Cheiromancer
Adventurer
Upper Krust recently proposed changing the scaling rules for CR. Doubling the number of creatures still increases the Encounter Level (EL) by +2 (just like the official rules do) and thus doubling the xp awarded. But he also proposed that CR x 2 = EL + 6.
It doesn't look like a big difference from the previous system of CR x 2 = EL + 4, but it means that to determine the "challenge" of a creature you have to cube its CR instead of squaring it. Something I have had some difficulty accepting.
The official rule is that CR + 2 = EL + 2. In other words, one CR 12 monster is worth the same amount as two CR 10 monsters or four CR 8 monsters or eight CR 6 monsters or 16 CR 4 monsters. The rule isn't supposed to hold for an EL gap of more than 8 or so (and might be only approximate at more than 5 or so), but is generally supposed to be valid from between EL 1 and EL 20.
For epic level encounters we're more concerned about it applying at the upper end of the scale. It is generally held that PCs don't increase *that* quickly in power at the upper levels. Sure, there are things like blasphemy that can convert a few levels difference into an overwhelming difference, but generally the progression of AC, hp, attack rolls, damage rolls, Save DCs and base saving throws don't produce such dramatic differences. A 30th level character is not twice as powerful as he was at 28th level, or 8 times as powerful as he was at 24th level.
The solution to this difficulty is to replace the exponential curve with a polynomial. v5 of the Challenging Challenge Ratings appendix is equivalent to approximating the WotC exponential curve with a quadratic (CR squared). Challenge = the sum of the square of the individual CRs.
However UK's recent proposal would approximate the exponential curve with a tertic formula (CR cubed). Challenge = the sum of the cube of the individual CRs. I don't like it because it means that treasure is no longer proportional to the challenge. Unless you make treasure follow a tertic formula too- but the cubic formula works much better. (Treasure = character level cubed, times 100 gp. (Treasure from an encounter = challenge x 100 gp. At minimum- if treasure is lost/spent then the wealth won't keep up with experience. Unless experience is lost/spent too!).
But it is a better fit to the exponential curve than the quadratic is. Make a table of CRs with 2 ^ (CR/2) and compare it with (CR^2)/3.125 and (CR^3)/31.25. The polynomials undershoot the exponential at low levels, but not by too much. But the cubic makes a better fit at higher levels. Especially if you can recalculate the CRs of various high CR monsters to make them higher yet.
For example, if a monster is four times as tough as a CR 16 monster, then according to the WotC formula it would be a CR 20. But if you follow the quadratic expression it would be CR 32. Or CR 25 if you are using the tertic formula. It is less jarring to say that a CR 20 monster is "really" a CR 25 than to make a CR 32.
PCs are a special case. UK is saying that the CR of a player character is not his character level. (An open secret, really; a CR 10 monster is much stronger than a 10th level character). Rather, the CR is 2/3 the character level. I'm not sure how much of an approximation this is. If the actual number were not 0.66667 but 0.62996 (the cube root of 0.25) then a party of 4 nth level characters would have a challenge of exactly n cubed.
This would suggest that an encounter between 4 nth level characters and a CR n encounter would be a 50/50 chance; as likely to be a TPK as not. Which is not the case. And so I wonder about this aspect, at least, of UK's calculations.
The cubic ratio works better than the quadratic ratio at predicting "fight club" match-ups between monsters in the monster manual. Run an old white dragon (CR 15) against 2 young adult brass dragons (CR 10 each). Although the (quadratic) challenge is almost the same (225 vs 200), the white seems to have a significantly bigger advantage. You need to have 3 young adult brass dragons before it becomes very close; the (tertic) challenge in this case is 3375 vs 3000. Which according to my calculations appears to be true; the old white will probably defeat 3 YA brass, but not four.
Not that fight clubs show much- but I think different sorts of dragons are as good a measure as any as to how CR and numbers of opponents will interact.
This has clear implications for how to scale class benefits and spell progressions. Should a 30th level spellcaster be 44% more powerful than a 25th level caster (as the quadratic model would dictate)- or 73% more powerful?
Whether or not it is more accurate, a change to this basic formula is going to have ripple effects in feature breakdown like UK does in v5. Really, it depends on how you playtest the monsters. Say that you decided that a given monster was CR 20 in the old system because it was equivalent to 4 CR 10 monsters. In the new system it is too weak to be a CR 20, since a CR 20 is equivalent to 8 CR 10s. So the old CR 20 has to be reduced to CR 16. Unless the old CR 20 was playtested by taking 4 of them against a CR 40. In which case (assuming the CR 40 is still CR 40) the CR 20 is really CR 32. And so the features that you priced assuming the monster was a CR 20 now have to be priced differently.
Unless UK took very careful notes as to how he playtested the CRs of the monsters (or was very consistent in his playtesting), he'll have to start from scratch to determine the new CRs. And thus to price the features that add up to that number. Which means that it will all be much delayed. I find it all very irritating.
