This calculator is meant to be a tool to give you information about which spec will utilize the most your gear's potential damage output. It uses lv 70 talents and abilities, and compares the three specs I personally believe to the most viable for pure damage; x/x/41+, 40/0/21 and 31/0/30.

http://www.savefile.com/files/297044

I ran into a few problems during the creation of this calculator, and I came here in search for help. Most of them have now been addressed, except for one: I still don't have information on whether or not Crusader Strike is normalized, in the calculator I assume it isn't.

The theorycraft-veterans will probably puke at my layout and awkward way of calculating things, but I'm still in the learning stage of Excel, and I've partially made this calculator in order to gain more experience. Some constructive criticism would be much appreciated, and please do tell if I've made any errors.

EDIT: There was an error to the calculation of SoC's DPS, which has now been updated.
EDIT2: Another update, this time incorporating a proper Vengaence uptime calculator.
EDIT3: Proper glancing blow, hit ratio and Avenging Wrath calculations incorporated.

No offense but assuming: 0 misses, continuous vengeance and 0 glancing blows is a bit crazy

Also what talents are you assuming in 41 ret?
2h spec, crusade, imp might, sanctity aura?
divine str from holy?

That aside,

It'd be nice to see what talents you've used for each build.

It looks like the difference between x/x/21 and x/x/41+ is very small -- on the order of 10%. How much of an increase is gained by those first 21 points? If a x/x/0 pally does something like 80% of the dps of a x/x/41+ pally, I'd find that very interesting. A spec-based damage differential of ~100dps is peanuts compared to other core damage classes' theorycrafted dps (on the order of 1000 dps).

I'm going to ask an ignorant question:

How will SoC / HoJ (trinket) / Reckoning & Windfury interact?

The reason for why I haven't included any examples of specs is that only a few key talents really makes any difference to the way I calculate the damage, how you spend the rest of your talents is irrelevant. These key talents are:

* Holy Shock (Holy Tree)
* Holy Guidance (Holy Tree)
* Crusade (Retribution Tree)
* Sanctity Aura (Retribution Tree)
* Two-Handed Weapon Specialization (Retribution Tree)
* Fanaticism (Retribution Tree)
* Crusader Strike (Retribution Tree)

Talents like Divine Strength and Conviction are not something I've included, as information from them can be taken directly from your character-tab in-game. I've also left the Protection Tree out of the calculation, as I do not see it as a viable way of doing damage. I might include it in the future though, perhaps a holy/protection build with SoR.

I know that leaving out misses, glancing blows etc. artificially makes the numbers a tad bit higher than they should, this is another thing I'm going to improve in the future. You'll still be able to get an impression of how good paladin-dps will be however, and for the purpose of comparing the specs it is just about irrelevant.

As for Reckoning, I havent included that for the reason mentioned above; protection isn't viable for raid-DPS. In addition, it requires you to get hit, something you'll not want as a damage dealer. HoJ and Windfury aren't included as of now, that's also on the to-do list. However, I'm not very familiar with Windfury, so I'll have to obtain some information on that first.

Oh, and writing my name at the end of each post is another bad habit of mine, I'll try to quit. :')

I'm finding that mob grinding is way more efficient with SoR with JotC debuff than SoC. My blood elf is 55 now.

There's something messed with JotC mulitplier applied to SoR. My SoR (rank 7) lists as 46 to 63. With a JotC debuff, its hitting for 112 per swing. That's pratically doubled. I'm using Taran Icebreaker which is a 2.30 speed fast weapon.

I'm not sure why JotC is increasing SoR so much. By doing so, its making the most effective DPS I've got. SoC just can't come close.

If anyone's got any good ideas as to how one could accurately calculate the uptime of Vengaence, please do tell, as I'm aware of the differences in uptime between a 31/0/30-build and x/x/41+. Perhaps by using the average number of attacks per second, I'll have to check that later. Still, if the modifier changed to for instance 1.07 instead of 1.1 for a 31/0/30-build, the difference in DPS-output would be marginal.

