CR Formulae
There is an awful lot of science in the way that 3e was designed, especially the integration of character level/CR/XP and all. There better be a "unified" mathematical formula at the heart of it all.
Wulf, I've gotta disagree with you on this. While, on the one hand, I think it's a terrific idea for designers to get under the hood and give the average player a system to easily construct monsters and place them confidently in the framework of the greater game, I also think such a system would be necessarily constrained in its overall utility. Not all of the most interesting monsters conform nicely to every adventuring group, or, so, to the CR scale, but they're part of the great creative empowerment of 3E.
If I want, for example, a monster that's a spinning pile of chains (MMII), then I just create a new ability for my monster that lets him spin around. So long as I have the freedom to invent any special ability and define it within the rules, the CR system is going to be a little fuzzy. I think it's better that way.
Not every adventuring group is alike, and it's not safe to assume too much about a PC party when you assign CR. It's not a sound practice, for example, to decrease a monster's CR because it is somehow vulnerable to clerics under the assumption that every PC group has a cleric. It's not safe to assume that the PCs will have a wizard with them who can counter another monster's powers. To some degree this happens, to be sure, but that's where the art comes in; the factors of experience, familiarity with the rules and flexibility. These things won't be genuinely modeled, in my opinion, by a formula.
One answer might be to offer discreet advice in the monster's entry on how a given monster is or is not a suitable threat to certain character types, but I think that's best left to the interpretation of the DM (since realizations about monster-character interactions are part of the fun that comes out of the skirmish game, in my experience). The more common answer is that the CR system needs to be revised or tweaked or strengthened.
Whatever mathematical forumla you come up with isn't going to be flexible enough to accurately position each monter on the statistical scale against every group of PCs, every strategy, every wacky fantasy world or every home-grown spell, class, weapon or other monster. The system needs to stay flexible to stay broadly applicable, I say. DM judgement needs to be preserved as an overriding factor in CRs.
I submit that DM education is the best method of appreciating the value of the CR system. DMs need a good guide on how, when and why to set a CR, adjust a CR and spot a CR that's sound for one group, but maybe not for theirs. I think this topic's more about game theory than it is about the statistical model.
As evidence, I hold up the separation of CR and EL in d20. A monster's CR is meant to be fixed, but the EL it appears under is supposed to be the flexible scale a DM has to get a sense of real control of the system. The malleability of ELs has gone underused, in my opinion, by adventure and game designers. An EL can convey a lot, suggest a bit more, and give more leeway to the interpretation of a CR. A monster's context can't render its CR invalid, for example. An EL is still only mildly more valuable to the average DM. Only a given party's DM can accurately assess the relationship between a monster, the encounter and her party.
Or so says me. I've written half a column on this right here, so I tip my hat to whomsoever has indulged me this far.
Totally different point: Wulf, is Bad Axe still in Lombard? I'm from the La Grange area originally.