[Paladin] Healing Efficiency
 

Introduction

First off, I apologize if this thread is a repeat of one someone else did. I did a quick search and found some related topics, but not really the same thing, so I thought it worthy of its own thread.

To give some background into why I did all this, I started looking into healing efficiency when two of the paladins in our guild received 4-piece Tier5. This has also come up again because of the choice between T6 and T5. Healing used to be straight-forward for me as a priest (you heal for x for y amount of mana), but things have become complicated as a paladin (faster casting times, illumination and crit %, BoL, mana cost reduction on spells, less +healing on down-ranked spells, spell haste, etc), and I thought it would be interesting to do the math and just see what paladin healing spells are most efficient.


The Goal

Find what ranks of Holy Light (HL) and Flash of Light (FL) are most efficient with different gear and how that efficiency scales with crit% and +healing.


Conclusions

Buffs and Gear
Blessing of Light (BoL) makes a significant difference to the efficiency of the lower ranks of HL. This is because BoL adds a flat bonus to all ranks of HL, which is a proportionately larger bonus at lower ranks. The Libram of Absolute Truth improves efficiency much more than the Libram of Souls Redeemed. The 4-Piece T5 paladin bonus makes HL cast 0.25s faster. These buffs and gear make HL4 a superior spell than FL7 in most regards.

Small Heals
If BoL is not on the target, FL7 is the best small heal to use. However, with BoL and some specific gear, HL4 becomes the most efficient small-heal spell in the paladin arsenal. HL4 also provides the additional benefit of keeping Light’s Grace active for times when your biggest heals are necessary.

Big Heals
Assuming the Libram of Absolute Truth is equipped along with the other stipulations: HL9 provides about 2.5x the healing/s of HL4 and is almost as efficient as HL7. HL11 provides about 3x the healing/s of HL4 and is the least efficient HL spell.

Scaling
Paladin healing spells scale linearly with +healing, but increase in efficiency faster with higher levels of crit %. Once a certain level of +healing is reached, paladins should aim for more crit % to improve healing/s and healing efficiency. Graphs that show this scaling are included in the spreadsheet.


The Setup

All of my calculations will be done assuming the following parameters are in play:

Buffs
Mana Restore (Insightful Earthstorm Diamond) = 300 mana on a spell cast with what I believe is an effective 2-3% chance proc rate.
Sancitified Light = 6% extra crit to HL
Light's Grace = -0.5 casting time for all HL spells cast in 15 seconds, proc'd when HL is cast
T5 4-piece = -0.25 casting time for HL
Healing Light = 12% extra healing on FoL and HL
- According to WoWWiki, this applies to both +healing and BoL (haven’t tested myself)

Equations
+healing to a max ranked spell: +healing_max_rank = cast time/3.5 * +healing
+healing for downranked spells: +healing_spell = ((level of spell + 5)/player level) * +healing_max_rank
Healing Done by a spell: Heal Average = (Spell Base + Blessing of Light + +healing_spell) * (Healing Light)

Gear/Buff Scenarios
(A) no extra modifiers
(B) Blessing of Light
(C) [Libram of Souls Redeemed] + BoL
(D) [Libram of Absolute Truth] + BoL

Assumptions
I’m going to use my gear for a base +healing of 2000, a base holy crit of 20%, and spell haste rating of 120 for the initial calculations and comparisons for each of the scenarios. I will also post some graphs for the last scenario (D) that show how the efficiency changes as +healing and crit% are scaled.

I will also assume that the down-ranking modifier is applied after the normal +healing calculation for the spell (i.e. they're multiplicative instead of additive).


The Calculations

Here is an example (for HL6) of how the calculations are performed to derive the healing/s, mana/s, and healing/mana numbers. These calculations are made in the same way for all of the ranks of HL and FL discussed, so there is no need to show the calculations for each rank.

