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<blockquote data-quote="Kinematics" data-source="post: 7322003" data-attributes="member: 6932123"><p>Continuing the examination of area issues, there are a couple other questions:</p><p></p><p>1) How does volume factor into things?</p><p>2) How does area trade off with damage?</p><p></p><p>For the first question, all of the regions that I estimated in the above post were areas, not volume, despite being spheres. A fireball doesn't have to be targeted at ground level; you could shoot that griffon rider flying overhead, and get the full sphere volume. </p><p></p><p>There's also the issue of comparing it with a cylindrical spell. Sleet Storm has a 40' radius and a 20' height. If it were a sphere, that 40' radius would mean that its max height was also 40'. Cylinders are generally designed to be cast at ground level, but even if you cast it on a target in the air, it would still only be 20' high.</p><p></p><p>In general, height is going to be less valuable than area. While there are some flyers, and targeting flyers is in itself valuable, the vast majority of all encounters (in low to mid levels, anyway) is going to be at ground level.</p><p></p><p>You also have to consider that, while a single 'square' for a person to occupy is 5' by 5', which gives plenty of room to maneuver, it probably is 10' high. A person is only a couple feet wide, at best, but can easily be 6' to 7' tall. The occupied region of a single person is thus closer to 5'x5'x10'.</p><p></p><p>Between the two above factors, I would probably divide the height of an AOE region in half in order to get a proper scaling value when combined with area. And in fact, it would likely be easier to compare using map grid 'units': 5'x5'x10' = 1 cubic unit.</p><p></p><p>Further, circular area doesn't translate well to map grid units, particularly when factoring in that the center point is typically the center of a grid square. A spell that hits everything within 5' of that square hits 9 total squares, whereas calculating it as a circle, it would only hit 3.</p><p></p><p>So, a little aside for some math.</p><p></p><p>[sblock=Math]</p><p>5' radius = 1 unit radius = 9 unit area</p><p>10' radius = 2 unit radius = 21 unit area (4 furthest corners on a square grid excluded)</p><p>All further unit radius areas can be approximated by: pi * (1.1*radius)^2</p><p></p><p>It's not exact, but it's close enough for comparison purposes, since we only want rough scaling.</p><p></p><p>So area comparison tiers:</p><p></p><p>1st — 5' = 9 units</p><p>2nd — 10' = 21 units</p><p>3rd — 15' = 34 units</p><p>4th — 20' = 61 units</p><p>5th — 25' = 95 units</p><p>6th — 30' = 137 units</p><p>7th — 35' = 186 units</p><p>8th — 40' = 243 units</p><p>9th — 45' = 308 units</p><p>10th — 50' = 380 units</p><p></p><p>Cylindrical volumes are easy to extrapolate from that. Just take the area units and multiply by +1 for every 10 feet in height. So, for example, Sleet Storm would use the 40' area (243 units) times 2 for being 20' tall (total of 486 volume units).</p><p></p><p>Conical I'll just take as area units only, as the vertical aspect is hard to figure or irrelevant. The PHB says the width of the cone is the same as its length, so its area is length time half length. EG: A 15' cone is 3 * 1.5 = 4.5 ⇒ 5 units. A 60' cone is 12 * 6 = 72 units.</p><p></p><p>Cube is easy enough. Control Winds is a 100' cube, so 400 area units and 4000 volume units. (Non-damaging spells tend to have larger areas.)</p><p></p><p>And the sphere... </p><p></p><p>At less than 20' radius, volume matches area * 2.</p><p>At 20' radius, you get an extra set of volume units: [ sqrt(20^2 - 10^2) = radius 17 ~= 44 units ] * 2.