How to Easily Compute Your DoT/HoT Haste Breakpoints

Posted 12/30/10 at 7:47 PM by Hamlet
Updated 08/13/12 at 8:46 PM by Hamlet

The advent of the new DoT haste scaling system has left many people wondering how to compute the values of haste at which they gain extra ticks. People frequently ask this on the Druid threads that I participate in here, and it seems to be a frequent question for many classes. Here I'm going to briefly give the correct computation.

Haste rating to obtain the k-th tick on a DoT or HoT is given by:
$\left(\frac{2k-1}{2n}\cdot\frac{1}{H}-1\right)\cdot R$

EDIT: apparently the embedded LaTeX isn't visible to everyone, so here it is in text form:
((2k-1)/(2nH) - 1) * R

k is the number of the tick we're trying to add
n is the default number of ticks for that spell
H is your haste factor from buffs (see below)
R is the haste rating conversion factor at level 85. It equals roughly 12,805.7.

The only tricky part about using this is finding H. Usually 1.05 in a raid, from Moonkin Aura or a similar buff. With no haste buffs, it's simply 1. If you have multiple haste buffs, multiply the values together. For example, if you have both Moonkin Aura and Dark Intent, H would be 1.05*1.03=1.0815. If you are also a Mage with the Netherwind Presence talent, it would be 1.05*1.03*1.03. Make sure you know what haste buffs are available to your class before you try to compute this.

For a brief example, Resto Druids often want to know how much haste rating they need in order to gain a 5th tick of Rejuv (a HoT with 4 ticks by default). In an ordinary raid situation, the only haste buff I'd have is Moonkin Aura. The formula becomes:
$\left(\frac{9}{8}\cdot\frac{1}{1.05}-1\right)\cdot 12805.7$
EDIT: ((9/8)/1.05 - 1) * 12,805.7

Throwing this into any calculator gives 914.7, which is exactly correct. Round up to find the desired breakpoint: 915 haste rating.

My Resto and Balance spreadsheets, TreeCalcs ( http://elitistjerks.com/f73/t110354-...ase/#TreeCalcs ) and WrathCalcs ( Druid: Balance PvE (updated for Cataclysm release) ), compute all these for Resto and Balance HoTs/DoTs. It would be very easy for anyone to do the same for other classes using the formula given here.

EDIT: Breakpoints in-game will occasionally vary from this slightly due to some internal rounding. For the computation of exact breakpoints taking all of those details into account, see these later posts:
http://elitistjerks.com/blogs/1152-h...ints_rounding/
http://elitistjerks.com/blogs/1152-h...points_update/

Posted in Math

Comments 15

Total Comments 15

Comments

	Great post and really really helpful, I always wanted to be able to calculate my exact breakpoints for each of my spells for any of my specs. Thank you.
	Posted 01/01/11 at 2:16 AM by Tassdrummer

If this formula is correct in all cases, and I've done my math correctly (the latter assumption being pretty dangerous), it would seem that any HoT or DoT that naturally ticks more than 9 times would gain an extra tick automatically from having a moonkin in the raid, and almost all DoTs and HoTs gain an extra tick when under the effects of Heroism/Bloodlust. However, gaining the second or higher extra tick is never automatic.

It also looks like, after the first extra tick, the second one is much more costly, but each subsequent extra tick requires a static amount of haste rating. Using the Rejuv example, the first extra tick requires 915 haste rating, the second requires an additional 3049 haste rating (3964 total), but the third also requires only an additional 3049 haste rating (7013 total). Not necessarily realistic numbers right now, but interesting to play around with the numbers all the same - especially when calculating how much extra healing or damage you get under large, short duration haste buffs.

