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[Cataclysm Beta] Haste and HoTs – A Quick Example

Posted by Malevica on September - 23 - 2010

Way back in April Blizzard were talking about making Haste (and Crit) affect HoTs and DoTs. Here’s what they said:

All HoTs and DoTs will benefit from Haste and Crit innately. Hasted HoTs and DoTs will not have a shorter duration, just a shorter period in between ticks (meaning they will gain extra ticks to fill in the duration as appropriate).

I should point out that this also applies to channelled spells as well, which will now have the possibility to gain extra ticks just like HoTs. Penance-lovers rejoice!
Update: This appears not to be applying to Penance on Live, as of 16th of October. I don’t know if this is a bug or not, but it was working on Beta. Feel free to comment if you spot a Blue confirmation either way.

To begin with, in response to a thread on PlusHeal, I first did a quick-and-dirty test on the Beta. I tested with Renew (nominal 12s duration, 3s tick interval) with whatever haste I was standing up in (7.53% total haste), a Potion of Speed (11.52% total haste) and Borrowed Time (23.46% total haste)

If you want the raw numbers, they’re available by clicking through, but in summary:

  • The total duration does initially reduce with haste as the ticks get shorter.
  • When you get a certain amount of haste you get an extra tick and the duration jumps back up again. It’s possible for the duration to go above the nominal duration (12s in the case of Renew).
  • If you cast a HoT while under a haste effect, such as Borrowed Time, all your ticks will be hasted, not just the ones that go off while the buff is active. However, the spell tooltip and the HoT buff you get both (misleadingly) update as soon as the haste effect fades.
  • Haste rating per 1% Haste = 128.11

Breakpoints

Erdluf and Zusterke at PlusHeal pointed out that the current thinking is that you gain the extra tick whenever the difference between the nominal duration and the actual duration gets to be more than half a tick, and that this certainly can lead to the total duration exceeding the nominal duration when the extra tick is added. This is consistent with the original statement from Blizzard that the duration won’t change, on average at least.
So if you can speed up the HoT enough to fit at least half a tick in, you get a full extra tick.

Based on this, here’s where the total haste breakpoints should be for various HoTs. The reason the HoTs have different breakpoints is because they have different tick intervals and total durations.

HoT Name         Breakpoints at (total haste):
Penance         25%, 75%
Renew         12.5%, 37.5%, 62.5%, 87.5%
                 
Rejuvenation         12.5%, 37.5%, 62.5%, 87.5%
Regrowth (HoT)         16.666%, 50%, 83.333%
Lifebloom         5%, 15%, 25%, 35%, 45%, 55%, 65%, 75%, 85%, 95%
Wild Growth         7.15%, 21.43%, 35.715%, 50%, 64.285%, 78.57%, 92.855%
                 
Riptide         10%, 30%, 50%, 70%, 90%

I went back and tested this in more detail on Renew, which is a 3s tick interval, 4-tick HoT, and it does appear that the transition to an extra tick does indeed happen at the 12.5% haste point as expected. Here’s the result of a few trials I did:

Healing per mana (HPM) and Healing per cast time (HPCT)

Here’s a look at the way haste affects the total duration and numbers of ticks of various HoTs:

Note that the numbers of ticks for Rejuvenation and Renew do not include the instant heal from Gift of the Earthmother and Divine Touch respectively, since these aren’t true ticks.

What you can see in this graph is the duration of the HoT decreasing as your haste increases (not quite linearly, haste does have a bit of a curve on it because of the way it’s calculated) and then when you reach the breakpoint the extra tick is added and the duration jumps up again, to somewhere above the nominal duration.
I’ve labelled the breakpoints to indicate the total number of ticks you’ll be getting from that breakpoint onwards as you increase your haste. So looking at the line for Riptide at the top, after the first breakpoint you’ll now be getting 6 ticks instead of the standard 5.

This graph also lets you see graphically the locations of the breakpoints for the HoTs, so if the table above wasn’t clear enough, you can use the graph instead. You can see on this graph, for example, the breakpoints for Renew and Rejuvenation at total haste percentages of 12.5%, 37.5% and 62.5%.

From a healing-per-mana (HPM) and healing-per-cast-time (HPCT) point of view, you want as many ticks as possible, because each extra tick adds a chunk of healing for no extra cost in time or mana. This makes it highly desireable to get above a breakpoint. However, HPM and HPCT only change at a breakpoint.

Healing per second (HPS)

I also wanted to look at things from an different angle: healing per second. In this case, since the result is similar for every HoT, I’ve just picked out Renew/Rejuvenation as an example. (I’ve arbitrarily given each tick a value of 2k, which is about right for Renew on the beta. Look at the shape, rather than the numbers.)

The thing to notice here is that the HPS curve increases linearly while your haste increases, it doesn’t change around breakpoints. So if you’re using your HoTs for their throughput, you’re not going to see a radical difference in HPS from stepping over a “breakpoint”.

Of course, you will notice the difference between a HoT with a 10.7s duration and one with a 13.2s duration (the biggest jump in duration for Renew/Rejuvenation) when you have to spend GCDs more often to refresh your HoT, and of course refreshing a HoT less often saves mana, so you will still want to get over that breakpoint.


Updated 3rd October: Improved clarity and readability. Added more HoTs and more detail to the main graph. Included all the breakpoints in tabular form as well, for reference.