Anyway, that's where I am.
It doesn't look like a big difference from the previous system of CR x 2 = EL + 4, but it means that to determine the "challenge" of a creature you have to cube its CR instead of squaring it. Something I have had some difficulty accepting.
The official rule is that CR + 2 = EL + 2. In other words, one CR 12 monster is worth the same amount as two CR 10 monsters or four CR 8 monsters or eight CR 6 monsters or 16 CR 4 monsters. The rule isn't supposed to hold for an EL gap of more than 8 or so (and might be only approximate at more than 5 or so), but is generally supposed to be valid from between EL 1 and EL 20.
For epic level encounters we're more concerned about it applying at the upper end of the scale. It is generally held that PCs don't increase *that* quickly in power at the upper levels. Sure, there are things like blasphemy that can convert a few levels difference into an overwhelming difference, but generally the progression of AC, hp, attack rolls, damage rolls, Save DCs and base saving throws don't produce such dramatic differences. A 30th level character is not twice as powerful as he was at 28th level, or 8 times as powerful as he was at 24th level.
The solution to this difficulty is to replace the exponential curve with a polynomial. v5 of the Challenging Challenge Ratings appendix is equivalent to approximating the WotC exponential curve with a quadratic (CR squared). Challenge = the sum of the square of the individual CRs.
However UK's recent proposal would approximate the exponential curve with a tertic formula (CR cubed). Challenge = the sum of the cube of the individual CRs. I don't like it because it means that treasure is no longer proportional to the challenge. Unless you make treasure follow a tertic formula too- but the cubic formula works much better. (Treasure = character level cubed, times 100 gp. (Treasure from an encounter = challenge x 100 gp. At minimum- if treasure is lost/spent then the wealth won't keep up with experience. Unless experience is lost/spent too!).
But it is a better fit to the exponential curve than the quadratic is. Make a table of CRs with 2 ^ (CR/2) and compare it with (CR^2)/3.125 and (CR^3)/31.25. The polynomials undershoot the exponential at low levels, but not by too much. But the cubic makes a better fit at higher levels. Especially if you can recalculate the CRs of various high CR monsters to make them higher yet.
For example, if a monster is four times as tough as a CR 16 monster, then according to the WotC formula it would be a CR 20. But if you follow the quadratic expression it would be CR 32. Or CR 25 if you are using the tertic formula. It is less jarring to say that a CR 20 monster is "really" a CR 25 than to make a CR 32.
PCs are a special case. UK is saying that the CR of a player character is not his character level. (An open secret, really; a CR 10 monster is much stronger than a 10th level character). Rather, the CR is 2/3 the character level. I'm not sure how much of an approximation this is. If the actual number were not 0.66667 but 0.62996 (the cube root of 0.25) then a party of 4 nth level characters would have a challenge of exactly n cubed.
This would suggest that an encounter between 4 nth level characters and a CR n encounter would be a 50/50 chance; as likely to be a TPK as not. Which is not the case. And so I wonder about this aspect, at least, of UK's calculations.
The cubic ratio works better than the quadratic ratio at predicting "fight club" match-ups between monsters in the monster manual. Run an old white dragon (CR 15) against 2 young adult brass dragons (CR 10 each). Although the (quadratic) challenge is almost the same (225 vs 200), the white seems to have a significantly bigger advantage. You need to have 3 young adult brass dragons before it becomes very close; the (tertic) challenge in this case is 3375 vs 3000. Which according to my calculations appears to be true; the old white will probably defeat 3 YA brass, but not four.
Not that fight clubs show much- but I think different sorts of dragons are as good a measure as any as to how CR and numbers of opponents will interact.
This has clear implications for how to scale class benefits and spell progressions. Should a 30th level spellcaster be 44% more powerful than a 25th level caster (as the quadratic model would dictate)- or 73% more powerful?
Whether or not it is more accurate, a change to this basic formula is going to have ripple effects in feature breakdown like UK does in v5. Really, it depends on how you playtest the monsters. Say that you decided that a given monster was CR 20 in the old system because it was equivalent to 4 CR 10 monsters. In the new system it is too weak to be a CR 20, since a CR 20 is equivalent to 8 CR 10s. So the old CR 20 has to be reduced to CR 16. Unless the old CR 20 was playtested by taking 4 of them against a CR 40. In which case (assuming the CR 40 is still CR 40) the CR 20 is really CR 32. And so the features that you priced assuming the monster was a CR 20 now have to be priced differently.
Unless UK took very careful notes as to how he playtested the CRs of the monsters (or was very consistent in his playtesting), he'll have to start from scratch to determine the new CRs. And thus to price the features that add up to that number. Which means that it will all be much delayed. I find it all very irritating.
Anyway, that's where I am.
