Retribution Level 90 (T6) Talent Confirmation (Mathslol)

[Lolretadin]

Hello great and illustrious Paladin community of MMO-Champion! Just wanted to ensure that my calculations were right for my theorycrafting for the Level 90 Paladin Talents, specifically what would be chosen as Retribution.

The following is done based upon both Exp and Hit Cap, excluding crit. Str for example is 10,000.
Total damage done by spells is indicative of what they should be if they are used on CD and is totalled as such; Min Damage, Max Damage, Total Damage Per Minute, Total Damage Over 7 Min Parse. First Parse is excluding Wings and GoaK, and assumes a 100% uptime on Inquisition. Second Parse is the increase in the average damage when including Avenging Wrath, while using on CD.
1 Str == 2.2 AP
10,000 Str == 22,000 AP
Sword of Light == 0.5 SP/AP
22,000 AP = 11,000 SP

First Parse:
Holy Prisim
Damage Calculation for Single Target (Cast on Enemy) == 1.3(14,523 <--> 17,750 (+142.8%SP))
Min Damage == 1.3(14,523+1.428(11,000)) == 39,300.3
Max Damage == 1.3(17,750+1428(11,000)) == 43,495.4
Average Damage == (39,300.3+43,495.4)/2 == 41397.85
DPM (3 Casts) == 124,193.55
Total Damage Over 7 Min (21 Casts) == 869,354.85
Average 2 Per Min (Over 7 Min Totals) == 579,569.9
Average 1 Per Min (Over 7 Min Totals) == 289,784.95

Damage Calculation for AoE (Cast on Friendly; Max Target == 5) == 1.3(9794 <--> 11969 (+96.2%SP))
Min Damage/Target == 1.3(9,794+0.962(11,000)) == 26,488.8
Max Damage/Target == 1.3(11,969+0.962(11,000)) == 29,316.3
Average Damage/Target == (26,488.8+29,316.3)/2 == 27,902.55
DPM/Target (3 Casts) == 83,707.65
Total Damage Over 7 Min/Target (21 Casts) == 585,953.55
Average 2 Per Min (Over 7 Min Totals) == 390,635.7
Average 1 Per Min (Over 7 Min Totals) == 195,317.95

Execution Sentence
Damage Calculation == 1.3(SP*5,936/1,000+26.72716306*486)
Average Damage == 1.3(11,000*5,936/1,000+26.72716306*486) == 101,771.0216
DPM (1 Cast) == 101,771.0216
Total Damage Over 7 Min (7 Casts) == 712,397.1514


Hammer of Light
Damage Calculation/Target== 1.3((3,268 <--> 3993 (+32.1%SP))*8)
Min Damage == 1.3(3,268+0.321(11,000)*8) == 70,709.6
Max Damage == 1.3(3,993+0.321(11,000)*8) == 78,249.6
Average Damage == (70,709.6+78,249.6)/2 == 74479.6
DPM (1 Cast) == 74479.6
Total Damage Over 7 Min (7 Casts) == 521,357.2


Parse 2:
Holy Prisim
Casts with Avenging Wrath == 2/AW (4 Total)
AW Average == (1.3(39,300.3+43,495.4))/2 == 53,817.205
Total Increase Per Use == 12,419.9335
Increase Over 7 Min == 49,677.42
New Total == 919,032.27

Execution Sentence
Casts with Avenging Wrath == 1/AW (2 Total)
AW Damage == 1.3(101,771.0216) == 132,302.3281
Total Increase Per Use == 30,531.30648
Increase Over 7 Min == 61,062.61296
New Total == 773,459.7644

Hammer of Light
Casts with Avenging Wrath == 1/AW (2 Total)
AW Damage == (1.3(70,709.6+78,249.6))/2 == 96823.48
Total Increase Per Use == 22,343.88
Increase Over 7 Min == 44,687.76
New Total == 566,044.96

As already stated, the parses are ONLY if the ability is used on CD, which makes the Holy Prisim Totals unrealistic. I have added slightly more realistic totals to the First Parse for Holy Prisim, so that the damage outside of Avenging Wrath will be a bit more, to be redundant, realistic.

Although Holy Prisim is a lot more damaging if used on CD, both Hammer of Light and Execution Sentence seem to come out on top in their respective instances; with Execution Sentence doing better overall damage on single-target, and Hammer of Light doing more damage in instances of having about 5+targets in the AoE.

[Meteoric]

Total damage done by spells is indicative of what they should be if they are used on CD

This is a problematic assumption, and is actually the reason ES wins for single-target. 3 Holy Prisms outdamage one ES, but the Prisms cost two extra GCDs. In fact, since it generates no Holy Power, Prism doesn't actually hit hard enough prioritize very highly, so it ends up getting used more like every 30s+, rather than every 20s.

Edit: I see that you have added mention of this in the latter part of the analysis, so this comment will appear somewhat superfluous.

[Lolretadin]

This is a problematic assumption, and is actually the reason ES wins for single-target. 3 Holy Prisms outdamage one ES, but the Prisms cost two extra GCDs. In fact, since it generates no Holy Power, Prism doesn't actually hit hard enough prioritize very highly, so it ends up getting used more like every 30s+, rather than every 20s.

I'm aware, I was making addendum as well as completing the post as I knew this point would come up. I was just making sure I was calculating the totals correctly and was drawing the correct conclusions from my observations.

[General_Typhus]

Man I love playing math

[Veliane]

Something is very wrong in your calculations if Prism is doing less overall damage over 7min as AoE on up to 5 targets than single target.

