My latest playtest adventure included an encounter in which a dhampir antipaladin challenged the party's human paladin to single combat. (The antipaladin, being an antipaladin, cheated during the duel, calling in an undead ally to tag-team the paladin.)
I ran the encounter three times. Some details follow.
Details:
In the first run-through, the paladin and antipaladin were both 8th-level/non-mythic characters, and the antipaladin's ally was a CR 2 shadow. The paladin engaged both opponents in melee, despite being designed as an archer. The paladin defeated both opponents handily, largely a result of the gap between PC and NPC ability scores and gear.
In the second run-through, the paladin was 8th-level/4th-tier with 8th-level PC gear, the antipaladin was 12th-level/non-mythic with 12th-level NPC gear, and the antipaladin's ally was a CR 5 greater shadow. The paladin engaged both opponents in melee, despite being designed as an archer. The antipaladin's superior class features and the greater shadow's ability drain combined to overwhelm any advantage provided by mythic tiers (including 'to the death') and the paladin was killed.
In the third run-through, the paladin was 8th-level/4th-tier with 8th-level PC gear, the antipaladin was 12th-level/non-mythic with 12th-level NPC gear, and the antipaladin's ally was intercepted and destroyed by the paladin's allies. The paladin was allowed to use his bow while the antipaladin relied primarily upon melee weapons and charge attacks. The paladin was able to overcome the antipaladin with difficulty by continually using fleet charge to retreat.
(In both of the run-throughs in which the paladin had mythic tiers, I was used amazing initiative option #2 from the Amazing Initiative Alternatives thread, and allowed the paladin to take one mythic swift action plus one non-mythic swift action each round; gaining the extra standard action from amazing initiative counted as the paladin's mythic swift action for the round.)
Summary
The 8th-level paladin PC easily defeated the 8th-level antipaladin NPC with a CR 2 minion.
The 8th-level/4th-tier paladin PC taking two standard actions per round was able, with difficulty, to defeat the 12th-level antipaladin NPC when the antipaladin had no minion and was prevented from making full attacks.
The 8th-level/4th-tier paladin PC taking two standard actions per round had a hard time competing with the 12th-level antipaladin NPC when the antipaladin had a CR 5 minion and was free to make full attacks.
Conclusion
In my playtest, adding four tiers (and no wealth) to an 8th-level paladin did not seem equivalent to adding four levels (and the appropriate amount of NPC gear) to an 8th-level antipaladin, even when the antipaladin's APL-6 minion was removed from the equation. The antipaladin, who was a push-over before adding these tiers and levels, was now a serious threat.
Had the paladin been equipped with 12th-level gear based on the wealth-by-level chart (instead of the 8th-level gear he possessed upon gaining four temporary mythic tiers), he would likely have retained more of his edge over the antipaladin. But in an adventure where PCs are granted four temporary mythic tiers, they aren't also guaranteed to get four levels' worth of gear to go with those mythic tiers.
This issue is going to be a problem when designing adventures that grant temporary mythic tiers. Even if one mythic tier is exactly equal to one class level in terms of power, you can't use this formula in adventures granting temporary tiers; characters with temporary tiers will likely end up dramatically under-equipped for their new APL, throwing off all calculations of encounter difficulty.
What about some equipment that only worked for mythic characters, in the cases of temporary mythic levels. That way bonus equipment could be given, without exceeding the WBL after the tier goes away.
That CR 12 antipaladin is an average encounter against 4 or 5 PCs though. Its not surprising at all that even a Mythic PC would have trouble against that "Challenging" CR 12 encounter as the PC is only APL 11.
I thought a 12th level NPC geared enemy CR 11, while a PC geared 12th level NPC would be CR 12. So the Paladin, PC geared and with 8 levels and 4 tiers, should be about CR 12 and the 12th level NPC geared antipaladin should be CR 11. Granted, CR 11 is only easy for 4 12th level PCs, not one 12thlevel equivalent PC, but it seems a fair test. If the paladin blows through the 8th level NPC as an 8th level PC, but has a hard time against a 12th level NPC as an 8th+4 tiers PC, it seems to indicate that levels and tiers aren't quite equivalent.
Have you tried the paladin at 12th level vs the 12th level NPC+ally, Epic Meepo? For the sake of completion I think that would be something useful to do. If the 12th level paladin has no problem handling the 12th level antipaladin while the 8th+4 tiers paladin had problems, barring outside variables like dice luck or lack of luck, it would support the conclusion more.
