I was just playing with the echoes behavior in dal before I made my post, and I was able to get it to tick for 10,000 per second with flash heal by the time my mana ran out. Its been 10 years since I took a math course, so i can barely recognize that math manipulation, but after reading your post, I logged back in and tried to stack heal as high as I could. Mine has a 1.97s cast, which I suspect is nearly the worst possible casting time, since I was unable to get my echo above 1200 per tick. My flash heal, on the other hand, is ~1.2 seconds and so I suspect casts ending in .1-.5 roll echoes much more rapidly. I suspect having a 1.01 second flash heal would be the fastest way to stack echoes, but perhaps the extra .2 seconds buffers against player error and latency variations.
Would I be correct in saying that you want your echo to refresh just after a tick and not just before in order to get it rolling?
I will explain it while answering another post
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.....
I'm rather authoritative here, but if the mastery hot rolls as I expect ...... 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...
I can see your concern Ellimbras, the reason why I thought the spell worked this way is that both I and others (see the post I quote) were able to get tick numbers that were about as big or bigger than the spell we are casting. I can definately see I made a mistake because I was using H for two different things and I confused them in the end. It should have been 0.1*H if H is the average amount healed by the spell. I will do it again more carefully this time.
The EoL HoT stacks as follows. When you cast a new spell before the current HoT is finished the remaining amount is transferred over to the next heal but the remaining duration left before the next EoL tick occurs DOES NOT get transferred. That means if you have a spell with a 1.5 second cast time and you spam it, then 1 second after the 1st spell hits you will get a tick and 0.5 seconds later a new spell will hit so that will refresh the hot duration causing the next tick to come after 1 second again. The result is that your EoL HoT ticks every 1.5 seconds instead of every 1 second. In my example with a 2.1 sec heal I get 2 ticks every 2.1 seconds instead of 1 tick every 2 seconds. I believe this to be correct based on my testing, but I need a more accurate test to substantiate it. The more accurate test will consist of casting a series of flash heals and then looking at the log to determine the number of EoL ticks during that time. The ticks should be the same as the number of Flashes + an extra 5 which will come after the last flash. I will do this at a later time
Now let as assume that I do a certain amount of healing in a period of time. Then the TOTAL amount that will be healed by EoL is the amount of healing I did. Thus if I healed for an amount H then in TOTAL the EoL hot will heal 10% of H or 0.1*H. The hot will begin after my first spell lands and will continue for 6 seconds after I cast my last spell. So if the time from the time my first spell hits to the time my last spell hits is T, the time period in which the healing from EoL was delivered is equal to T+6 seconds. Therefore the OVERALL HPS added by EoL equals 0.1*H/(T+6), but H equals my average HPS*T. That means EoL HPS = HPS*10/100*T/(T+6) = HPS*T/[(10(T+6)]. Thus the formula I came up with before is correct. The OVERALL HPS is approximately 10% of your HPS, but that is the overall HPS. In order to get that, you need to spend a period of time stacking the HoT, during which your HPS will be lower, but later on the HoT HPS will be higher to compensate.
So now lets consider how the stacking works. If you are spam casting you always cut the HoT short, you transfer some of the current amount into the next HoT. This will continue until you reach a steady state where the amount added by your last cast is equal to the amount expended by the HoT in the ticks that occured between your last cast and your second one. We can calculate this two ways. 1) Set the ticks between casts equal to 10% of the average heal or 2) Try to directly calculate the amount.
1) This method is very simple. If your spell heals for X then during the steady state the amount of healed by the ticks dthat fit into the cast time will be equal to 0.1*X.
2) Now lets try to calculate the actual amount healed directly. I cast a spell with a 2.1 second timer, which heals for an amount equal to Y. The first spell will add an EoL amount of 0.1*Y but only 2 of the 6 ticks will be used up. Thus 0.1*Y*2/3 will be transferred to the next heal. The next heal will also add 0.1*Y. To this we will add 0.1*Y*2/3, so after the second heal that total amount to be healed by the EoL HoT will be 0.1*Y(1+2/3). Again the 1st two ticks will be expended so 0.1*Y*(1+2/3)*2/3 will be transferred to the next cast. The 3rd cast will also add a 0.1*Y HoT. That means the total amount will be 0.1*Y*(1+2/3)*2/3+0.1*Y = 0.1*Y*(1+2/3+(2/3)^2). This will continue in the same way until the nth spell this amount will be 0.1*Y*[1+2/3+(2/3)^(2)+........+(2/3)^(n-1)]. This is a geometric progression so its equal to 0.1*Y*[(1-(2/3)^(n)]/(1-2/3) = 0.1*Y*3*[(1-(2/3)^(n)]. At n=infinity that is 0.3*Y and since there are 6 ticks each tick is 0.1*Y/2. Since two ticks get used between spells the total amount healed between two spells is 0.1*Y. So we come up to the exact same result for the steady state but in this way we also get the formula for the what the HoT value is before the steady state is achieved. I.e. 0.1*(average amount healed)*[(1-a^n)/(1-a)]
Thus with my numbers the steady state HPS of heal spam in the heal chakra will be 3.35k HPS, which is roughly half the HPS of gheal spam. When you add however the heal from the flash heals that should rise a little higher to 3.5k HPS. Even 3.5k HPS will be more than sufficient for the rotation I proposed. 3.5k HPS is equivalent to flash heal spam in the previous patch.
However this is not the behaviour that the spell has currently in game. You can actually get it to EoL to stack very high, which means something is broken. If the poster above was getting 1200 per tick and he gets exactly 1 tick between spells due to the cast time being less than 2sec, that means the HPS from EoL is ~600, which is more than twice to what you can expect (since his haste is quite a bit higher than mine I presume his gear is much better).
So either EoL does not work the way we think or there is a bug. I will go have a look at the data and try to figure out what is happening exactly.
Nevertheless I still think my original conclusion stands that you can tank heal very effectively in the heal chakra even in the current content. 3.5k HPS for your basic heal is very respectable and you can tailor your HPS exactly to the incoming damage by using the rest of your heals