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*Dungeons & Dragons
Evaluating Range versus Damage (SS vs GWM) - putting a price on range
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<blockquote data-quote="clearstream" data-source="post: 7233752" data-attributes="member: 71699"><p>In another thread I wanted to understand a revision I'm making to <strong>Sharpshooter</strong>, adding "<strong><em>Once per turn</em></strong>" to the power-attack. An obvious question is "<em>If this is good, </em>w<em>hy not apply it to Great Weapon Master, too?</em>" 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 <strong>up-time</strong> and <strong>damage mitigation</strong>.</p><p></p><p>First background numbers. At <strong>11th level</strong> against an expected <strong>AC 17</strong></p><ul> <li data-xf-list-type="ul"><strong>GWM+Str+Str </strong>(20 Strength)<strong> Battlemaster </strong>(<strong>GWF </strong>style) with <strong>Greatsword </strong>with <strong>Precision Attack</strong> available, likely needs 8 to hit</li> <li data-xf-list-type="ul"><strong>Once per turn SS+Dex+Dex </strong>(20 Dex)<strong> Battlemaster </strong>(<strong>Archery </strong>style) with <strong>Longbow</strong> with <strong>Precision Attack </strong>available, likely needs 7 to hit</li> <li data-xf-list-type="ul">Choosing to use <strong>−5/+10</strong> that is 13 and 12 respectively, and some misses can be made into hits with the maneuver</li> <li data-xf-list-type="ul">Both use <strong>Precision</strong> whenever they miss by 3 or less (aiming to expend 2.5 superiority dice per combat)</li> </ul><p></p><p>We expect our <strong>GWM fighter </strong>to deal about <span style="color: #ff0000"><strong>43</strong> </span>damage/turn from 5' while our <strong>SS archer </strong>("once per turn" revision) deals about <span style="color: #ff0000"><strong>32*</strong></span> damage/turn from up to 600'. My thesis is that <strong>range </strong>makes up the difference, i.e about one-third of effective damage. *<em>With PHB Sharpshooter and Crossbow Expert (losing one Dex increase), using Hand Crossbow, our SS archer deals instead about <strong>40</strong> damage/turn from up to 120'.</em></p><p><u></u></p><p><u><strong>Up-time</strong></u></p><p>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 <strong>melee fighter</strong> gains about 90% up-time. On average, at least every other combat, one attack is lost to closing, repositioning or whatever. Our <strong>ranged fighter</strong> 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 <span style="color: #ff0000"><strong>39</strong></span> damage per turn, while SS continues to deal about <span style="color: #ff0000"><strong>32</strong></span>. Our average combat is lasting 5 turns. Note that combats can vary widely and all I am really asserting here is that <strong>ranged enjoys <em>at least</em> 10% more up-time than melee</strong>. I'm mindful that sometimes ranged will be in melee and want to disengage.</p><p><u></u></p><p><u><strong>Damage Mitigation</strong></u></p><p>Damage-mitigation is how much of a foes possible damage we avoid taking. At the relevant levels, <strong>foes </strong>with <strong>+10 to hit</strong> have <strong>Multiattacks</strong> that deal an average of <strong>20 damage/attack</strong>, 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 <strong>23 damage/turn</strong>. Sometimes a ranged attacker will be hitting them without their being in contact. Other times they'll prevent a counter-attack even occurring.</p><p></p><p>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 <strong>50%</strong> contact plausible over many combats, for <strong>13 damage/turn</strong>. 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!)</p><p></p><p>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 <span style="color: #ff0000"><strong>+6</strong></span> "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 ("<em>Once per turn</em>"), 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.</p><p></p><p>-------------------------------------------------</p><p></p><p>I hope the concepts of <strong>up-time</strong> and <strong>damage-mitigation</strong> 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.