May 7, 2008

Haste VS Healing, The Showdown

There are two ways you can increase your healing per second (HPS).  You can either get more +healing or more +haste.  The addition of +healing is kind of obvious in that the more healing you have, the more you'll generate every second.  Haste is subtle by making you cast faster, which results in more heals generated in a fixed amount of time.  But what if you're trying to compare one item with more healing to one with more haste?  Which will give you more HPS?
There are a couple of things you'll need to know first, before you can figure it out.  One is your haste rating while wearing each item.  Haste doesn't have a linear relationship with faster casting, so you can't evaluate differences without knowing your total value.  You also need the average amount you heal per cast while wearing your normal gear.  Being a paladin, I need this value for both Flash and Light, so I grab it off a WWS report.
Decide how long your example boss fight is.  For me, I go with 6 min since that's how long Brutallus and Kalecgos are.  The longest fight I know of is Illidan at ~20 min.  You can get a decent idea from either WWS or Deadly Boss Mods for your particular boss.
Now that you have your information, you're going to want to set up something that looks like the table below.  For each item you want to compare, you'll need to do another table.  For each healing spell, you'll want to add a column.
Boss Fight Time: X minutes
Wearing Item1
Base Cast Time:           Y
Haste Rating:                Z
New Cast Time:            Y/(1+(Z/1570)) = A
Avg Heal Per Cast:        B
Total Healing:                ((X*60)/A)*B = C
HPS:                            C/(X*60)
These calculations assume that you have unlimited mana and are chain casting that one spell for the full duration.  That's ok, though, because you're trying to compare them against each other, not against reality.  The only issue is if you have such high lag that you can't benefit from haste to begin with.
The problem I've been facing is which of 3 rings to use, Band of the Eternal Restorer (Exalted), Ring of Flowing Life (JC crafted), and Band of Lucent Beams (Kalecgos).  I used the above formulae to get a rough result, something I could compare.  For the BotEternal Restorer, I used my WWS numbers to come up with a proc % chance per cast.  Here's how I did it below.
No. of Procs:  D
Additional Healing per Proc: E
Total number of healing casts: F
Percentage Chance of Proc: D/F = G
Total Number of Casts: ((X*60)/A) = H
Additional Healing: E*H*% healing for your spell
The % healing for your spell is the amount of your +healing that's applied per cast. For example, only 43% of healing is applied to Flash because of its 1.5 sec cast time. I then just took this additional healing number and added it to my total healing, C, above.  In this particular example, BoER can really proc off any cast, but that would only become a factor if you're mixing it up with some dps.
Looking at my particular ring issue, there's a slight increase in HPS for the haste ring over the healing ring.  The actual numbers were 1373 HPS vs 1369 HPS.  In a 6 min fight that means Ring of Flowing Life has the potential to heal for about 1350 more with Flash or 2657 with Light.  I'll be the first to tell you that the difference is small at best.
For these rings, there's more to it than just HPS.  The Ring of Flowing Life is craftable.  That means not only am I guaranteed to get it, I'll spend 0 DKP doing so.  And even if I don't use a drop of haste, I'm only out 1548 healing in a 6 min fight.  I can easily compensate for that by using my Essence of the Martyr more (or at all >.<).

Edited to fix RotER calcs

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