is lost to closing, repositioning or whatever. Our ranged fighter is online from the get-go and scarcely needs to reposition. I'm going to assert 99% up time. Counting up-time, GWM deals about 39 damage per turn, while SS continues to deal about 32. Our average combat is lasting 5 turns. Note that combats can vary widely and all I am really asserting here is that ranged enjoys at least 10% more up-time than melee. I'm mindful that sometimes ranged will be in melee and want to disengage.
Damage Mitigation
Damage-mitigation is how much of a foes possible damage we avoid taking. At the relevant levels, foes with +10 to hit have Multiattacks that deal an average of 20 damage/attack, against GWM's plate armor needing 8s: for about 26 a turn while in contact. We've asserted they're in contact only 90% of the time so let's call it a 23 damage/turn. Sometimes a ranged attacker will be hitting them without their being in contact. Other times they'll prevent a counter-attack even occurring.
It is difficult to predict how often our SS fighter is in contact with the foe. Certainly less than GWM fighter who actively seeks out contact. I find a worst case of 50% contact plausible over many combats, for 13 damage/turn. In given combats it could be a lot less, even 0%. Or more, even 100% against other ranged opponents (but then, GWM could be kited and get to make 0 attacks!)
A common ratio for damage-mitigation to damage-dealt is 3/5 i.e. damage mitigated is worth only 60% of damage dealt. On that basis, our archer counts about +6 "damage" gain per turn from mitigation. Leading to a conclusion that SS after putting a value on ranged is worth nearly as much as GWM (38:39) using my revision for the power attack ("Once per turn"), and greatly more than GWM using RAW. Noting too that I ignore the benefits of focus fire, and probably low-ball the up-time and damage mitigation discrepancies.
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I hope the concepts of up-time and damage-mitigation will prove helpful in balancing ranged versus melee attacks, through being able to equate damage with range. As a closing aside, these principle apply equally well to ranged versus ranged, where the greater range will usually enjoy more up-time and damage-mitigation than the lesser range.
Aside from combatant and foe stats, the key values are
Up-time
% of turns in reach/range over turns out of reach/range
Up-time discrepancy = combatant A's% − combatant B's%
Discrepancy can be applied as a simple multiplier to one combatant's damage expectation
Damage Mitigation
Contact assumption = number of turns a foe has a chance to make an attack against our combatant / average turns of combat
Damage / turn calculated as average damage * attacks * chance to hit * contact assumption
Mitigated damage worth = 3/5 against dealt damage
Gain = combatant A's worth − combatant B's worth
The side with the greater range will usually enjoy a beneficial up-time discrepancy and effective damage gain.
[Edited to bring case up to date with discussion in thread.]
First background numbers. At 11th level against an expected AC 17
- GWM+Str+Str (20 Strength) Battlemaster (GWF style) with Greatsword with Precision Attack available, likely needs 8 to hit
- Once per turn SS+Dex+Dex (20 Dex) Battlemaster (Archery style) with Longbow with Precision Attack available, likely needs 7 to hit
- Choosing to use −5/+10 that is 13 and 12 respectively, and some misses can be made into hits with the maneuver
- Both use Precision whenever they miss by 3 or less (aiming to expend 2.5 superiority dice per combat)
We expect our GWM fighter to deal about 43 damage/turn from 5' while our SS archer ("once per turn" revision) deals about 32* damage/turn from up to 600'. My thesis is that range makes up the difference, i.e about one-third of effective damage. *With PHB Sharpshooter and Crossbow Expert (losing one Dex increase), using Hand Crossbow, our SS archer deals instead about 40 damage/turn from up to 120'.
Up-time
Up-time means over an average 5-round combat (and over many such combats) how often can I expect to be able to deal my damage? I'm going to assert that the melee fighter gains about 90% up-time. On average, at least every other combat, one attack is lost to closing, repositioning or whatever. Our ranged fighter is online from the get-go and scarcely needs to reposition. I'm going to assert 99% up time. Counting up-time, GWM deals about 39 damage per turn, while SS continues to deal about 32. Our average combat is lasting 5 turns. Note that combats can vary widely and all I am really asserting here is that ranged enjoys at least 10% more up-time than melee. I'm mindful that sometimes ranged will be in melee and want to disengage.
Damage Mitigation
Damage-mitigation is how much of a foes possible damage we avoid taking. At the relevant levels, foes with +10 to hit have Multiattacks that deal an average of 20 damage/attack, against GWM's plate armor needing 8s: for about 26 a turn while in contact. We've asserted they're in contact only 90% of the time so let's call it a 23 damage/turn. Sometimes a ranged attacker will be hitting them without their being in contact. Other times they'll prevent a counter-attack even occurring.
It is difficult to predict how often our SS fighter is in contact with the foe. Certainly less than GWM fighter who actively seeks out contact. I find a worst case of 50% contact plausible over many combats, for 13 damage/turn. In given combats it could be a lot less, even 0%. Or more, even 100% against other ranged opponents (but then, GWM could be kited and get to make 0 attacks!)
A common ratio for damage-mitigation to damage-dealt is 3/5 i.e. damage mitigated is worth only 60% of damage dealt. On that basis, our archer counts about +6 "damage" gain per turn from mitigation. Leading to a conclusion that SS after putting a value on ranged is worth nearly as much as GWM (38:39) using my revision for the power attack ("Once per turn"), and greatly more than GWM using RAW. Noting too that I ignore the benefits of focus fire, and probably low-ball the up-time and damage mitigation discrepancies.
-------------------------------------------------
I hope the concepts of up-time and damage-mitigation will prove helpful in balancing ranged versus melee attacks, through being able to equate damage with range. As a closing aside, these principle apply equally well to ranged versus ranged, where the greater range will usually enjoy more up-time and damage-mitigation than the lesser range.
Aside from combatant and foe stats, the key values are
Up-time
% of turns in reach/range over turns out of reach/range
Up-time discrepancy = combatant A's% − combatant B's%
Discrepancy can be applied as a simple multiplier to one combatant's damage expectation
Damage Mitigation
Contact assumption = number of turns a foe has a chance to make an attack against our combatant / average turns of combat
Damage / turn calculated as average damage * attacks * chance to hit * contact assumption
Mitigated damage worth = 3/5 against dealt damage
Gain = combatant A's worth − combatant B's worth
The side with the greater range will usually enjoy a beneficial up-time discrepancy and effective damage gain.
[Edited to bring case up to date with discussion in thread.]
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