</p><p></p><p>Aside from combatant and foe stats, the key values are</p><p></p><p><u><strong>Up-time</strong></u></p><p><strong>%</strong> of turns in reach/range over turns out of reach/range</p><p>Up-time <strong>discrepancy </strong>= combatant A's<strong>%</strong> <strong>−</strong> combatant B's<strong>%</strong></p><p><strong>Discrepancy </strong>can be applied as a simple multiplier to <strong>one</strong> combatant's damage expectation</p><p></p><p><u><strong>Damage Mitigation</strong></u></p><p><strong>Contact assumption</strong> = number of turns a foe has a chance to make an attack against our combatant / average turns of combat</p><p><strong>Damage / turn</strong> calculated as average damage * attacks * chance to hit * contact assumption</p><p>Mitigated damage <strong>worth </strong>= 3/5 against dealt damage</p><p><strong>Gain </strong>= combatant A's worth <strong>−</strong> combatant B's worth</p><p></p><p>The side with the greater range will usually enjoy a beneficial up-time discrepancy and effective damage gain.</p><p></p><p></p><p>[Edited to bring case up to date with discussion in thread.]</p></blockquote><p></p>
[QUOTE="clearstream, post: 7233752, member: 71699"] In another thread I wanted to understand a revision I'm making to [B]Sharpshooter[/B], adding "[B][I]Once per turn[/I][/B]" to the power-attack. An obvious question is "[I]If this is good, [/I]w[I]hy not apply it to Great Weapon Master, too?[/I]" 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 [B]up-time[/B] and [B]damage mitigation[/B]. First background numbers. At [B]11th level[/B] against an expected [B]AC 17[/B] [LIST] [*][B]GWM+Str+Str [/B](20 Strength)[B] Battlemaster [/B]([B]GWF [/B]style) with [B]Greatsword [/B]with [B]Precision Attack[/B] available, likely needs 8 to hit [*][B]Once per turn SS+Dex+Dex [/B](20 Dex)[B] Battlemaster [/B]([B]Archery [/B]style) with [B]Longbow[/B] with [B]Precision Attack [/B]available, likely needs 7 to hit [*]Choosing to use [B]−5/+10[/B] that is 13 and 12 respectively, and some misses can be made into hits with the maneuver [*]Both use [B]Precision[/B] whenever they miss by 3 or less (aiming to expend 2.5 superiority dice per combat) [/LIST] We expect our [B]GWM fighter [/B]to deal about [COLOR=#ff0000][B]43[/B] [/COLOR]damage/turn from 5' while our [B]SS archer [/B]("once per turn" revision) deals about [COLOR=#ff0000][B]32*[/B][/COLOR] damage/turn from up to 600'. My thesis is that [B]range [/B]makes up the difference, i.e about one-third of effective damage. *[I]With PHB Sharpshooter and Crossbow Expert (losing one Dex increase), using Hand Crossbow, our SS archer deals instead about [B]40[/B] damage/turn from up to 120'.[/I] [U] [B]Up-time[/B][/U] 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 [B]melee fighter[/B] gains about 90% up-time. On average, at least every other combat, one attack is lost to closing, repositioning or whatever. Our [B]ranged fighter[/B] 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 [COLOR=#ff0000][B]39[/B][/COLOR] damage per turn, while SS continues to deal about [COLOR=#ff0000][B]32[/B][/COLOR]. Our average combat is lasting 5 turns. Note that combats can vary widely and all I am really asserting here is that [B]ranged enjoys [I]at least[/I] 10% more up-time than melee[/B]. I'm mindful that sometimes ranged will be in melee and want to disengage. [U] [B]Damage Mitigation[/B][/U] Damage-mitigation is how much of a foes possible damage we avoid taking. At the relevant levels, [B]foes [/B]with [B]+10 to hit[/B] have [B]Multiattacks[/B] that deal an average of [B]20 damage/attack[/B], 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 [B]23 damage/turn[/B]. 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 [B]50%[/B] contact plausible over many combats, for [B]13 damage/turn[/B]. 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 [COLOR=#ff0000][B]+6[/B][/COLOR] "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 ("[I]Once per turn[/I]"), 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 [B]up-time[/B] and [B]damage-mitigation[/B] 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 [U][B]Up-time[/B][/U] [B]%[/B] of turns in reach/range over turns out of reach/range Up-time [B]discrepancy [/B]= combatant A's[B]%[/B] [B]−[/B] combatant B's[B]%[/B] [B]Discrepancy [/B]can be applied as a simple multiplier to [B]one[/B] combatant's damage expectation [U][B]Damage Mitigation[/B][/U] [B]Contact assumption[/B] = number of turns a foe has a chance to make an attack against our combatant / average turns of combat [B]Damage / turn[/B] calculated as average damage * attacks * chance to hit * contact assumption Mitigated damage [B]worth [/B]= 3/5 against dealt damage [B]Gain [/B]= combatant A's worth [B]−[/B] 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.] [/QUOTE]
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