Originally Posted by sjogren
You mean like this?
I think there's a lack of understanding of the probability theory concept "expected value" here, let me see if I can explain what I mean in another way.
With 10% proc chance per tick, it takes on average 10 ticks to get a proc. Most of the time it'll take more than 10 ticks or less than 10 ticks, but on average it takes 10 ticks. This means 30s until a proc, on average. This is true both for Serpent Sting and Black Arrow.
With the 3.0.9 behaviour, serpent sting and cooldown, after you get a proc you have a 30s window where you can't get any procs, whether you have serpent sting up or not. On average, this means 50% of the time.
With black arrow and no cooldown, you would be able to get procs on any tick, even if you just got a proc, but since the duration is 15s and with a 30s cooldown, you only have 50% uptime.
This gives the same average number of procs over time.
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Originally Posted by sjogren
Are you seriously claiming that the 30s cooldown on LnL doesn't affect the average number of procs per minute?
The expected number of ticks to get a proc is 10 in both cases, but in the 3.1 BA case (assuming there is no cooldown on LnL in 3.1 as I've been saying all along) we start "counting" again right away while in the 3.0.9 SrS case we have to wait 30s to start "counting".
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Before we go into this, I will agree that this probability would appear to be an additive probability of the form P(A U B) = P(A) + P(B) and not P( A n B ) = P(A) * P(B). In other words, each tick should be allowed to be treated independently, and the only link between any two probabilities in this chain will be if a LnL cooldown occurs, and subsequent probabilities are 0 until the cooldown exhausts itself.
You are "supposed" to have a 10% chance to proc this every tick, and a tick occurs every 3s. Over 1 minute, you will have the following chances to proc with the 3.0.9 and 3.1 systems (serpent sting vs black arrow, respectively).
3.0.9 possible procs per minute (SS) = 60 total seconds of 3 second refresh = 20
3.1 possible procs per minute = 30 total seconds of 3 second refresh = 10
Let's assume for a moment that things really do come out to an average of one every 10 cooldown free proc chances will proc, that the LnL cooldown stays at 30 seconds, and that BA remains the only reliable proc mechanism on most bosses. Out of a minute of combat, these proc chances would look like this:
3.1.0 BA probability table for 1 minute
.1 .1 .1 .1 .1 0 0 0 0 0 .1 .1 .1 .1 .1 0 0 0 0 0
3.0.9 SS probability table for 1 minute
.1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1
Now, add the 30 second cooldown into the picture. Let's say that the proc happens on the 3rd possible in both scenarios.
3.1.0 BA probability table for 1 minute
3.1.0 BA probability table for 1 minute
.1 .1 .1 0 0 0 0 0 0 0 0 0 0 0 .1 0 0 0 0 0
3.0.9 SS probability table for 1 minute
.1 .1 .1 0 0 0 0 0 0 0 0 0 0 0 .1 .1 .1 .1 .1 .1
So, out of this time slice for one minute, the 3.0.9 SS method has more than twice the proc chances possible, and it's extremely improbable of getting more than 1 proc per minute with BA.
That being said, I'm positive the proc rate for the previous LnL mechanism was less than the 10% promised per tick. Without trap dancing, I had never seen more than 1 proc per minute (using a ceiling (time), so that a 3.5 minute fight would still possibly proc 4) without trap dancing.
Take this Patchwerk pug I did the other day (eventually leaving the raid because the healing and dps was terrible).
Wow Web Stats
I only proc'd LnL 3 times in a 3:59 fight. Unfortunately, this is the norm and not an outlier. It appears the proc rate is closer to 5% instead of the 10% indicated in the talent. Assuming this percentage actually stays implemented in the 3.1, and BA only procs 5% of the time (not 10% as displayed in the current talent), expect the LnL procs to go from on average once per minute, to once per two minutes, simply because it will take 2 minutes for BA to reach the 20 procs that are required for the average.
Another example:
Wow Web Stats
A VoA with a kill time of nearly 4 minutes. This time I proc LnL 4 times (satisfying the ceiling(time) I mentioned earlier). This is just something we've come to expect out of LnL. The proc rate each tick is closer to 5%, not 10%.
Another example:
Wow Web Stats
A Patchwerk of 3:35. Again, 4 procs.
Before I get jumped on, a probability table for BA over 2 minutes, showing the required 3s time slices to get 20 proc possibles.
3.1.0 BA probability table for 2 minute
.1 .1 .1 .1 .1 0 0 0 0 0 .1 .1 .1 .1 .1 0 0 0 0 0
.1 .1 .1 .1 .1 0 0 0 0 0 .1 .1 .1 .1 .1 0 0 0 0 0
So, in conclusion, if the 10% proc chance were actually implemented correctly, you may be right about the current BA with 10% chance would match the proc rate per minute of the current SS LnL proc mechanism, but I disagree that the current % chance is correctly implemented as 10%, and you are currently comparing 10% chance with 5-6% chance that seems to actually be implemented. What I think people are worried about is that the system seems to currently exhibit a 5-6% chance per proc, and this same legacy system will be inherited by the BA system, resulting in an average proc every 2 minutes.
P.S. I understand your point about if LnL's cooldown is taken out, it should mimic the current implementation. However, assuming the LnL cooldown will be removed in the Live version may be expecting much. Have we seen anyone mention this? I must have missed it.
If the BA proc rate is actually 10%, then we may see something close to a 1 proc per minute rate from BA, but with the cooldown, it will be a little bit under 1 per minute (probably once every 1:15, due to the cooldown overlapping most of the proc chances of BA at the tail end of the 1st minute, resulting in less proc chances and more variability due to RNG.
P.P.S. If the proc rate is too low, they'll fix it.