I don't think anyone has mentioned a big advantage of having damage mitigation, i.e. "effective" health versus actual health:
If you talk half as much damage then you will require half as much healing, i.e. your health per second regeneration will heal you twice as quick, or you'll require half as many healing spells - so you'll need less downtime out of combat.
Actually, priests heal percentage-wise, so it really doesn't matter either way (health regen and DG healing skills are still flat values.)
To Lieu: Effective HP is an edge case. It assumes you have 100% non-spell damage coming your way. That's kind of like, to use your chess analogy, finding a perfect strategy to fight against somebody who only moves his pawns. Your chess theory argument is strawman; you make it sound like it's related to chess theory, and of course saying chess theory is useless would be dumb. But it's not related to chess theory, at least not that strongly. There are plenty of useful theories, and useless theories. For example, a good example of theory would be "I can get more "net" damage (% rate the opposing Demigod loses HP, IE 10%HP/Sec to %rate my Demigod takes damage) by stacking HP instead of attack." That's useful theory. Saying "I can have effectively X more HP if I buy these items and don't get hit by any spell damage at all" is a bad edge case because spell damage is such a huge exception to make that it's hard to find any real application for it.
The accuracy of effective HP is proportional to the % of damage taken that is not spell based. With a few games of testing with various different Demigods, most builds wind up getting around 70% nonspell damage and 30% spell damage [though it changes; an Ooze UB at level 12 gets roughly 50% spell damage and 50% attack damage, but once you hit level 18 where you have all 6 points in stats, it becomes 66.6...% AA to 33.3...% spell, again roughly.) Standard deviation was the wrong term, and I admit it. What I was trying to say is basically that the average build, from playing against other Demigods using various different builds (and with myself using different builds), about 70% of the damage was nonspell, with builds going from 40% to 100% attack damage being fairly common (only TB ever got close to 100% spell damage).
There are obviously exceptions; if UB spits on somebody and they run, 100% spell damage for that encounter, and if he has no mana it will be 100% AA damage. And obviously, my data-set was small (maybe... 20 different builds encountered over the course of a few games?) However, the stats are still important, because that allows you to make an educated guess as to how much armor is actually going to affect you, while effective HP isn't.
Also, since you seem to have misconceptions about what I am saying, I am not saying armor is useless. I am saying the calculation for effective HP, which assumes 100% armored damage, is fairly close to useless (its an edge case, and it does have some merit against AA regulus and strictly tower Rook [which I am finding uncommon these days; a lot more people are going towers until level 7, then switching over to boulder roll + hammer smash.] Armor is useful, obviously. But instead of figuring out effective HP, just figure out what % damage is probably going to be dealt to you from armor-reducing methods, and then calculate your HP.