In reply to the post above, this is meant to be more of a tool to figure out your paladin's maximal DPS at level 70. If you're going to use SoR then you would have to be covered in huge amounts of spelldamage before it becomes more viable then SoC when you reach the proper gear level. SoB on the other hand, is a Seal that can compete with SoC in terms of damage, and I might include that one in a future update. Just a shame that I'm a human paladin, so I won't get to utilize it myself. :'(

Understand that I wasn't trying to disparage your work. It's an interesting piece of analysis.

The most effective way to look at it, IMO, is to look at a single weapon swing and say "What is the chance that Vengeance was up for this swing?" That's equivalent to asking: What is the chance that something crit in the last 8 seconds? So you figure that there were two weapon swings in the last 8 seconds, and possibly one or two SoC procs that could have crit, along with one JoC that could have crit.

Chance for a white crit is obviously just the base crit rate. Chance for an SoC crit is chance of a white hit times chance of an SoC proc times base crit rate. Chance of a JoC crit is base crit rate, plus 15% if Fanaticism is present. Should be straightforward to compute, if somewhat complicated.

After some brainstorming, I've come up with the following calculator for Vengaence uptime:

http://www.savefile.com/files/279582

Currently it only supports a x/x/41+ -build, but it'll be easy make it cover all of them later, when I'm not this tired. It might in fact be a more interesting piece on its own than the DPS-calculator. I'll merge them later, thanks for making me do this. ;)

Do you have both Improved SoR and Improved SotC? Because if you do, 112 would actually be correct (63 * 1.15 + 140 * 1.15 * 2.3 * 0.108 = 112). As far as I can tell, it's intentional too. From the numbers I've seen on the Seals in Beta, it seems like Blizzard intentionally made SoR scale "better" than SoC for anything faster than 3.4 speed 2H.

Rough average Vengeance uptime formulas, assuming you use SoC and judge every 8 seconds (italics describe what each section means):

For 31/0/30:
1 - (chance you won't crit on Holy Shock: (1 - spell crit / 100) * 8 / 15) * (chance you won't crit on Judgement: 1 - melee crit / 100) * ((chance you won't crit: 1 - melee crit / 100) ^ ((number of attacks within the Vengeance duration: 8 / weapon speed) * (1 + number of SoC procs: 7 * weapon speed / 60))

For x/x/41 (assuming you have Fanaticism):
1 - (chance you won't crit on Judgement: 0.85 - melee crit / 100) * ((chance you won't crit: 1 - melee crit / 100) ^ ((number of attacks within the Vengeance duration: 8 / weapon speed) * (1 + number of SoC procs: 7 * weapon speed / 60))

Heh. That's certainly simpler than mine. :) How do you figure out the number of critical hits made per minute though?

Unless my uptime-calculator is wrong, I think I'll continue using it as it's easier to pull different pieces of information from it. That's some interesting formulas though, they're certainly much simpler than the method I'm using. However, I've got no clue as to how I should use Fiola's formula in an Excel-sheet. ;p

Well first you count how many weapon swings you make. Say you have a 3.40 speed weapon:

60 seconds / 3.4 seconds per swing = 17.64 swings

Then you get the PPM of Seal of Command, which is 7 procs.

If you judge Command every 8 seconds, 60/8 = 7.5 judgements.

Crusader Strike every 10 seconds, so 6 strikes.

So autoattack + SoC + CS = 30.64 swings. Assume a 15% crit rate, that's 4.60 crits.

JoC has 30% crit rate with Fanaticism, so 2.25 crits.

4.60 + 2.25 = 6.85 crits a minute.

Mind you, I can't remember off the top of my head whether Crusader Strike can proc Seals or not and whether Windfury Totem can proc Seals or be procced off SoC procs and/or Crusader Strike, so this is just an example of how to find the number of crits per minute, as opposed to a "real" example.

