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Also you have 10% added as a hot. To calculate the contribution lets take any length of the time T, then during that time the amount of healing done H = T*HPS. 10% of that heal will fuel the Echo of Light HoT, so you will get 10%*H healing from it in total and the time in which the healing will be done will be T+6. So HPS from Echo of Light should be 10%*H/(T+6) = HPS*T/[10*(T+6)]. However its important to realise that in a short period of time the heal is end-loaded. That means there is a period where the HPS for echoes will be lower than this and another period where the HPS will be higher. Eventually a steady state will be reached where the HPS is constant.

Let us try to obtain a formula for the steady state: Using heal means that you only get 2 tick in between casts, which means you transfer 4/6 = 66.7% of the HoT amount to the next one. So if the amount that is to be healed after the 1st spell then amount to be healed after the 2nd spell is H*(1+2.3). Conversely the amount to be healed after the 3rd spell is H*(1+2/3)*2/3+H = H[1+2/3+2/3^(2)]. Clearly after the nth spell the amount to be healed is H*K(n-1)

Where K(n), with n an integer is the sum from i=0 to n of 2/3^(n). [I know I know I should use latex. I will fix it later]

This is basically a geometric progression of the form m*r^(n) whose sum is dead easy to calculate it is

H*(1-2/3^(n))/(1-2/3).

This series clearly converges (take +infinity limit) towards H*1/(1-2/3) = 1/(1/3) = 3*H.

So at infinity this HoT will tend to do 3*H healing over 6 seconds, so it will tick for H/2 per second.

As a result heal spam after a relatively large number of casts will effectively double the HPS of heal by adding 2 ticks of H/2 every 2.1 seconds. (Remember that the duration is reset). With stacked mastery this can be considerably higher due to the nature of the formula.

I have difficulties to follow your math. I guess that's because you don't state clearly your assumptions, and mostly because your notation is fluctuating.

However, I think there is a flaw in your math. You seem to confuse two things, both denoted by H in your post:

1/ the amount of direct healing in an interval of size T;

2/ The amout of mastery healing after a single heal.

I'm rather authoritative here, but if the mastery hot rolls as I expect (ie. as Ignite / Deep Wound, that is to say that there is a "bank" for the hot, which is increased by 10% (or more) of each direct heal, and decreased by the amount of each tick when the tick happens, and ticks happen every second for 1/6 of the bank), then from the mass transportation principle in Palm theory, I'm sure that the mastery adds an expected 10% (or whatever mastery percentage you have) of your direct hps. By no way it can double it...

If you want a quick "first impression" of it, consider the easy case with 2.0s cast time and a expected size (crit included) of H. Assume that your mastery hot ticks exactly as T = 0s, 1s, 2s, 3s ,..., and that your heals lands at T=0.1s, 2.1s, 4.1s, 6.1s, etc.

Then the amount of the bank Bn at T=n s, just before the mastery tick, follows the relation:

In particular, you have the relation :

Taking the limit with n to infinity, we have that the limit B* verify :

.

So at odd seconds, we get a tick that is [latex] H * 18/ (55 * 6) = H * 3/55 " alt=" B* = H * 36 / 110 = H * 18 / 55 " alt=" B^* = B^* * 25/36 + H * 0.1[\latex]

and we conclude easily that [latex] B* = H * 36 / 110 = H * 18 / 55 " />.

So at odd seconds, we get a tick that is [latex] H * 18/ (55 * 6) = H * 3/55 " />

At even seconds, the bank before the tick is 5/6 * B*, ie H* 3/11, and the tick is H * 1/22.

Every two seconds, you hence get as expected mastery healing of value [latex]H * 3/55 + H* 1/22 = H * 1/10 " alt=" B* = H * 36 / 110 = H * 18 / 55 " />.

So at odd seconds, we get a tick that is [latex] H * 18/ (55 * 6) = H * 3/55 " alt=" B* = H * 36 / 110 = H * 18 / 55 " alt=" B^* = B^* * 25/36 + H * 0.1[\latex]

and we conclude easily that [latex] B* = H * 36 / 110 = H * 18 / 55 " />.

So at odd seconds, we get a tick that is [latex] H * 18/ (55 * 6) = H * 3/55 " />

At even seconds, the bank before the tick is 5/6 * B*, ie H* 3/11, and the tick is H * 1/22.

Every two seconds, you hence get as expected mastery healing of value [latex]H * 3/55 + H* 1/22 = H * 1/10 " />

The behavior is the same when everything is not phased in the best way, but the proof is more complicated. Of course, everything works nicely with more mastery, and a different mastery percentage.

Edit : it seems that there is a weird behavior for the mastery hot, where you have a high incentive in keeping it rolling. It might be the old behavior of similar dots / hots, where the hps / dps of the hot is increased by the new addition, and duration is refreshed. It means that as long as you keep it rolling, you only add hps in the hot, with not limit at all.

I haven't done any testing, and it might be the case, but in that case, I don't expect it really staying for a long time in live. We have control on the fact that we can keep it rolling, and the mechanism is clearly not what is stated, and not intentional or equilibrated from Blizzard.

Edit 2: there might be also a second reason for a weird behavior. When the mastery hot ticks about the same time that the new heal lands, there is some time a database concurrent actions issue. Both events reads the state of the current bank, both update the local value, and commit it to the database. Then the last event overwrites the previous event.

In short, the following sequence can happen:

- Current bank is B;

- Mastery tick. Server reads the current bank B, and heal for B/6.

- Heal lands for H. Server reads the current bank B.

- Server computes the new bank after the hot, which is B * 5/6, and stores it.

- Server computes the new bank after the heal, which is B + H*01, and

**overwrites** the previous bank.

You got a free tick from the mastery here, that was not deduced from the bank. Note that this can happen in the other way, where your heal is not added to the bank, if the events happens in the other order. In this case, the "ideal" behavior is to have near 1s heal, phase with the hot, which happens just after the hot. And once again, you have not limit on the amount of your bank, because it is never decreased. If you use a 2.0s heal, correctly synchronized, you can't reach impossible amounts of bank, but you double your mastery healing.