Base spell stats:
HL6 - level 38: 364 mana, 698 to 780 healing

Cast-time modifier:
HL is base 2.5 seconds casting time, so this reduces the +healing gained:
HL: 2.5/3.5 * 2000 = 71.4% * 2000 = 1428

Level-Modifier:
((38+5)/70) * +healing = 61.4% * 1428 = 877 +healing

Adding it all up- (Base Spell, + healing bonus) * Healing Light Bonus (12% extra healing):
1764 to 1855 healing

If we cast 100 spells and assume a perfect world (i.e. you’ll get 29 crits with a 29% crit percentage):
2 of those should have 300 mana back (from Mana Restore) = 600 mana
26 will be crits with 1.5x healing and 60% mana back = 218 mana a piece

So total we will be doing:
(1764*74) + (1764*1.5)*26 = 199332 min healing
(1855*74) + (1855*1.5)*26 = 209615 max healing

In this amount of time (remember, 120 spell haste):
100 * 1.61 seconds = 161 seconds (2.68 minutes)

And we will have received back this amount of mana:
26 * 218 + 600 = 6268 mana

199332 to 209615 healing over 161 seconds = 1238 to 1301 healing/s
Total mana spent = 364*100 – 6268 = 30132 mana = 187 mana/s

Final Values:
1238 to 1301 healing/s
187 mana/s

1238/187 = 6.62 healing/mana min
1301/187 = 6.96 healing/mana max


Example Spreadsheet Results

Scenario (D): +2000 healing and 20% crit with BoL and Libram of Absolute Truth:

HL4: 1131 – 1167 healing/s, 79 mana/s, 14.54 average healing/mana
HL5: 1403 – 1451 healing/s, 123 mana/s, 11.60 average healing/mana
HL6: 1693 – 1758 healing/s, 170 mana/s, 10.15 average healing/mana
HL7: 2015 – 2100 healing/s, 223 mana/s, 9.23 average healing/mana
HL8: 2380 – 2492 healing/s, 283 mana/s, 8.61 average healing/mana
HL9: 2747 – 2889 healing/s, 325 mana/s, 8.67 average healing/mana
HL10: 2897 – 3053 healing/s, 351 mana/s, 8.48 average healing/mana
HL11: 3304 – 3500 healing/s, 419 mana/s, 8.12 average healing/mana

FL4: 785 – 805 healing/s, 48 mana/s, 16.56 average healing/mana
FL5: 924 – 949 healing/s, 63 mana/s, 14.87 average healing/mana
FL6: 1066 – 1099 healing/s, 78 mana/s, 13.88 average healing/mana
FL7: 1223 – 1267 healing/s, 101 mana/s, 12.33 average healing/mana


Final Note

Please have a look at the spreadsheet and play around with it. All you have to do is put in a few values in the blue boxes (+healing, crit%, and spell haste), and everything else should calculate out for you.

Let me know if you see any errors or anything I’ve left out and I’ll get it fixed as soon as I can.

I haven’t taken a look, yet, at T6 bonuses versus T5 and whether the crit on HL and extra healing on FoL make things more/less efficient than the T5 bonuses.

Spreadsheet

Spreadsheet can be found here: Pally_Healing_Efficiency_v1.xls

Good effort on an updated spreadsheet for this sort of thing, the layout is clear and simple to use compared to other similar ones, however the results are largely obvious and match up with general common sense.

Perhaps consider adding a bar graph which maps healed amount for all ranks on the y axis ordered from worst to best efficiency on the x axis, for an entered heal and crit %.

In my experience people who have mana problems in a long fight (when not in a shadow priest group) are using ranks that heal for too much for the general amount of periodic damage the raid is taking. People using R11 exclusively instead of 4,7 9 for example.

My guild is still working on Kael at the moment so the mileage of my comments may vary :)

I'm wondering at what number of +healing should one start stacking crit. I notice many many high end paladins going for straight plus healing, with almost exclusive +22 healing gems. At what point (however high) does this become worse than gaining some crit? I don't have the knowledge of ingame mechanics or the mathmatical background to attempt finding this out, but adding something like that to the spreadsheet would be cool.

I think the general theory for stacking +healing is that efficiency can be replaced by chain-chugging mana pots, but there is no equivilant consumable for throughput.

There was a thread before, I'm pretty sure its in the archives now that had a spreadsheet that you could input your character stats, choose your buffs that you would have in a group/raid, and it would give you a list of items that would be a best upgrade for you.

It was originally based off of the sheet that Overen from the Blackhand server made, but someone else had modified it for 2.1 and adjusted the item stat weighing a bit. I tried to find an updated version of it, but there wasn't one out on the net that I could find. Once I realized what items were missing from his spreadsheet, and realized how to add them to the auto-sorting lists, it didn't take long to update it with all of the BT/Hyjal loot.