That CR 12 antipaladin is an average encounter against 4 or 5 PCs though. Its not surprising at all that even a Mythic PC would have trouble against that "Challenging" CR 12 encounter as the PC is only APL 11.
I might have agreed with you if I hadn't run the 8th-level paladin vs. 8th-level antipaladin fight first. But that fight established that a mid-level PC with appropriate PC gear had little trouble with an NPC of the same level with appropriate NPC gear.
I really do think the 8th-level/4th-tier paladin would've had a relatively easy time with the 12th-level antipaladin, had the paladin's wealth not been 75,000 gp below that suggested for a PC of his effective character level.
As it was, the paladin's gear was worth only 12,000 gp more than that of the antipaladin NPC, making paladin's AC, attacks, and damage rolls about equal to those of the antipaladin. Add 75,000 gp to the paladin's gear and his AC, attacks, and damage rolls could each increase by +3.
Have you tried the paladin at 12th level vs the 12th level NPC+ally, Epic Meepo?
I didn't try that, mainly because that level combination couldn't have reasonably happened during the course of the adventure I was running. For the sake of playtesting, I may have to go back and run it, though.
Without running the 12th-level vs. 12th-level fight, I can say the paladin would have a +4 attack and damage advantage over the antipaladin if using 8th-level PC gear, +7 if using 12th-level PC gear. Even if the paladin ate some ability damage before destroying the greater shadow, his numbers would remain higher than those of the antipaladin.
I took a quick look at the Wealth-by-Level chart, and the Paladin should have better gear than both the 8th level and 12th level Anti-Paladin, by virtue of having more money to spend on equipment. A normal 8th level Paladin PC vs a normal 8th level Anti-Paladin NPC should have the upper hand, due to superior funds to buy superior equipment. A mythic 8th level Paladin PC (effective level 12, due to 4 mythic tiers) vs a normal 12th level Anti-Paladin NPC should be a fight on more equal footing, since their funds to buy gear are much closer, so they're probably bringing a lot of the same guns to the fight. Suddenly throw an additional enemy up against the same fight between a mythic 8th level Paladin PC vs a 12th level Anti-Paladin, and the fight will no longer be in the Paladin's favor.
I don't know if this line of thinking actually means anything, but from my own musings, that's the conclusion I come to and it seems to match up with what your tests concluded with.
You are correct that an 8th-level/4th-tier paladin with equipment comparable to that of a 12th-level antipaladin should have a tough time defeating that antipaladin, especially if another opponent shows up on the scene.
The problem here is that the core rules for encounter design are built assuming an APL 12 PC doesn't have equipment comparable to that of a 12th-level NPC. The PC should have an advantage of roughly 80,000 gp over the NPC, an advantage which temporary mythic tiers don't provide. That disparity between normal level advancement and temporary mythic advancement needs to be accounted for in the rules for mythic encounter design.
Have you thought of running it as a Paladin/Guardian (Sudden Block!)? Or with all the different Paths? I'd be curious to see how they stack up against the same opponent.
You are correct that an 8th-level/4th-tier paladin with equipment comparable to that of a 12th-level antipaladin should have a tough time defeating that antipaladin, especially if another opponent shows up on the scene.
The problem here is that the core rules for encounter design are built assuming an APL 12 PC doesn't have equipment comparable to that of a 12th-level NPC. The PC should have an advantage of roughly 80,000 gp over the NPC, an advantage which temporary mythic tiers don't provide. That disparity between normal level advancement and temporary mythic advancement needs to be accounted for in the rules for mythic encounter design.
I wonder if the disparity will be as bad if you were to pit the same PC against a monster, something that doesn't get its stats from magical equipment.
I have no possible clue what kind of creature you could go up against for a meaningful test, though...
I thought a 12th level NPC geared enemy CR 11, while a PC geared 12th level NPC would be CR 12.
You're right the Antipaladin would be CR 11. But remember APL is determined by how many characters are in a party, with 3 or fewer PCs taking a -1 to APL (though I'd argue a lone PC should be -2).
However assigning CR should also account for the realtive wealth of the party (or NPC), so in this case with the Mythic hero having only the standard WBL of his normal class levels (not counting his mythic tiers) the CR of the encounter goes up by +1 This is technically a bump you'd give the NPC due to having PC level gear, but since the disparity is with the PC it works the same way. So you still have an APL 11 party taking on a CR 12 encounter thus the "Challenging" descriptor.