Ah, sorry. I should've been more clear with my question. I was asking if the formula had any assumptions that'd change the number of critical hits made in a minute in some non-obvious way. I did a quick calculation at 15% melee crit rate as well without factoring in CS, and I came up with 57% uptime (1 - exp(-0.143 * 5.946)), as opposed to 45% from my own formula, so I was wondering what I was missing.

Edit: Never mind. Apparently, I can't plug in numbers correctly. :P Mine matches Fiola's.

With a 15% critrate I get an uptime of 58,94% through my calculator, I can't really figure out the cause of the small difference. A good night's worth of sleep might help. :)

I was under the impression that Windfury was no longer considered a melee hit, and thus wouldn't get procs or generate rage.

I believe Fiola's formula is going to be slightly inexact since it assumes the crits will be distributed entirely at random throughout each minute of combat, which is not exactly true. For example, fanaticism will tend to make a greater proportion of the crits happen on JoC, and those are always spaced eight seconds apart. However, I expect it would still provide numbers pretty close to reality (e.g., the 2% difference shown here.)

I've now updated the calculator to incorporate the proper Vengaence-calculations. Next in line is misses and glancing blows.

Here's the math proof I promised. I'm too lazy to clean it more. And yes, the result is an approximation. With my math, factoring that in was too much bother. (And hey, it's not like you'll notice a 2% difference in a small number. >_> )


VENGEANCE UPTIME:

Vengeance boosts physical holy damage output by 15% for 8 seconds after dealing a critical strike. Essentially, it's a function of the number of critical hits over a given time interval.

Let's call it Vt(N) [Vengeance Time]

*N is the # of critical hits you make per minute


Each extra critical hit increases the amount of vengeance time by an amount less than the previous, on average proportional to the % of non-Vengeance time. (Diminishing returns)


Vt(0) = 0
Vt(1) = [1 - V(0)/60]*8 + V(0) = 1*8 = 8
Vt(2) = [1 - V(1)/60]*8 + V(1) = 52/60*8 = 8 = 14.93
Vt(3) = [1 - V(2)/60]*8 + V(2) = 45.07/60*8 + 14.93 = 20.94


Assume Vt() is in the form 60(1-e^kn)

Vt(0) = 60(1-e^0) = 60(1-1) = 0
Vt(1) = 60(1-e^k) = 8 -> 1-e^k = .133 -> e^k = 0.866 -> k = ln(0.866) = -.143
Vt(2) = 60(1-e^2k) = 14.93 -> 1-e^2k = .2488 -> e^2k = .7512 -> 2k = ln(.7512) = -.286 -> k = -.143


So Vt(N) = 60*(1-e^-.143N)

As N approaches infinity, e^kn goes to 0, and Vt() is 60, as it should be. [If you crit every hit, Vengeance should be up 100% of the time] Note that k = -.143 is for N per 60 seconds - you could scale k for a different time interval if you so wished. ie: N critical hits per 30 seconds would have a different value for K.


For % uptime, just divide Vt(N) by 60 and multiply by 100%, which yields:

Vengeance Uptime:
(1 - exp(-.143 * N) * 100%

I'm now done with a major update, and have incorporated proper calculations for glancing blows, hit ratio and Avenging Wrath. (I looked at Deathwing's calculations for help with the glancing blows, if you've got a problem with that then please do tell.) The calculator should now be next to 100% accurate, the only thing that's missing is is Windfury and Hand of Justice, which will be coming in another update together with calculations for Seal of Righteousness-DPS.

http://www.savefile.com/files/297044

There's a lot of this on the beta forums. I think a great deal of it, though, is just gear selection. SoC is not a great damaging seal when you have a 12% crit rate and a one-hander. You have to work fairly hard to get a good crit rate with a paladin while still maintaining anything resembling a decent mana pool (even in TBC), but really that is the bread-and-butter of a SoC ret build. Get your crit to 20-25% and and you'll blow SoR out of the water.