Originally Posted by Selmarix
10% proc chance with 30s internal cooldown results in around 1 ppm.
10% proc chance on BA with its 50% uptime without internal cooldown results in around 1 ppm but with the danger of losing a proc because of 2 procs too close to each other (before you can use it).
So no, there is no current 5% proc chance and it was never intended for LnL to have a proc rate of 2 ppm.
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Before I go into a rant about this, could we possibly get a validation of Reach's test on there being no cooldown with BA LnL?
Better yet, could someone do a test over 24-30 minutes of BA usage and detail the following (with no trap usage whatsoever):
How many LnL procs happened in that span? If it's 24-30 (respectively), then you guys are right and there is not cooldown. If it's closer to 18-26 (respectively), then there is still a 30s cooldown, and I detail that reason below.
The rest of this assumes a cooldown, and if you don't want to go there, then stop reading.
I really didn't mean to imply that our proc rate should trend towards 2 ppm. I really meant to state that the proc rate would trend towards that without the cooldown in place since at the time we seemed to be using P (A U B) probabilities where each event was mutually exclusive. That is entirely my fault, and I probably got my sentences twisted in that because I was on two trains of thought. My apologies.
Now, what should worry you about the BA mechanic (with a cooldown) is the fact that you might get 1 proc per minute, but only about 2/3 of the time. BA at 10% (assuming cooldown) will be much more susceptible to RNG problems than the current SS LnL, and I outlined part of the reason earlier when I mapped out the tables. Let's assume that the rate is 10% proc chance per damage application. For BA, you have the following probability that no proc will happen at all in any given minute of a fight.
.9 .9 .9 .9 .9 .9 .9 .9 .9 .9 = .9 ^ 10 = 0.3486784401 = 35%
One out of every 3 minutes of a boss fight, you should expect no LnL procs whatsoever, if there's still a cooldown. Again, if you guys verify that the cooldown is definitely gone without using traps, then I think everyone will breathe a sigh of relief.
With the SS LnL system currently in place (assuming 10% proc chance), the worst case will only happen:
.9 ^ 20 = 0.12157665459056928801 = 12% of the time.
and as noted before, even with a 30s cooldown, you have a decent chance of proccing 2 LnLs with the SS system (because if every tick is 10% chance with SS), you still have a decent probability of proccing in the last half of the minute. In fact, here are the probabilities for that (with time set to the proc slice out of each minute).
.1 0 0 0 0 0 0 0 0 0 0 .1 .1 .1 .1 .1 .1 .1 .1 .1 = 90% chance of proccing 2 LnLs, given proc at time = 1
.1 .1 0 0 0 0 0 0 0 0 0 0 .1 .1 .1 .1 .1 .1 .1 .1 = 80% chance of proccing 2 LnLs, given proc at time = 2
.1 .1 .1 0 0 0 0 0 0 0 0 0 0 .1 .1 .1 .1 .1 .1 .1 = 70% chance of proccing 2 LnLs, given proc at time = 3
.1 .1 .1 .1 0 0 0 0 0 0 0 0 0 0 .1 .1 .1 .1 .1 .1 = 60% chance of proccing 2 LnLs, given proc at time = 4
.1 .1 .1 .1 .1 0 0 0 0 0 0 0 0 0 0 .1 .1 .1 .1 .1 = 50% chance of proccing 2 LnLs, given proc at time = 5
.1 .1 .1 .1 .1 .1 0 0 0 0 0 0 0 0 0 0 .1 .1 .1 .1 = 40% chance of proccing 2 LnLs, given proc at time = 6
.1 .1 .1 .1 .1 .1 .1 0 0 0 0 0 0 0 0 0 0 .1 .1 .1 = 30% chance of proccing 2 LnLs, given proc at time = 7
.1 .1 .1 .1 .1 .1 .1 .1 0 0 0 0 0 0 0 0 0 0 .1 .1 = 20% chance of proccing 2 LnLs, given proc at time = 8
.1 .1 .1 .1 .1 .1 .1 .1 .1 0 0 0 0 0 0 0 0 0 0 .1 = 10% chance of proccing 2 LnLs, given proc at time = 9
These probabilities will require chaining the probability of the specific event sequence occurring before the proc and result in the following probabilities (please correct me if I'm wrong here):
.1 * .9 = .09
.9 * .1 * .8 = 0.072
.9^2 * .1 * .7 = 0.0567
.9^3 * .1 * .6 = 0.04374
.9^4 * .1 * .5 = 0.032805
.9^5 * .1 * .4 = 0.0236196
.9^6 * .1 * .3 = 0.01594323
.9^7 * .1 * .2 = 0.009565938
.9^8 * .1 * .1 = 0.0043046721
total = 9 + 7.2 + 5.67 + 4.374 + 3.2805 + 2.36196 + 1.594323 + .9565938 + .43046721
total = 34.86784401% chance to proc 2 LnLs per minute to correct the 12% chance you won't get any LnL procs in a minute.
Consequently, SS LnL should produce a tendency to have more than 1 ppm, even with the cooldown.
Now, looking at the probabilities that are possible to "catch up" for BA and still get an average of one proc per minute, you have the following possibilities in a BA (cooldown) scenario.
Base (just for my own reference):
.1 .1 .1 .1 .1 0 0 0 0 0 .1 .1 .1 .1 .1 0 0 0 0 0
.1 0 0 0 0 0 0 0 0 0 0 .1 .1 .1 .1 0 0 0 0 0 = 40% chance of proccing 2 LnLs, given proc at time = 1
.1 .1 0 0 0 0 0 0 0 0 0 0 .1 .1 .1 0 0 0 0 0 = 30% chance of proccing 2 LnLs, given proc at time = 2
.1 .1 .1 0 0 0 0 0 0 0 0 0 0 .1 .1 0 0 0 0 0 = 20% chance of proccing 2 LnLs, given proc at time = 3
.1 .1 .1 .1 0 0 0 0 0 0 0 0 0 0 .1 0 0 0 0 0 = 10% chance of proccing 2 LnLs, given proc at time = 4
Unless someone can point out a math error here, these probabilities are all linked together and should have the following chances, respectively:
.1 * .4 = .04
.9 * .1 * .3 = 0.027
.9^2 * .1 * .2 = 0.0162
.9^3 * .1 * .1 = 0.00729
total = 4 + 2.7 +1.62 + .729 = 9.049 chance to proc 2 LnLs per minute to correct the 34.9% chance you won't get any LnL procs in a minute.
Consequently, if we still have a LnL cooldown that is specific to BA, then we will see a trend of less than 1 ppm, trending towards one proc every 1.2 minutes (unless my math is incorrect)