</p><p>At 30' radius, you get two extra sets of volume units: [ sqrt(30^2 - 10^2) = radius 28 ~= 120 units ], [ sqrt(30^2 - 20^2) = radius 22 ~= 74 units ]</p><p>At 40' radius, you get three extra sets of volume units: [ sqrt(40^2 - 10^2) = radius 39 ~= 231 units ], [ sqrt(40^2 - 20^2) = radius 35 ~= 186 units ], [ sqrt(40^2 - 30^2) = radius 26 ~= 103 units ]</p><p></p><p>So volume unit comparisons:</p><p></p><p>1st — 5' = 9 units hemisphere / 9 units sphere</p><p>2nd — 10' = 21 units hemisphere / 42 units sphere</p><p>3rd — 15' = 34 units hemisphere / 68 units sphere</p><p>4th — 20' = 105 units hemisphere / 210 units sphere</p><p>5th — 25' = 139 units hemisphere / 278 units sphere</p><p>6th — 30' = 314 units hemisphere / 628 units sphere</p><p>7th — 35' = 380 units hemisphere / 760 units sphere</p><p>8th — 40' = 763 units hemisphere / 1526 units sphere</p><p></p><p></p><p>Since I want to aim at a set of guidelines, I don't need exact values, and can just use numbers that allow approximating what I want as I change the shapes.</p><p></p><p>Level — area units / hemisphere units / volume units</p><p>1st — 10 / 10 / 10</p><p>2nd — 20 / 20 / 40</p><p>3rd — 35 / 35 / 70</p><p>4th — 60 / 100 / 200</p><p>5th — 100 / 150 / 300</p><p>6th — 150 / 300 / 600</p><p>7th — 200 / 400 / 800</p><p>8th — 250 / 500 / 1000</p><p>9th — 300 / 750 / 1500</p><p>10th — 400 / 1000 / 2000</p><p></p><p>Area units would be the most important. Hemisphere and Sphere units would be smaller factors. Each area unit approximates the ground area of a sphere with radius 5'xLevel.</p><p></p><p>Area scaling above 5th level should be taken with a grain of salt. Up to 5th level, each additional level increased the area by a factor of about 1.7. Above 5th level, the above chart increases much more slowly.</p><p></p><p>It could be that above a 30' radius, the increase should be in increments of 10' instead of 5'. I can't think of any spells that have a 35' radius; only 30' and 40'.</p><p></p><p>If we focus more on scaling level-to-level, above 5th level the progression would look more like this:</p><p></p><p>Level — area units / hemisphere units / volume units</p><p>1st (5') — 10 / 10 / 10</p><p>2nd (10') — 20 / 20 / 40</p><p>3rd (15') — 35 / 35 / 70</p><p>4th (20') — 60 / 100 / 200</p><p>5th (25') — 100 / 150 / 300</p><p>6th (30') — 150 / 300 / 600</p><p>7th (40') — 250 / 750 / 1500</p><p>8th (50') — 400 / 1200 / 2400</p><p>9th (60') — 600 / 1800 / 3600</p><p>10th (80') — 1000 / 3000 / 6000</p><p>11th (100') — 1500 / 5000 / 10000</p><p></p><p>[/sblock]</p><p></p><p>Now, back to Tidal Wave. The default spell has an area of 12 units (30'x10' = 6x2 = 12). Its volume is the same, since it's 10' high. That puts it on par with a 1st level spell.</p><p></p><p>My rework would give it an area of 32 units (40'x20' = 8x4 = 32) or 30 units (50'x15' = 10x3 = 30), which is more on par with a 3rd level spell.</p><p></p><p></p><p>Next, the question of how area and damage trade off with each other.</p><p></p><p>For this, I'm gonna try a small cheat, and look at Melf's Minute Meteors. [Caveat: The math below this shows that this is not in any way workable.]</p><p></p><p>With MMM, you get 6 small fireballs that each can damage a 5' radius area, and do 2d6 damage each. You can thus view this as a 2d6 damage AOE that covers 6*9units = 54 units area, or a 12d6 damage AOE that covers a single 5' radius (9 units) area.</p><p></p><p>2d6 on multiple targets is a 1st level spell, according to the DMG chart. 12d6 is 7th level.</p><p></p><p>9 unit AOE is a 1st level spell area. 54 units is a 4th level spell area.</p><p></p><p>So increasing area by 3 levels decreases damage by 6 levels, and vice-versa. Given the relatively small changes in damage per spell level, compared to a relatively large area change, and thus increase in the number of potential targets, I could see a 2:1 ratio for damage vs area. Probably a little less, though, for single-event spells.</p><p></p><p></p><p>If you apply that to, say, Tidal Wave, its 1st level area size (-2 levels) would mean +4 levels in damage (maybe +3 levels). Its original damage was 4d8, which is level 2.5 (possibly reduced because of damage type?). Scaling it up 3 levels to 5.5 would make it 8d8 damage.</p><p></p><p></p><p><strong>valid?</strong></p><p></p><p>So, using Tidal Wave as an example, given its area (30'x10'), does 8d8 seem reasonable damage for a 3rd level spell?