Posted 01/03/11 at 3:37 PM by Kurgosh Kurgosh is offline

	I think I found an error in your formula that makes a huge difference. Originally you have: ((2k-1)/(2nH) - 1) * R. But when you do your calculations you present the following: EDIT: ((9/8)/1.05 - 1) * 12,805.7 Should the formula be written as (((2k-1)/(2n)/H)-1)R, instead of ((2k-1)/(2nH)-1)R?
	Posted 01/18/11 at 11:53 AM by Amaren

	I'm not seeing what the difference is between those two.
	Posted 01/18/11 at 12:26 PM by Hamlet

One thing to remember is that tick times are being rounded to 4 digit precision.

I observed this pattern of rounding when attempting to determine why warlocks, under the influence of Dark Intent, Improved Soulfire (+15% haste in 4.0.3), and Wrath of Air were not getting their 7th tick on Immolate or Unstable Affliction until 581 haste, when conventional math indicates that behavior should happen at 580.

Posted 01/19/11 at 4:34 PM by Keldion Keldion is offline

	I've been recently looking into this, you can see some posts on the Druid forum Resto/Balance threads. I assumed it was some kind of rounding of tick rates, and hadn't figured it out exactly. Have you worked out exactly how the rounding is happening (is there a longer writeup somewhere)? When you say "4-digit," do you mean milliseconds or tenths of a millisecond?
	Posted 01/19/11 at 4:49 PM by Hamlet

	For all intents and purposes, it rounds to the thousandths. Destruction in Cataclysm \| The Demonic Mage
	Posted 01/19/11 at 5:01 PM by Keldion

	That had been my guess as well after looking at some Druid spells. I think I've seen some which it didn't explain perfectly, but it's really hard to test this in detail due to the limitations of reforging.
	Posted 01/19/11 at 5:11 PM by Hamlet

Additional notes on using bankers rounding.

https://docs.google.com/spreadsheet/...kMWFxWmc#gid=0 - Healer breakpoint cards

Code:

=$B$1/($A7-0.5)

Used this to work out the break point in MS where B1 is duration and A7 is the number of ticks. This was used in cell B7 for the next formula

Code:

=IF(MOD($B$1,ROUND(B7,1))/B7=0.5,IF(ISEVEN($B$1/B7),FLOOR(B7-1,1)+0.4999,FLOOR(B7,1)+0.4999),FLOOR(B7,1)+0.4999)

This is where the bankers rounding came in. I split out the first part to reduce the complexity of this part.

From there it's a simple case of converting that time value into a haste percentage.

Posted 07/17/12 at 6:27 PM by Binkenstein Binkenstein is offline

	Does anyone know if the haste rating conversion factor has changed with the 5.01 patch. Or know the calculations needs to finds out? I don't mind doing the math
	Posted 08/29/12 at 9:50 AM by Warstorms

	I think it's 42,500.
	Posted 08/29/12 at 9:56 AM by Hamlet

	what equation(or source) did you use to find this?
	Posted 08/29/12 at 5:35 PM by Warstorms

	I haven't checked in a little while myself, it's just what I remember from people testing on the beta.
	Posted 08/29/12 at 5:58 PM by Hamlet

	I'd really like to write the new thread for how affliction works in MoP (with some extensive testing of course). However, I'd need to know that conversion as to be sure that my calculations are correct. Is there a way I may be able to source this conversion rate, shy of having access to beta? Even a point in the general direction would be great. That way I can begin to hunt that which I seek ^_^
	Posted 08/29/12 at 11:05 PM by Warstorms

	Not off the top of my head, it's just come up a lot when I've been helping people with beta stuff. Easiest is probably to find someone who's been making a MoP spreadsheet and ask them.
	Posted 08/29/12 at 11:10 PM by Hamlet

Total Trackbacks 0

Trackbacks

No other blogs currently reference this blog entry

Trackback Link

Recent Blog Entries by Hamlet

Balance Feedback MoP Beta (04/02/12)
Theorycraft 101: Regen vs. Throughput Choices for Healers (08/09/11)
Theorycraft 101: Haste Breakpoints, update. (08/06/11)
StarCraft 2 Speedrun (07/28/11)
Theorycraft 101: Haste Breakpoints and Rounding (07/18/11)