The only things I didn't put in there, was any item that wasn't strictly +Heal. If it's +dmg/heal, I skipped it... same for the tanking items (for some reason, he has some tanking items and +dmg/heal gear listed in the list.)

Updated Paladin Healing Calculator

I apologize for not being holy specced and not having my raiding holy gear on currently with armory, but this is how I gear up and my mentality.

As a tank healer, I want a steady stream of mid to large sized heals landing on the tank. My stats unbuffed are something like 2050 healing, 43% holy light crit, and 108 mana per 5. Ideally if I got the endgame gear I wanted currently (missing T6 BP, Naj boots, ring, felstone bulwark, and either the mace off Illidan or the Hammer of Atonement from Kaz'rogal), I'd be at like 2200 or so healing and just about 50% holy light crit raid buffed/consumable.

I assume BoL is on the tank as well as improved amp magic, which adds an additional 360 healing. A noncrit rank 7 holy light will heal for about 3000, and a crit will bring it to 4500. With the libram of absolute truth, the noncrit mana cost is 438, the crit is 186. Averaging this all out (since you're at 50% crit, that's pretty often), the average cost of the heal is 312 and heals for ~3750, so you're at about 12 health per mana.

While it's not the MOST efficient, it's a decent sized heal for a pretty cheap cost. Generally I find there to be plenty of +healing on gear as you upgrade it, and attainable through buffs... so the only thing left to really aim for to increase efficiency at the fastest rate, is spell crit. Baseline mot is essential to have as well, but there's also lots of gear swapping that can be done if needed for a more mot-friendly fight.

Also I can't ever see the point of downranking below 7 on holy light, since I assume 90% of raiding paladins aren't raiding with global Light being on the raid. (Only 3 paladins typically). Because of that we're MT healers, and tanks have Light - but you aren't using small heals on them that heal for 1000. 7 is the lowest I go for HL, only on lighted targets, I have 7 9 and 11 also obviously bound. Then it's just Flash for everyone else (or a 9 or 11 HL if mana isn't valuable), and R1 flash for very situational odd type things.

That's the thing, though... HL4 doesn't heal for 1000; it heals for 1900 non-crit and about 3k crit on a MT. It's a little less healing/s than FoL, but not much. It's the same as using FoL spam on a tank for Mother, but more efficient.

What you really want is the slope of the lines (delta mana efficiency / delta crit% and delta mana efficiency / delta +healing). You can do this pretty easily on the spreadsheet using the SLOPE worksheet function. If you then divide the crit % slope by the +healing slope, you can see how crit% and +healing compare to each other.

As an example, one crit % gives you about the same mana efficiency as 58 healing with 15% crit on HL4. In the upper ranges (40-50% crit), one crit % gives you the same mana efficiency as 100 healing.

The real answer to your question is entirely subjective. How much +healing do you need to feel that you're putting out enough healing per second to keep people alive? Once you reach that +healing, go for crit%.

It's all a reasonably moot point, however, since paladins in BT/Hyjal don't have THAT many gear choices. There's a random piece or two here and there that gives you a choice, but mostly you're stuck with what's available. Personally, you sacrifice too much if you go for a much lower ilvl item just to get, say, 10 extra crit rating.

Sure, except on Mother your healing stats are seriously nerfed, and I'd bet FoL is then going to still be a lot more efficient. But I hate utilizing any type of quicky-tiny-spammy function of a paladin, so I don't even like delegating that task to people on Mother to begin with :) (But yes, we do currently do it, whatever keeps us one shotting her!). On every other fight it's basically HL on the MT, of sufficient sized chunks of heals to actually keep him topped.


Yep, to an extent. It's obvious which items in BT/Hyjal are the best for a paladin, they're the plate ones with healing stats and nothing wasted on spell haste. Then it's just up to the player to decide what they want from sockets: 5-6 spell crit, 30ish Mp5, or 220ish healing. Or some mix thereof!

Although yes there are a few choices you can make even further still with miscellaneous pieces, but that about sums it up. Personally I'm loving the general focus on additional spell crit on gear, since it will always be my belief (unless Illumination gets further nerfed) that it scales the best for us, point for point.