</p><p></p><p>Actually, before going there, lets look at the spell damage chart, because we do have an upper limit to consider — how much damage a spell does to a single target (limit as area approaches 0).</p><p></p><p>[code]</p><p> Single Area </p><p>Level Damage Points Damage Points Ratio Single/Area</p><p>C 1d10 5.5 1d6 3.5 1.571</p><p>1 2d10 11 2d6 7 1.571</p><p>2 3d10 16.5 4d6 14 1.179</p><p>3 5d10 27.5 6d6 21 1.310</p><p>4 6d10 33 7d6 24.5 1.347</p><p>5 8d10 44 8d6 28 1.571</p><p>6 10d10 55 11d6 38.5 1.429</p><p>7 11d10 60.5 12d6 42 1.440</p><p>8 12d10 66 13d6 45.5 1.451</p><p>9 15d10 82.5 14d6 49 1.684</p><p>[/code]</p><p></p><p>One thing to note is that level 2 single-target spells are significantly underpowered compared to every other level. For almost all levels, single-target damage is estimated at 30% to 60% higher than area target damage, with an average of 1.486 (excluding level 2). At 2nd level, though, it's under 20%. Increasing single-target damage from 3d10 to 4d10 would fix that inconsistancy, bringing the ratio up to 1.571 like level 1 and cantrips.</p><p></p><p>I would recommend increasing the crafted target damage for 2nd level single-target spells to 4d10, or 22 points.</p><p></p><p></p><p>Now, given that, we then see that the maximum increase we want to allow to the damage value of an AOE spell is about 50%. So a 4d8 AOE spell should never increase to more than 6d8 damage due to reduced area, because eventually it will reach the point where it's equivalent to a single-target spell.</p><p></p><p>So based on <em>that</em>, I would increase the damage value for Tidal Wave (assuming it kept its original area) by about 35%. Based off of its original 4d8 damage, I'd change it to 7d6 (18 damage to 24.5 damage). Based off of a standard 3rd level damage rating, I'd change it to 6d8 (21 damage to 27 damage).</p><p></p><p></p><p><strong>Summary</strong></p><p></p><p>1) Accounting for volume would seem to give more points to consider when balancing a spell, though it appears relatively easy to balance that on a different column of the spell size comparisons.</p><p></p><p>2) Increasing or decreasing damage in proportion to changes in AOE size seems relatively simple, once you know the limits to work with. Increasing damage with decreasing area should have a limit of +50%, and can be inverted if increasing the AOE size (-33%) [3/2 vs 2/3]. Need to figure out what the limit on size increases are, but not sure how to do that right now.</p><p></p><p>Errata: 2nd level single-target spells should have a target damage value of 4d10, not 3d10.</p></blockquote><p></p>
[QUOTE="Kinematics, post: 7322003, member: 6932123"] Continuing the examination of area issues, there are a couple other questions: 1) How does volume factor into things? 2) How does area trade off with damage? For the first question, all of the regions that I estimated in the above post were areas, not volume, despite being spheres. A fireball doesn't have to be targeted at ground level; you could shoot that griffon rider flying overhead, and get the full sphere volume. There's also the issue of comparing it with a cylindrical spell. Sleet Storm has a 40' radius and a 20' height. If it were a sphere, that 40' radius would mean that its max height was also 40'. Cylinders are generally designed to be cast at ground level, but even if you cast it on a target in the air, it would still only be 20' high. In general, height is going to be less valuable than area. While there are some flyers, and targeting flyers is in itself valuable, the vast majority of all encounters (in low to mid levels, anyway) is going to be at ground level. You also have to consider that, while a single 'square' for a person to occupy is 5' by 5', which gives plenty of room to maneuver, it probably is 10' high. A person is only a couple feet wide, at best, but can easily be 6' to 7' tall. The occupied region of a single person is thus closer to 5'x5'x10'. Between the two above factors, I would probably divide the height of an AOE region in half in order to get a proper scaling value when combined with