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9th level spells compared by equivalent lower level spell value
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<blockquote data-quote="BlivetWidget" data-source="post: 7841531" data-attributes="member: 6912801"><p>Though this isn't exactly the angle you're going for, I feel like this is an appropriate place to put an analysis of spell power.</p><p></p><p>If we're going to compare the <em>power </em>of spells at level A with level B, the only sensible approach is to look at damaging spells (the utility of being invisible in a way that still allows casting or turning a friend into a giant ape is somewhat more difficult to measure). My first instinct was to look at the table on DMG p283, which proposes guidelines for creating custom spells. The table looks nice and neat, but comes with the rather significant issue that the game designers clearly did not come anywhere near to using the table when they made the spells in the rulebooks.</p><p></p><p>So I picked out some classic damaging spells of varying level. Fire Bolt, Magic Missile, Scorching Ray, Fireball, Vitriolic Sphere, Cone of Cold, Otiluke's Freezing Sphere, Crown of Stars, Sunburst, and Meteor Swarm. Average damage from the dice was calculated with a weighting factor of 1 for save for half and 0.75 for attack / save for nothing. The breakthrough was in finding DMG p249 (Adjudicating Areas of Effect) for the number of targets various AoEs could expect to hit and using that as the multiplier to find total damage from the spell.</p><p></p><p>The best simple equation I could come up with (obviously you could fit the data exactly with enough terms) was still actually pretty decent at predicting the power of canonical damaging spells: 6 * 2**level</p><p></p><table style='width: 100%'><tr><td>Spell Level</td><td>Expected Damage Across All Targets (6 * 2**level)</td></tr><tr><td><p style="text-align: right">0</p> </td><td><p style="text-align: right">6</p> </td></tr><tr><td><p style="text-align: right">1</p> </td><td><p style="text-align: right">12</p> </td></tr><tr><td><p style="text-align: right">2</p> </td><td><p style="text-align: right">24</p> </td></tr><tr><td><p style="text-align: right">3</p> </td><td><p style="text-align: right">48</p> </td></tr><tr><td><p style="text-align: right">4</p> </td><td><p style="text-align: right">96</p> </td></tr><tr><td><p style="text-align: right">5</p> </td><td><p style="text-align: right">192</p> </td></tr><tr><td><p style="text-align: right">6</p> </td><td><p style="text-align: right">384</p> </td></tr><tr><td><p style="text-align: right">7</p> </td><td><p style="text-align: right">768</p> </td></tr><tr><td><p style="text-align: right">8</p> </td><td><p style="text-align: right">1536</p> </td></tr><tr><td><p style="text-align: right">9</p> </td><td><p style="text-align: right">3072</p> </td></tr></table><p></p><p>The takeaway here is that each level is predicted to be twice as powerful as the previous level, but it's probably better to think of them as ranges. So a level 9 spell should be about 2x as powerful as a level 8 spell, but anything from 1x to 4x (non-inclusive terminus) would not be out of place. Similarly, a level 9 spell should be about 4x as powerful as a level 7 spell, but anything from 2x to 8x (non-inclusive terminus) could be justified.</p><p></p><p>Just a fun bit of math for you.</p></blockquote><p></p>
[QUOTE="BlivetWidget, post: 7841531, member: 6912801"] Though this isn't exactly the angle you're going for, I feel like this is an appropriate place to put an analysis of spell power. If we're going to compare the [I]power [/I]of spells at level A with level B, the only sensible approach is to look at damaging spells (the utility of being invisible in a way that still allows casting or turning a friend into a giant ape is somewhat more difficult to measure). My first instinct was to look at the table on DMG p283, which proposes guidelines for creating custom spells. The table looks nice and neat, but comes with the rather significant issue that the game designers clearly did not come anywhere near to using the table when they made the spells in the rulebooks. So I picked out some classic damaging spells of varying level. Fire Bolt, Magic Missile, Scorching Ray, Fireball, Vitriolic Sphere, Cone of Cold, Otiluke's Freezing Sphere, Crown of Stars, Sunburst, and Meteor Swarm. Average damage from the dice was calculated with a weighting factor of 1 for save for half and 0.75 for attack / save for nothing. The breakthrough was in finding DMG p249 (Adjudicating Areas of Effect) for the number of targets various AoEs could expect to hit and using that as the multiplier to find total damage from the spell. The best simple equation I could come up with (obviously you could fit the data exactly with enough terms) was still actually pretty decent at predicting the power of canonical damaging spells: 6 * 2**level [TABLE] [TR] [TD]Spell Level[/TD] [TD]Expected Damage Across All Targets (6 * 2**level)[/TD] [/TR] [TR] [TD][RIGHT]0[/RIGHT][/TD] [TD][RIGHT]6[/RIGHT][/TD] [/TR] [TR] [TD][RIGHT]1[/RIGHT][/TD] [TD][RIGHT]12[/RIGHT][/TD] [/TR] [TR] [TD][RIGHT]2[/RIGHT][/TD] [TD][RIGHT]24[/RIGHT][/TD] [/TR] [TR] [TD][RIGHT]3[/RIGHT][/TD] [TD][RIGHT]48[/RIGHT][/TD] [/TR] [TR] [TD][RIGHT]4[/RIGHT][/TD] [TD][RIGHT]96[/RIGHT][/TD] [/TR] [TR] [TD][RIGHT]5[/RIGHT][/TD] [TD][RIGHT]192[/RIGHT][/TD] [/TR] [TR] [TD][RIGHT]6[/RIGHT][/TD] [TD][RIGHT]384[/RIGHT][/TD] [/TR] [TR] [TD][RIGHT]7[/RIGHT][/TD] [TD][RIGHT]768[/RIGHT][/TD] [/TR] [TR] [TD][RIGHT]8[/RIGHT][/TD] [TD][RIGHT]1536[/RIGHT][/TD] [/TR] [TR] [TD][RIGHT]9[/RIGHT][/TD] [TD][RIGHT]3072[/RIGHT][/TD] [/TR] [/TABLE] The takeaway here is that each level is predicted to be twice as powerful as the previous level, but it's probably better to think of them as ranges. So a level 9 spell should be about 2x as powerful as a level 8 spell, but anything from 1x to 4x (non-inclusive terminus) would not be out of place. Similarly, a level 9 spell should be about 4x as powerful as a level 7 spell, but anything from 2x to 8x (non-inclusive terminus) could be justified. Just a fun bit of math for you. [/QUOTE]
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