As I said in the other topic as well, I realize that having 4/5 t5 opens up serious options for downranking, to an extent that could make lower ranks of HL comparable to FoL spam. But, as I posted in the other topic, I think FoL r7 is the bare minimum of HPS you have to keep up. Dropping lower then this means you're healing way below what you could be doing in means of tank healing. HL5 is maintainable for sure, and HL6-7 are maintanable with a bit of consumable abuse.

I really cant see the point of using HL4, where you could have been using FoL r7. FoL r7 isnt a strain on your mana pool at all, so why go for something cheaper?

Other then that, cool spreadsheet. Oh, the insightful earthstorm diamond has a 2% proc chance.

I think it was said in another post, about us downranking spells.. HL4 and FoL7 would heal for roughly the same ammount with BoL, correct? I know mine do. Going from FoL7 to HL4, you spend 10mp more, takes 0.5 seconds more (1.0 without Light's Grace), and you get 5% more crit.

I think it highly depends on the situation on whether one needs FoL7 or HL4.

If the target has BoL, it's probably a tank. And if you are a paladin healing a tank, you are probably there for throughput and longevity at the same time, something you don't use very tiny heals for. (1000-2000). Basically, I find that 'very low downranking' appeal to be largely useless in the majority of real raid situations, because I'm sure most people raid with 3 paladins, which puts light on like 3 classes - Warriors, Druids, and Paladins. If you're raid healing, they don't have BoL so you can't really use any rank of HL, and if you're tank healing, you need big heals, not small ones.

Rank 4 and 7 work well depending on how you have tank healing setup. We usually raid with 1-3 trees, 3-4 Pallies and 1-2 Priests. Tree hots on the tank allow for me to use 4 without any issues.

It also depends on the fight. Harder hitting bosses and you want to uprank.

I tend to agree. While theorycraft and numbers are nice when it comes to efficiency -- our primary responsibility (at least in most cases) is keeping a tank up and at that point ~1-2kish heals are just not going to cut it. I simply do not go under HL7 in 99.9% of the cases where I am healing on a raid (other thank HL1 to prep LG). Add to this the fact that mana really ceases to become an issue with current content to the point that I have to change what I personally feel is the best set of spells for a given fight (chugging mana pots etc. included)

Personally, I'll re-evaluate gemming and such when I hit 4pc T6, but at this point I still enjoy primarily using various ranks of HL for healing on tanks (together with 4pc T5) -- so once I hit my target for +healing I'll be trying to round off my crit and then add enough mp5 to be at ~100 unbuffed. Balance and regen work a lot better for me now with the current healing style I utilize. That said I agree with the post above too -- since we started raiding with 2 restoration druids things have changed and I find myself using lower ranked HL and FoL a lot more.

I think the main point is that regardless of the best efficiency on paper, a lot of it is very adaptive (raid composition, fight, healing strategy).

is there a certain amount of +healing to shoot for before going for crit? i looked at all the holy pallies in the top guild on my server and it looked like every one of them put +22 healing in every socket and were only rolling with about 21-22% holy crit unbuffed. if i look at DnT's holy pallies it seems every one of them sockets their gear differently.

I only spam FoL max rank and have HL R4 on my bars for LG prep, and max rank HL for those "uhoh" situations with DI. I broke 2k unbuff +heal, so I just began stacking crit as much as possible even with the utter crap of our non-set drops (abysmal drop rates for us so far....), and I lost quite a bit of MP5 in the process. I really can't say I miss it - the additional crit % is very, VERY nice. And really once your flash heals are hitting for 2k, there is no reason to go any higher with +heal imo.

Admittedly I am not a great healer when it comes to efficiency, I tend to border 45-50% OH, and just spam pots when necessary.

I'm still in a bit of a bind in regards to gear choices - Xav/Moz or anyone else with some T6 any advice? I haven't taken any T6 just because we're still learning content (Illidan) and I feel that the -.25 on HL is a bigger gain than the set bonuses on T6 for pure progression. But once we have everything on farm, I am going to get full T6 I think just due to the raw stats on that gear (I want stupid stat #'s like 13k HP/15k mana/20k armor raid buffed just for epeen.).

Sorry for the derail :).