area. And in fact, it would likely be easier to compare using map grid 'units': 5'x5'x10' = 1 cubic unit. Further, circular area doesn't translate well to map grid units, particularly when factoring in that the center point is typically the center of a grid square. A spell that hits everything within 5' of that square hits 9 total squares, whereas calculating it as a circle, it would only hit 3. So, a little aside for some math. [sblock=Math] 5' radius = 1 unit radius = 9 unit area 10' radius = 2 unit radius = 21 unit area (4 furthest corners on a square grid excluded) All further unit radius areas can be approximated by: pi * (1.1*radius)^2 It's not exact, but it's close enough for comparison purposes, since we only want rough scaling. So area comparison tiers: 1st — 5' = 9 units 2nd — 10' = 21 units 3rd — 15' = 34 units 4th — 20' = 61 units 5th — 25' = 95 units 6th — 30' = 137 units 7th — 35' = 186 units 8th — 40' = 243 units 9th — 45' = 308 units 10th — 50' = 380 units Cylindrical volumes are easy to extrapolate from that. Just take the area units and multiply by +1 for every 10 feet in height. So, for example, Sleet Storm would use the 40' area (243 units) times 2 for being 20' tall (total of 486 volume units). Conical I'll just take as area units only, as the vertical aspect is hard to figure or irrelevant. The PHB says the width of the cone is the same as its length, so its area is length time half length. EG: A 15' cone is 3 * 1.5 = 4.5 ⇒ 5 units. A 60' cone is 12 * 6 = 72 units. Cube is easy enough. Control Winds is a 100' cube, so 400 area units and 4000 volume units. (Non-damaging spells tend to have larger areas.) And the sphere... At less than 20' radius, volume matches area * 2. At 20' radius, you get an extra set of volume units: [ sqrt(20^2 - 10^2) = radius 17 ~= 44 units ] * 2. At 30' radius, you get two extra sets of volume units: [ sqrt(30^2 - 10^2) = radius 28 ~= 120 units ], [ sqrt(30^2 - 20^2) = radius 22 ~= 74 units ] At 40' radius, you get three extra sets of volume units: [ sqrt(40^2 - 10^2) = radius 39 ~= 231 units ], [ sqrt(40^2 - 20^2) = radius 35 ~= 186 units ], [ sqrt(40^2 - 30^2) = radius 26 ~= 103 units ] So volume unit comparisons: 1st — 5' = 9 units hemisphere / 9 units sphere 2nd — 10' = 21 units hemisphere / 42 units sphere 3rd — 15' = 34 units hemisphere / 68 units sphere 4th — 20' = 105 units hemisphere / 210 units sphere 5th — 25' = 139 units hemisphere / 278 units sphere 6th — 30' = 314 units hemisphere / 628 units sphere 7th — 35' = 380 units hemisphere / 760 units sphere 8th — 40' = 763 units hemisphere / 1526 units sphere Since I want to aim at a set of guidelines, I don't need exact values, and can just use numbers that allow approximating what I want as I change the shapes. Level — area units / hemisphere units / volume units 1st — 10 / 10 / 10 2nd — 20 / 20 / 40 3rd — 35 / 35 / 70 4th — 60 / 100 / 200 5th — 100 / 150 / 300 6th — 150 / 300 / 600 7th — 200 / 400 / 800 8th — 250 / 500 / 1000 9th — 300 / 750 / 1500 10th — 400 / 1000 / 2000 Area units would be the most important. Hemisphere and Sphere units would be smaller factors. Each area unit approximates the ground area of a sphere with radius 5'xLevel. Area scaling above 5th level should be taken with a grain of salt. Up to 5th level, each additional level increased the area by a factor of about 1.7. Above 5th level, the above chart increases much more slowly. It could be that above a 30' radius, the increase should be in increments of 10' instead of 5'. I can't think of any spells that have a 35' radius; only 30' and 40'. If we focus more on scaling level-to-level, above 5th level the progression would look more like this: Level — area units / hemisphere units / volume units 1st (5') — 10 / 10 / 10 2nd (10') — 20 / 20 / 40 3rd (15') — 35 / 35 / 70 4th (20') — 60 / 100 / 200 5th (25') — 100 / 150 / 300 6th (30') — 150 / 300 / 600 7th (40') — 250 / 750 / 1500 8th (50') — 400 / 1200 / 2400 9th (60') — 600 / 1800 / 3600 10th (80') — 1000 / 3000 / 6000 11th (100') — 1500 / 5000 / 10000 [/sblock] Now, back to Tidal Wave. The