I think I see some of the confusion people have with the DoT damage averages on a Normal Distribution.
The main issue with DoTs is they do have a cap, because proccing them again doesn't give you double DoT damage. However, you can only get 2 procs per minute at maximum, which means this really isn't a problem in practice. Basically if you could get 132 PPM (1 proc per second), you would only do 544 DoT Damage + 132 x 40 Direct Damage = 5,824 Damage. A 100 Damage DD would do 13200 Damage by comparison.
https://www.project1999.com/forums/s...&postcount=523 - In this example the JBB Shaman with Blight, Hammer of the Scourge is enganged in a fight that lasts 132 seconds. The Proc is a spell called Scourge, which lasts 126 seconds, and does 40 DD + 24 Damage a tick.
The Shaman has 1.3 PPM normally because they have 135 DEX. Since they are spamming JBB, they get 7.5/12.77 swings. This means your PPM is reduced to 0.76 PPM after accounting for the number of missed swings.
Here are the possible places you can proc and tick, since we are casting JBB. I am assuming the cast starts halfway through the first two ticks, which is why we start at 3 seconds. The numbers in paranthesis are ticks, and the bracketed number is the 0.5 swings triggering:
(0), 3, (6), 11, (12), (18), 19, (24), 27, (30), 35, (36), (42), 43, (48), (54), 51, [59], (60)
Using the numbers above, we could get a full 10 ticks from the DoT if you land it at the start. Our damage table will have 8 values for the 8 places where you could proc.
I will be using (t=x) to describe the seconds at which the proc occured. t=3 is 3 seconds into the fight:
[280 (t=3), 256 (t=11), 208 (t=19), 184 (t=27), 160 (t=35), 112 (t=43), 64 (t=51), 40 (t=59)] = (1304 damage / 8 values) = (163 average damage / 60 seconds) = 2.72 DPS x 0.76 PPM = 2.06 DPS
The 0.76 PPM is taking into account the chance of simply not procing at all. It is the same with DD Procs. If you have 0.5 PPM and your DD proc does 400 damage, you would end up doing (400 damage / 60 seconds) = 0.66 DPS x 0.5 PPM = 0.33 DPS.
Because the fight lasts 2 minutes, you have a total of 1.56 procs. This means you are guaranteed 1 DoT proc somehwere within the fight on average. The DoT lasts two minutes, so it can last the full duration of the fight. This means you have 4 possibilities on average: [Max DoT Damage, Zero Dot Damage, 1/4 DoT Damage, 3/4 DoT Damage] = [544, 0, 160, 400] = (1104 / 4) = 276 / 132 = 2.09 DPS, which is basically number we got from the 1 minute fight.
Since we do have the 0.56 procs still floating around, you would get an extra 40 DD half of the fights. So an extra 40 damage x 0.5 PPM = 20 damage / 132 seconds = 0.15 DPS.
So the total DPS would be 2.2 DPS per 2 minute fight, which is what I was using originally. Remember this still does not include white damage.