[Lolretadin]

Something is very wrong in your calculations if Prism is doing less overall damage over 7min as AoE on up to 5 targets than single target.

You need to pay attention to the parameters; the Holy Prisim AoE is done per target. It is the damage that it would do to each individual target, hence the /target suffix. If I calculated the damage for max. targets, then Hammer of Light would easily win out against everything else as it does full damage to up to 10 targets.

[Sturmcantor]

The other enormous problem with your calculations is that you are assuming 22k AP. I have 35k AP buffed and am not all that geared (484 ilvl). Even at 463 ilvl you will have more AP than that. That makes a difference in scaling.

You also will never get 2 Holy Prisms off with AW per use unless you are using SancWrath.

[Lolretadin]

The other enormous problem with your calculations is that you are assuming 22k AP. I have 35k AP buffed and am not all that geared (484 ilvl). Even at 463 ilvl you will have more AP than that. That makes a difference in scaling.

You also will never get 2 Holy Prisms off with AW per use unless you are using SancWrath.

The scaling difference will be negligible for the calculations I made. Unless someone is being daft and Strength stacking, which is sub-optimal and something every PvEer should know at this point, the difference you're looking at is MAYBE 4 - 5k SP. Even then, the order of usefulness would still be the same. As we are taking a percentage of Spell Power, we aren't looking at a problem in which one increases at an exponential rate in the sense that one will overtake the others.

Also, as I've stated before, I added more realistic values for Holy Prisim looking at 1 cast and 2 casts per minute.

[Meteoric]

Stacking Strength via gems is actually still favorable for many setups. That's why you should sim your own stat weights rather than relying on example weights from a guide. And even without Strength gems, 22k AP is way low for an estimate. Even in my avg ilvl 474 "dungeon, valor, and LFR" gear, I'm at ~33k buffed, which is 16.5k spellpower. (Edit: Actually, more like 36k. I forgot to include flask & food.)

That matters because both spells have a base damage component as well as a scaling component, and these are not proportional. Specifically, Prism has proportionally more base damage and less scaling than ES, so increased spellpower will shift the comparison in favor of Execution Sentence.

If I plug in that 16.5k spellpower, Prism hits for 51.6k single-target, and ES for 144k. This is considerably more favorable to ES, before even counting the way it combines better with cooldowns/procs - each ES is now worth 2.8 Prisms, rather than 2.4. That doesn't totally reverse the conclusion, and Prism still has more flexibility between single-target and AoE, but it's not a negligible change from the original calculation.

[Lolretadin]

Stacking Strength via gems is actually still favorable for many setups. That's why you should sim your own stat weights rather than relying on example weights from a guide. And even without Strength gems, 22k AP is way low for an estimate. Even in my avg ilvl 474 "dungeon, valor, and LFR" gear, I'm at ~33k buffed, which is 16.5k spellpower.

That matters because both spells have a base damage component as well as a scaling component, and these are not proportional. Specifically, Prism has proportionally more base damage and less scaling than ES, so increased spellpower will shift the comparison in favor of Execution Sentence.

If I plug in that 16.5k spellpower, Prism hits for 51.6k single-target, and ES for 144k. This is considerably more favorable to ES, before even counting the way it combines better with cooldowns/procs - each ES is now worth 2.8 Prisms, rather than 2.4. That doesn't totally reverse the conclusion, and Prism still has more flexibility between single-target and AoE, but it's not a negligible change from the original calculation.

I generally don't trust most sims as I don't find many of them reliable, if you can suggest any that are I would be happy to give them a look.
Also, even at about 33k buffed, as you said around 16.5k SP:
ES New Total (With Inq) == 144,213.4216
ES With AW == 187,477.4481

HP New Total (With Inq) == 51,608.05/Cast

The new estimate shows that a single Execution Sentence is equal to about 2.79 Holy Prisim at 33k AP; at 22k AP the difference is 2.45. The difference is increased by about 0.34 Holy Prisims per Execution Sentence. The change isn't so great that it is worth taking into account, as it doesn't change the conclusion I drew from the data which I stated in the initial post. All that changes is that Execution Sentence gains more per spell power than Holy Prisim.

The conclusion I stated was that "Although Holy Prisim is a lot more damaging if used on CD, both Hammer of Light and Execution Sentence seem to come out on top in their respective instances; with Execution Sentence doing better overall damage on single-target, and Hammer of Light doing more damage in instances of having about 5+targets in the AoE."
I even stated that the 3 Holy Prisim per minute was unrealistic and that's why I added new totals to show the difference between 3 casts, 2 casts, and 1 cast per minute.

Also, on stat weights, I say not to Strength stack because 1 Strength should not be greater than 2 Haste due to their respective stat weights as I don't believe we have a threshhold at which Haste becomes less valuable, that being said I could be wrong.

[Meteoric]

Simcraft seems to be pretty reliable. Balhale is actually the dev for the Ret module; you can ask him if you have specific questions about its reliability. But anyway, yes, we definitely do have thresholds at which Strength is more than twice as good as Haste; in fact, Haste tends to not become preferable until raid-quality gear, possibly even requiring 4p t14. But that depends heavily on the details of any given gear setup, which again, is why you should sim your own weights. Any stat weights you're using come from a sim already; the only thing you avoid by not simming your own is having weights that are actually accurate

But yeah, I'm not really objecting to the overall qualitative conclusion. Just discussing the math behind it.

[anaxie]

You understand any ES cast with guaridian / pots would take almost 6 prisms to make up for dont you.

Winged es's proc es's

Hell rolling everything i can get 36K STRENGTH on cast with ES.
Have fun catching up on that damage without delaying better attacks.