default spell has an area of 12 units (30'x10' = 6x2 = 12). Its volume is the same, since it's 10' high. That puts it on par with a 1st level spell. My rework would give it an area of 32 units (40'x20' = 8x4 = 32) or 30 units (50'x15' = 10x3 = 30), which is more on par with a 3rd level spell. Next, the question of how area and damage trade off with each other. For this, I'm gonna try a small cheat, and look at Melf's Minute Meteors. [Caveat: The math below this shows that this is not in any way workable.] With MMM, you get 6 small fireballs that each can damage a 5' radius area, and do 2d6 damage each. You can thus view this as a 2d6 damage AOE that covers 6*9units = 54 units area, or a 12d6 damage AOE that covers a single 5' radius (9 units) area. 2d6 on multiple targets is a 1st level spell, according to the DMG chart. 12d6 is 7th level. 9 unit AOE is a 1st level spell area. 54 units is a 4th level spell area. So increasing area by 3 levels decreases damage by 6 levels, and vice-versa. Given the relatively small changes in damage per spell level, compared to a relatively large area change, and thus increase in the number of potential targets, I could see a 2:1 ratio for damage vs area. Probably a little less, though, for single-event spells. If you apply that to, say, Tidal Wave, its 1st level area size (-2 levels) would mean +4 levels in damage (maybe +3 levels). Its original damage was 4d8, which is level 2.5 (possibly reduced because of damage type?). Scaling it up 3 levels to 5.5 would make it 8d8 damage. [b]valid?[/b] So, using Tidal Wave as an example, given its area (30'x10'), does 8d8 seem reasonable damage for a 3rd level spell? Actually, before going there, lets look at the spell damage chart, because we do have an upper limit to consider — how much damage a spell does to a single target (limit as area approaches 0). [code] Single Area Level Damage Points Damage Points Ratio Single/Area C 1d10 5.5 1d6 3.5 1.571 1 2d10 11 2d6 7 1.571 2 3d10 16.5 4d6 14 1.179 3 5d10 27.5 6d6 21 1.310 4 6d10 33 7d6 24.5 1.347 5 8d10 44 8d6 28 1.571 6 10d10 55 11d6 38.5 1.429 7 11d10 60.5 12d6 42 1.440 8 12d10 66 13d6 45.5 1.451 9 15d10 82.5 14d6 49 1.684 [/code] One thing to note is that level 2 single-target spells are significantly underpowered compared to every other level. For almost all levels, single-target damage is estimated at 30% to 60% higher than area target damage, with an average of 1.486 (excluding level 2). At 2nd level, though, it's under 20%. Increasing single-target damage from 3d10 to 4d10 would fix that inconsistancy, bringing the ratio up to 1.571 like level 1 and cantrips. I would recommend increasing the crafted target damage for 2nd level single-target spells to 4d10, or 22 points. Now, given that, we then see that the maximum increase we want to allow to the damage value of an AOE spell is about 50%. So a 4d8 AOE spell should never increase to more than 6d8 damage due to reduced area, because eventually it will reach the point where it's equivalent to a single-target spell. So based on [i]that[/i], I would increase the damage value for Tidal Wave (assuming it kept its original area) by about 35%. Based off of its original 4d8 damage, I'd change it to 7d6 (18 damage to 24.5 damage). Based off of a standard 3rd level damage rating, I'd change it to 6d8 (21 damage to 27 damage). [b]Summary[/b] 1) Accounting for volume would seem to give more points to consider when balancing a spell, though it appears relatively easy to balance that on a different column of the spell size comparisons. 2) Increasing or decreasing damage in proportion to changes in AOE size seems relatively simple, once you know the limits to work with. Increasing damage with decreasing area should have a limit of +50%, and can be inverted if increasing the AOE size (-33%) [3/2 vs 2/3]. Need to figure out what the limit on size increases are, but not sure how to do that right now. Errata: 2nd level single-target spells should have a target damage value of 4d10, not 3d10. [/QUOTE]
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