Hate to be that guy, but I believe the word "logarithmically" is wrong to describe the growth of encounter power. Total encounter power is n^2 where n is a number of boblins. This is a quadratic expression, not logarithmic. Quadratic expression indeed grow faster than linear, while logarithmic are eventually outpaced by linear expressions. The growth speed (or derivative) of a logarithmic expression in inversely proportional to its arguments.
One thing that drives me nuts with this article: a value that increases proportionally to a square increases quadratically, not logarithmically. Logarithmic growth doesn't even have the runaway effect squared numbers do.
While I agree with you in general, I think one thing that might be overlooked is that many monsters have debilitating conditions that they inflict which can inflate a monster's effective power.
For example, if you have a level 10 party that faces an encounter that is balanced for their level, you wouldn't expect a CR 1 creature to have much impact. But if that creature is a ghoul, and a party member fails the saving throw (which isn't that unlikely, since not all saves automatically progress with level), then a single CR 1 creature has not only denied one of the PC's their actions, but also made them take a considerably higher amount of damage if they're hit by other monsters, since melee attacks will be auto-crits. I think this is where the action economy, independent of monster hp or damage, matters a lot more, since more monsters will be able to inflict these conditions more often.
That being said, I applaud you for trying to make sense of the CR system, and I look forward to giving the CR 2.0 system a spin!
Hate to be that guy, but I believe the word "logarithmically" is wrong to describe the growth of encounter power. Total encounter power is n^2 where n is a number of boblins. This is a quadratic expression, not logarithmic. Quadratic expression indeed grow faster than linear, while logarithmic are eventually outpaced by linear expressions. The growth speed (or derivative) of a logarithmic expression in inversely proportional to its arguments.
Fair! I'm no math expert, so I appreciate the comment. I'll correct the article accordingly.
One thing that drives me nuts with this article: a value that increases proportionally to a square increases quadratically, not logarithmically. Logarithmic growth doesn't even have the runaway effect squared numbers do.
Fair! I'm no math expert, so I appreciate the comment. I'll correct the article accordingly.
While I agree with you in general, I think one thing that might be overlooked is that many monsters have debilitating conditions that they inflict which can inflate a monster's effective power.
For example, if you have a level 10 party that faces an encounter that is balanced for their level, you wouldn't expect a CR 1 creature to have much impact. But if that creature is a ghoul, and a party member fails the saving throw (which isn't that unlikely, since not all saves automatically progress with level), then a single CR 1 creature has not only denied one of the PC's their actions, but also made them take a considerably higher amount of damage if they're hit by other monsters, since melee attacks will be auto-crits. I think this is where the action economy, independent of monster hp or damage, matters a lot more, since more monsters will be able to inflict these conditions more often.
That being said, I applaud you for trying to make sense of the CR system, and I look forward to giving the CR 2.0 system a spin!