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[Math] WotC Challenge Ratings
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<blockquote data-quote="Cheiromancer" data-source="post: 3431193" data-attributes="member: 141"><p>I'll say it here, so it isn't buried in the post somewhere: if a PC's CR is two less than the character's level in the WotC exponential system, this translates to being 63% of its level in a cubic system. And in place of M in the first post, use CR[sup]3[/sup] divided by 30. (Or 31.25, if you want it to match exactly at CR 10. But it doesn't matter; it's only the ratio of M values that are important).</p><p></p><p>So anyway, if AC and attack bonuses both scale at +1/CR (or faster!) then it is very easy to see how a low CR creature can be utterly demolished by a higher CR creature, who is demolished in turn by one higher yet. Having a 20 to 1 advantage (missing only on a 1 vs hitting only on a 20) multiplies any other advantages the more powerful creature might have; hit points, damage dealt, number of attacks, etc..</p><p></p><p>It doesn't only have to be combat stats; spell resistance and caster level exhibit the same mechanic, and (to a lesser extent) save DC and saving throw bonus. Abilities tied directly to hit dice (the <em>blasphemy</em> mechanic is the most obvious example) also reinforce this mechanic.</p><p></p><p>So what? Well, if you want to design monsters so that the WotC paradigm continues to function, you'll have to use these d20 mechanical factors; SR, AC, saves and attacks. If you don't, then you'll have to let them slip aside. Have it so that AC falls behind attacks, say, or saves increase faster than save DCs. Or something- anything that makes that 20:1 advantage disappear. </p><p></p><p>If damage and hit points are roughly proportional to CR (and hitting isn't a problem) then the combat effectiveness of a creature will scale according to the square of its CR. Still, a higher CR creature will probably have a bigger attack bonus than it knows what to do with; some power attack will come into play. Or other kinds of special abilities. These will probably work out to be a third linear factor, and that would yield a cubic progression.</p><p></p><p>I'll have to think about what rate these things will have to change with. 2/3 would probably work (or 0.63, the cube root of 1/2). So AC would increase more slowly than attacks, save DCs would increase more slowly than saving throw bonuses. Caster level more slowly than SR. </p><p></p><p>Spells are for buffs, healing, transportation, dealing with mooks and lackeys - but there are too many save or die effects for the system to favor offense. Offensive combat options, though- that's a different story. Fighters should be able to hit an equal CR challenge on a 2, at least with their first attack. And, at high enough levels, with the second and subsequent attacks too. If the critter's CR is more than 50% of their own, however, this should not be so straightforward. </p><p></p><p>That's probably doable.</p><p></p><p>Or maybe one could dump the cubic system and try to stay within the WotC framework. Make it so that creatures do double in power every 2 CR. Make it so that a 40th level character outstrips a 20th level character in the same way that a 20th level character outstrips a 1st level character. 1000 times as powerful- not merely 8 times as powerful, as is presupposed by the mathematics underlying UK's system. (Let alone the x4 multiple of the quadratic design mode). To do this you'll have to have AC, attacks, SR and caster level all increase at a rate of at least 1/2 levels. So the 40th level character can hit the 20th level character except on a 1, but the 20th level character needs a 20. And similarly for saves, SR and so on.</p><p></p><p>I don't think epic characters and monsters quite follow this progression, do they? For it really to work then the typical balanced combat PC would hit its own AC 50% of the time; a spellcaster PC would have a 50% chance of penetrating their own SR, and a 50% chance of making the save if they did so. And similarly for monsters. I don't recall anymore what the "self-attack" percentages are for epic characters and monsters, but I think they are more off-center than that. And if the self-attack percentages are off-center, then we're probably talking about a cubic progression. Maybe only quadratic, but likely a higher degree than that.</p><p></p><p>But if we did wrestle with treasure, feats and class abilities so that the self-attack numbers were centered, then you could extend the exponential progression out quite a way. A 40th level exponential character would be equivalent to a 200th level cubic character in Krusty's system. And a E-30th level would be like a C-63rd level character. You could certainly introduce powerful feats a lot sooner!</p><p></p><p>I probably got some of those improvement rates wrong. I think caster level is easier to increase than SR, isn't it? That'll probably cause problems. I'm just thinking out loud, really- but when Sep and I get going on this again, it will probably be a helpful reference.</p><p></p><p>Maybe to figure out baseline stats for a monster- and if one of its critical stats (AC, SR, whatever) is out of whack, then another stat can be moved to compensate. Same for characters- if they spend feats or treasure to improve one critical stat, another should be weaker than the baseline.</p><p></p><p>[edit] When it comes time to work out the baseline stats for monsters, rycanada's <a href="https://www.enworld.org/index.php?threads/192437/" target="_blank">DM's Best Friend Table</a> definitely deserves attention. Regularizing the table so it follows certain theoretical trendlines would be nice. The stat block of monsters could be distilled down (see thread) and any exceptions noted. Rakshasas would have unusually high SR for their CR, for example.</p></blockquote><p></p>
