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Message: <blockquote data-quote="mearls" data-source="post: 705831" data-attributes="member: 697">Math Is Our FriendThere is no reason why mathematical models cannot be used to determine a creature's CR. Let's take a look at the problem.A creature's CR is defined in relation to the 11 core classes. A creature of CR X should drain 20% of the resources available to 4 level X player characters equipped with items as per table 5-1 from the DMG.Now, the problem here is that not all level X characters are created equal. Players who make sub-optimal choices are going to have weaker than normal characters. For instance, I ran one game where a player kept taking levels in random classes that meshed together very poorly (fighter/bard/rogue/sorcerer, with rogue taken after level 1) and who make bad choices with feats and skills. A human fighter with Skill Focus, Alertness, and Exotic Weapon Proficiency (kukri) at level 1 is nowhere near as effective as one who takes Weapon Focus (longsword), Improved Initiative, and Dodge. However, we can assume that players will generally make half-decent skill and feat selections. Thus, it is possible to construct a typical character for each class from levels 1 to 20.There are a limited number of ways in which a monster can interact with characters via the system, and vice versa. I call these interactions "touches." A monster touches a PC's AC when it makes an attack with its base attack bonus. If it hits, it touches the PC's hit points with its damage spread. You can graph these interactions across different characters and different levels. The surprising thing is that when you sit down and look at the system this way, there are very few areas in which monsters and PCs touch each other. At low levels, it's all about AC and hit points. At higher levels, it transitions over to saving throws.Given these relationships, and given the definition of CR, we can create a series of profiles that yield what a given CR can do in terms of its touches against PCs. If you know that on average a CR 1 monster can inflict 3.8 points of damage per round, you can play around with the probabilities of attack and damage touches to build a wide range of monsters that drop into that 3.8 damage on average per round. Even AC comes into the equation when you plot out how long the monster can expect to survive combat.Now, you might be thinking that this is all well and good, but what does it mean for the game?A lot.If you can describe CRs in more concrete terms, ranges of base attacks, damage, SR, basically categories of all these areas where monsters and adventurers touch each other via the game system, you can create an interlocking set of values.Now, Will is right that the CR system is fuzzy. Try going against undead without a cleric. The barbarian's nifty Improved Critical feat is suddenly useless, as are the enchanter's spells and the rogue's sneak attack. Personally, where I in charge of 3.5E I would've dropped the blanket immunities that certain creatures receive. They really exacerbate the all groups are not created equal problem. If you have the Monster's Handbook, you can see that I come out and say that not all CRs are equal.So what does this all mean?Monsters and PCs interact in predictable ways in terms of the system. Given that CR is defined in terms of character level and resources, we can construct a range of interlinked values for damage, base attack bonus, AC, saves, and so on and graph the combat results those values generate in relation to the level of a typical party of adventurers.I think a lot of game designers are afraid of math. There's a general sense that math and other scientific studies somehow run counter to the creative process. I think things couldn't be farther from the truth, and that a dose of mathematics and computer modeling would go a long way to building better RPG systems.</blockquote>

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