Trying another one of these since I think the mana regen one turned out pretty well. This one is going to be slightly different. Many people have written descriptions of how these work, since it was a clear and interesting new topic. So I'm going to give a pretty terse summary of the basic computation, and then outline one further detail which is missed by most popular write-ups: the exact way the rounding works in-game. With that knowledge, you can compute breakpoints that are exact to a single point of rating.

 

Contents

1Introduction 2Variables 3Review of basic computation 4Rounding 5Example

[top]Introduction

In Cataclysm, all DoT/HoT effects have their tick rate increased by haste. Since this causes the DoT duration to not be an integral number of ticks, the game rounds the duration to the closest whole number of ticks. Haste breakpoints are those amounts of haste at which you get a whole tick added on.

Breakpoints are important for gearing because the haste contribution to your DPS and healing jumps up at certain points. For some classes (Resto Druids are the best example), it is worth it to modify your gear setup quite significantly to obtain a whole extra tick on a spell that you use often.

[top]Variables

Throughout this post:

• D is the default duration of the HoT or DoT in question.
• n is the default number of ticks.
• t is the default tick time (equal to D/n)
• k is the number of the tick we're trying to add (i.e. if we're computing the haste needed for the 5th tick of Rejuvenation, k=5).
• H is your combined haste from %-based haste buffs (so if you have both Moonkin Aura and Dark Intent, H would be 1.05*1.03=1.0815).
• s is your haste rating.
• R is the "haste constant", equal to 12,805.7.

[top]Review of basic computation

To determine the number of ticks a DoT will have, the game does the following:

• Apply your total haste to the default tick rate to determine the final tick rate.
• Divide the default duration by the final tick rate to find the (fractional) number of ticks.
• Round that number up or down to the nearest integer to determine the final number of ticks (and adjust duration up or down to accommodate).

Mathematically:
Your total haste factor is:


Therefore, buffed tick time of the DoT is:


Number of ticks before rounding is:


In order for the DoT to achieve k ticks, that number must be high enough to be rounded up to k. In other words, it must be at least (k - 1/2). Therefore the breakpoint occurs at:

Solving for s:

(Note that D and t have nicely dropped out--only the default number of ticks n is needed)

This is the derivation for the formula that I have in this post a while back:
http://elitistjerks.com/blogs/1152-h...e_breakpoints/

[top]Rounding

For a while class, theorycrafters used the above equation or something identical to it to predict their breakpoints. Problem is, it didn't work out exactly in-game. You'd gain the extra tick somewhere close to the predicted amount (within 5 rating usually), but not exactly at it. It was clear that the game was rounding something at some step of the way.

This was hard to test since it was necessary to keep adjusting haste by very small amounts near various breakpoints (since different guesses at how the rounding worked only changed the results to the tune of a few points of rating). I was looking into it, as were people on other EJ class forums like Warlocks. Eventually a hypothesis came out which predicted all breakpoints exactly, which is the following:

• After haste is applied to the tick time, that tick time is rounded to the nearest millisecond (0.001 seconds) before the total number of ticks is computed.
• If the number of ticks before rounding is an exact half-integer, the game rounds down instead of up (EDIT: this has been revised slightly--read update here: http://elitistjerks.com/blogs/1152-h...points_update/ ).

So the resulting calculation is modified as follows.
Tick time before rounding was:


Tick time after rounding to the nearest millisecond is:
.
(The half-brackets are the floor operator--I'm using them here to mean "round down to the nearest 0.001 seconds." I'm expressing the rounding by adding half a millisecond and then rounding down, because it simplifies a later computation).

The number of ticks before rounding is:

Sadly, due to the rounding, the D/t doesn't nicely drop out anymore. Different duration DoTs can have different breakpoints even if they have the same number of ticks.

To find the final tick value, round that expression to the nearest integer, with the above proviso that exact half-integers are rounded down.

What we really want to do though is solve for s as we did before to find the breakpoint. Once again, the pre-rounding number of ticks must be greater than (k - 1/2).


Juggling the algebra here is a bit more of a pain due to the ceiling operator, but it goes like so:

What happens here is a bit tricky. Remember that the right side of the equation is an integral number of milliseconds, and the left side is the maximum tick time that will allow for the kth tick to occur. If you think about this for a minute, we can say that the number of milliseconds we need to "reach" is the ceiling of the expression on the left:

From here, solving for s is simple algebra:





The expression on the right is our haste breakpoint (again, the ceiling operator rounds the internal expression up to the nearest thousandth of a second, or 0.001 seconds).

This is an Excel expression that will give the needed amount of rating:
Simply fill in the appropriate cells in your spreadsheet for D, T, K, H, and R.

(EDIT: Once more, find a slight update to this here: http://elitistjerks.com/blogs/1152-h...points_update/ , which will change the result slightly in a small number of cases)

[top]Example

Once again, an example. As a Resto Druid, my only haste buff is the raid's Moonkin aura (H = 1.05), and I want to know how much haste rating is needed to reach the 13th tick of Lifebloom (a 10 second, 10 tick HoT by default). Variables:

• D = 10
• t = 1
• k = 13
• H = 1.05
• R = 12,805.7.

0.800 second is an integral number of milliseconds (800 milliseconds), so the ceiling of it is still 0.800.

The final expression is then:

12805.7*(1/ (1.05*(0.800 - 0.0005)) -1) = 2448.715.

And that gives us the exact amount needed to get that 13th tick: 2449 haste rating.

Note that if you used the earlier formula, without rounding, you would have gotten 2440 as your breakpoint, potentially causing you to miss the extra tick if you tried to gem to exactly 2440.