[QUOTE="Cheiromancer, post: 3431193, member: 141"] I'll say it here, so it isn't buried in the post somewhere: if a PC's CR is two less than the character's level in the WotC exponential system, this translates to being 63% of its level in a cubic system. And in place of M in the first post, use CR[sup]3[/sup] divided by 30. (Or 31.25, if you want it to match exactly at CR 10. But it doesn't matter; it's only the ratio of M values that are important). So anyway, if AC and attack bonuses both scale at +1/CR (or faster!) then it is very easy to see how a low CR creature can be utterly demolished by a higher CR creature, who is demolished in turn by one higher yet. Having a 20 to 1 advantage (missing only on a 1 vs hitting only on a 20) multiplies any other advantages the more powerful creature might have; hit points, damage dealt, number of attacks, etc.. It doesn't only have to be combat stats; spell resistance and caster level exhibit the same mechanic, and (to a lesser extent) save DC and saving throw bonus. Abilities tied directly to hit dice (the [i]blasphemy[/i] mechanic is the most obvious example) also reinforce this mechanic. So what? Well, if you want to design monsters so that the WotC paradigm continues to function, you'll have to use these d20 mechanical factors; SR, AC, saves and attacks. If you don't, then you'll have to let them slip aside. Have it so that AC falls behind attacks, say, or saves increase faster than save DCs. Or something- anything that makes that 20:1 advantage disappear. If damage and hit points are roughly proportional to CR (and hitting isn't a problem) then the combat effectiveness of a creature will scale according to the square of its CR. Still, a higher CR creature will probably have a bigger attack bonus than it knows what to do with; some power attack will come into play. Or other kinds of special abilities. These will probably work out to be a third linear factor, and that would yield a cubic progression. I'll have to think about what rate these things will have to change with. 2/3 would probably work (or 0.63, the cube root of 1/2). So AC would increase more slowly than attacks, save DCs would increase more slowly than saving throw bonuses. Caster level more slowly than SR. Spells are for buffs, healing, transportation, dealing with mooks and lackeys - but there are too many save or die effects for the system to favor offense. Offensive combat options, though- that's a different story. Fighters should be able to hit an equal CR challenge on a 2, at least with their first attack. And, at high enough levels, with the second and subsequent attacks too. If the critter's CR is more than 50% of their own, however, this should not be so straightforward. That's probably doable. Or maybe one could dump the cubic system and try to stay within the WotC framework. Make it so that creatures do double in power every 2 CR. Make it so that a 40th level character outstrips a 20th level character in the same way that a 20th level character outstrips a 1st level character. 1000 times as powerful- not merely 8 times as powerful, as is presupposed by the mathematics underlying UK's system. (Let alone the x4 multiple of the quadratic design mode). To do this you'll have to have AC, attacks, SR and caster level all increase at a rate of at least 1/2 levels. So the 40th level character can hit the 20th level character except on a 1, but the 20th level character needs a 20. And similarly for saves, SR and so on. I don't think epic characters and monsters quite follow this progression, do they? For it really to work then the typical balanced combat PC would hit its own AC 50% of the time; a spellcaster PC would have a 50% chance of penetrating their own SR, and a 50% chance of making the save if they did so. And similarly for monsters. I don't recall anymore what the "self-attack" percentages are for epic characters and monsters, but I think they are more off-center than that. And if the self-attack percentages are off-center, then we're probably talking about a cubic progression. Maybe only quadratic, but likely a higher degree than that. But if we did wrestle with treasure, feats and class abilities so that the self-attack numbers were centered, then you could extend the exponential progression out quite a way. A 40th level exponential character would be equivalent to a 200th level cubic character in Krusty's system. And a E-30th level would be like a C-63rd level character. You could certainly introduce powerful feats a lot sooner! I probably got some of those improvement rates wrong. I think caster level is easier to increase than SR, isn't it? That'll probably cause problems. I'm just thinking out loud, really- but when Sep and I get going on this again, it will probably be a helpful reference. Maybe to figure out baseline stats for a monster- and if one of its critical stats (AC, SR, whatever) is out of whack, then another stat can be moved to compensate. Same for characters- if they spend feats or treasure to improve one critical stat, another should be weaker than the baseline. [edit] When it comes time to work out the baseline stats for monsters, rycanada's [URL="https://www.enworld.org/index.php?threads/192437/"]DM's Best Friend Table[/URL] definitely deserves attention. Regularizing the table so it follows certain theoretical trendlines would be nice. The stat block of monsters could be distilled down (see thread) and any exceptions noted. Rakshasas would have unusually high SR for their CR, for example. [/QUOTE]
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