First revision was posted on my guild forums - a friend suggested that I could get some higher quality feedback posting here.

I was wondering how one might comprehensively compare the two main damage seals the paladin class has. Seal of Righteousness (SoR, base ability) versus Seal of Command (SoC, 11pt Ret talent). So . . . Theorycraft ahead. And please excuse the jargon/acronyms - I was going to post the final version on the official paladin forums, where most of the terms are well known.



Original post:
"SoC vs. SoR

[. . . ]

Variables:
Weapon Attack Speed (WAS)
Weapon Damage (WDPS)
Melee Crit % (MC%)
Attack Power (AP)
Miss/Parry/Dodge(MPD%)
+dmg (D)
+holy dmg (HD, apparently JotC acts differently then generic +dmg for the purposes of SoC)


Some equations:
Weapon damage = [Avg. Weapon damage] + [AP/14] * WAS = WDPS * WAS + AP/14 * WAS = WAS * (AP/14 + WDPS)
SoC damage over a minute:
(7ppm)*(0.7 Weapon damage/proc) + (7ppm) (0.2*D + 0.29*HD) = 4.9 * WAS * (AP/14 + WDPS) + 1.4*D + 2*HD
SoR damage over a minute:
(60 seconds) * ([16/24 DPS] + [10%/12.5%] * (D + HD) / WAS) = [960/1440] + [6/7.5]/WAS*(D + HD)


A quick analysis of the damage equations:
SoC - [4.9 * WAS * (AP/14 + WDPS) + 1.4*D + 2*HD] * (1+MC%-MPD%)
SoC scales with your melee damage, and is also boosted by +dmg. In addition, since SoC crits for double, its damage output is increased by whatever your melee crit % is. However, it also suffers from your miss/dodge/parry %.

SoR - [960/1440] + [6/7.5]/WAS*(D + HD)
SoR only depends on +dmg and the inverse of your WAS - faster weapons are better. It will generally scale faster with +dmg than SoC.

So . . . What does that mean? Plug in some numbers for AP, WAS, WDPS, and D, and you can find which seal does more damage. HD is fixed at 140 if included- you either have JotC up or not (ignoring talents).


Since I'm not sure how to account for crit% *and* miss/parry/dodge%, I've ignored both.

1H, 2.00 WAS
[SoC dmg] = [SoR dmg]
4.9 * 2.00 * (AP/14 + WDPS) + 1.4*D + 2*HD = [960] + [6]/2.00*(D + 0)
0.7*AP + 9.8*WDPS + 1.4*D + 2*HD= 960 + 3*D + 3*HD
9.8*WDPS + 0.7*AP = 1.6*D + HD + 960
WDPS + AP/14 = 8/49*D + 5/49*HD + 98


If we use a 40 DPS weapon, no JotC, then
AP = 14 * (8/49*D + 58)
0 D -> 812 AP
200 D -> 1269 AP
Those are AP thresholds for SoC to equal SoR.

If we use a 50 DPS weapon and throw in JotC, then
AP = 14 * (8/49*D + 62)
0 D -> 868 AP
200 D -> 1325 AP

Taking a break from further calculations until I can factor in MPD%."


Based on some stuff I read in the Combat Mechanics thread, seems that I could factor in MPD% by simply taking (1 - MPD% + Crit%) for the damage modifier of SoC. What's a reasonable value to assume for the Miss/Parry/Dodge rate on same level targets? 15%? (5% miss, 5% dodge, 5% parry)