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[Cataclysm Beta] Priest Spells and Numbers

Posted by Malevica on September - 23 - 2010

With Cataclysm’s release creeping closer, I’ve started rebuilding my personal spreadsheet for my Priest, so I can better understand the spells and talents I’m using. It’s not as advanced as some of the insanely complicated ones you can find out there on the net, but I like having it to tell me:

Since I’ve spent the time generating these numbers, I figured I might as well put them up for information purposes. I’ll be doing a bit more conclusion-drawing in a later post, once I’ve had more of a chance to put this stuff into practice.

In the following, all values relate to beta build 12984, and were taken over the last 2-3days on Malevica who at level 85 had approximately 5k SP, 10% crit, 500 haste rating and 750 mastery rating, and a Disc spec with 2% Haste from Darkness (the trees have changed, so the link broke). When Cataclysm goes live you’ll probably have slightly better gear, but the general conclusions will all hold.

A final reminder that this is beta and all numbers are subject to change.

Stat Conversions

The first thing that’s needed is the set of conversion factors that let you convert ratings into percentages or points (in the case of Mastery):

Crit rating per %: 179.3134458. Haste rating per %: 128.1138737 Mastery rating per point: 179.1809524

I generated these by standing around unbuffed and untalented and slowly removing gear to generate a series of data points, and then using a linear regression to extract the conversion factor.

By way of example, here’s a graph of the results for Haste:

Haste Rating to Haste % Conversion Chart

Because of the way I chose to plot this graph, the gradient (0.0078055559) of the graph is the haste% per point of haste rating, so the haste rating required for 1% haste is 1/ that value: 1/0.0078055559 = 128.1138733501.

Spell mana costs, cast times and coefficients

Now for some information about the spells themselves.

Mana costs are typically expressed within the game as a percentage of base mana, which is your mana pool with no gear or buffs on. (This is what lets the spell costs scale smoothly with your level.)

For a level 85 Priest, base mana = 20590

Using this number, I could work out the baseline (untalented and unglyphed) spell costs, and I also verified them in-game. Here are the current numbers (Blizzard does some funky things with rounding and tooltips so I’ve left the first decimal place for calculation purposes):

Flash Heal: 5765.2; Greater Heal: 6588.8; Heal: 1853.1; Penance: 2882.6; PW:S: 3912.1; PW:B: 13383.5; Renew: 4323.9; Prayer of Healing:	7412.4

Spell coefficients are trickier to get at, and have to be worked out empirically.

When calculating how much a spell should hit for, you take the base heal amount, and add your spellpower modified by another number which can be changed to affect how spells scale with spellpower.
The basic formula is:

Heal amount = Base heal amount + (Coefficient x Spellpower)

Here are the base heal amounts and coefficients I calculated:

Flash Heal: 5649.7, 0.60391843; Greater Heal: 7532.9, 0.80590514; Heal: 2824.8, 0.30190914; Penance:	7513.4, 0.80393165; PW:S: 3906.0, 0.41800560; PW:B: 3247.4, 0.91785502; Renew: 4897.1, 0.52421638; Prayer of Healing: 3112.4, 0.33301546

These were obtained by standing untalented and unbuffed (except PW:B, for obvious reasons) and recording the average heal amounts at varying spellpower levels. Like with the combat ratings, a linear regression was used to extract the base heal value (the intercept of the graph where SP=0) and coefficient (the gradient of the graph).

Here’s the values in graph format, for those interested:

The scaling on PW:B is a bit odd, since it scales very well with spellpower. That might change as the beta goes along, but remember that having such a long cooldown on a spell allows it to be a bit more highly-powered because it can’t end up dominating at high gear levels.

Typical hits and crits

Armed with the information above, I was able to work out what a typical heal should land for. In doing this, I have also included the ability to take into account the various talents available and their effects on the spells.

To work out the average hit, I used the following general formula:

Heal amount = [Base heal amount + (Coefficient x Spellpower)] x [1 + (% effect from talent A / 100)] x [1 + (% effect from talent B / 100)] x …

Those “6% increase” type talents are multiplicative, rather than additive, so if you get 6% from Twin Disciplines and 15% from Empowered Healing, you get at 22% increase, not the 21% you might expect (1.06 * 1.15 = 1.219).
At this time I want to say a huge thank you to Blizzard for trimming some of those passive healing increase type talents, it made my life a lot easier!

Anyway, for information purposes, here are the numbers untalented:

And in a typical Disc spec:

In these and the other tables (BT) means the spell is being cast while Borrowed Time is up, (G) refers to either a glyphed version of a spell (Renew) or the glyph component of a spell (PW:S). The numbers in brackets after PoH are the number of targets the spell hits.

What I’ve included in the second table is a column of typical crits (heal x 1.5) and then a weighted average illustrating what all of your casts, a mix of hits and crits, would average out to over time.

These tables are really useful for helping with spell selection. If you have an idea of how much each spell heals for, you’re able to pick the right size for the job, and understand where they fit into the healing toolkit.

Healing per second and healing per mana

As well as raw healing amounts, healers also need to know how quickly they can crank out healing with a spell, and how mana-efficient those spells are, especially in Cataclysm.

Here are the values untalented, assuming no crits:

And once again, in a typical Disc spec:

Once again, I’ve added extra columns to the second table. The HPS and HPM columns are based on that weighted average I talked about in the previous section, and should give a better estimate of the HPS and HPM you might achieve if you consider a whole fight.

I’ve not included HPS for PW:B because it’s not a repeatable cast, and I’ve not included HPM for the Glyph of PW:S because it’s essentially cost-free.



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