I'm amazed this bug made it through to live.
Time length does matter because it is a proc which is base off of events which happen in time. More time = more potential procs = higher likelyhood.
So you are correct that the probability of a FDCL proc on each given tick doesn't increase with time, and the probability of a MS copy doesn't either... taken as a series of independent events it becomes more likely to occur over an increased period of time (and also with haste to some degree).
Ultimately it will fit to a poisson distribution with some mean expected value that can be expressed in occurrences/time.
That being said I based what I said on some dummy time and seat of the pants feel, it occurred very often in a ~30min session for me, far too much for my liking.
I doubt FDCL gives a damage benefit great enough vs Mindbender to be worth even 1 reapplication in a fight. (Especially, as you said, if it happens to wipe DP)
I know that we agree on the outcome But, likelihood of procs remains the same over time, more time does mean more procs, but it also means more time to average them out over - likelihood remains the same.
Because the duration of any dot (assume 100% uptime over a 5 minute fight with one GCD intervals in your distribution), is independent of which GCDs you will cast Mind Spike on, it is no more likely to occur on the GCD immediately following application as it is to be the GCD penultimate to the dot reapplication. Likelihood of a mind spike proc on FDCL wiping dots X times per fight will fit to a poisson, but it shouldn't correlate to how long the dot has been active I don't think.So you are correct that the probability of a FDCL proc on each given tick doesn't increase with time, and the probability of a MS copy doesn't either... taken as a series of independent events it becomes more likely to occur over an increased period of time (and also with haste to some degree).
Ultimately it will fit to a poisson distribution with some mean expected value that can be expressed in occurrences/time.
Just thinking outloud: The longer the dot has been active, the more FDCL procs you throw at the dot - each with a chance to wipe it - if the number of FDCL procs/time greatly exceeds the duration of the dot (ratio higher than 1) - then you could assume multiple FDCL's per dot application, which would result in multiple chances per dot application to wipe dots. Under those conditions (many FDCL's thrown at the same dot application), then the likelihood of a dot wipe would increase the greater the number of instances (GCDs) since the event first occurs (dot application) up to a maximum limit (maximum dot duration, 15 seconds). Ok, so I think this is what your saying - if you are throwing multiple FDCLs per dot application, then the chances that a wipe occurs increase over the duration of the dot application.
That makes sense. But it's predicated on the assumption that FDCL procs occur multiple times per dot application (and this isn't true for the scenarios I was thinking about, so I'll outline when it is and isn't true).
The dot in question here has to be VT (even though FDCL wipes all dots, so it doesnt really matter, but we can't think about Pain for example) because if VT isn't applied, then FDCL does not proc - this matters because every time a dot wipe occurs, FDCL cannot proc (on a single target, but i'll get to multi-target scenarios in a moment - the short answer is the likelihood of procs declines even in multi-target scenarios proportionally to the number of VTs active: if you wipe a VT, the chances of FDCL proccing drops 15% until you re-apply it, more detail later). VT has a duration of 15 seconds, ticks every 3 seconds, and has a 15% chance per tick to proc FDCL, so with 100% uptime:
3 seconds / 60 seconds = 20 ticks per minute per target, lets assume 25% haste, so 25 VT ticks per target per minute after haste. 25 ticks at 15% chance to proc is 3.75 procs per minute. VT lasts 15 seconds, so about 4 VT applications per minute occur per target. 3.75 / 4 = 0.93, or 93% chance per VT application for an FDCL proc to occur when you have 25% haste. What if you have VT+2? Then you have 7 ticks per VT, 4 VTs per minute, so 28 VT ticks per target per minute. 28 VT ticks times 15% chance of an FDCL proc is 4.2 procs per minute, 4.2 / 4 = 1.05, 105% chance per VT application for an FDCL proc to occur. So we can say that generally, we have about one FDCL proc per VT application that goes full duration.
One proc per application means one chance per application for a dot wipe to occur (but only 3-5% of these chances will result in a dot wipe of course, but thats irrelevant to our math since it entirely random and could be any FDCL proc). Since FDCL procs do not auto-self-cast when they occur - they can be saved - an FDCL proc can for example occur on the final tick of a VT, VT can be reapplied, and then FDCL can be expended and wipe VT before the first tick even occurs - or it could occur 3 GCDs prior to VT reapplication but Halo and Mindbender and Mindblast came off cooldown and it was saved all that time, VT was re-applied - and then FDCL, which wiped VT before the first tick again. Since FDCL is near the bottom of our spell priorities, the likelihood of us saving it to cast other (higher priority) spells at any given time is very high - it's filler, and therefore - mostly occurs on random GCDs: this means its uncorrelated to a rotation where for example, FDCL is always the third spell after VT is cast (which is not the case, its entirely independent).
So to recap, for any single target fight, and for any achieveable value of haste, FDCL procs occur about once per application on average and therefore the likelihood of a dot wipe is not correlated to the duration the dot has been active. For very high values of haste where we are inundated with FDCL procs - meaning gimmick fights like Sinestra, Alysrazor, and Madness of Deathwing - we could be casting many FDCLs per dot application and thereby increase the chances (but not the likelihood per chance) of a dot wipe per application, and increase the number of dot wipes per fight (because we have more FDCLs being cast, so that makes sense).
In a multi-target scenario, where we are putting VT on say, 3 targets with 100% uptime - then the chance of an FDCL proc occuring is tripled. Let's assume for the sake of argument, that even though we're dot cleaving - we're always focus casting our FDCL procs on a primary target. Triple the FDCL procs - assuming none go to waste (a bad assumption, but lets use it just to prove when there is a correlation between dot wipes and and dot duration remaining) - means three chances per VT duration for a dot wipe to occur, so the longer the dot is active - the more likelihood a dot wipe will occur - now we see a correlation!
Final Summary: only occurs in very high haste gimmick fights, and multi-dot fights where our single target damage must be directed toward a primary target - and only occurs when FDCL procs are not wasted, despite that these fights result in us having fewer GCDs for FDCL (very high haste fights make single gcd Mind Flays or Mind Sears better than FDCL procs, and multi-dot fights require more GCDs for dot reapplication. So in practice, while a correlation can exist in the above scenarios - it's not very likely (if even possible).
#TeamMindbendersTillMoP ^^That being said I based what I said on some dummy time and seat of the pants feel, it occurred very often in a ~30min session for me, far too much for my liking.
I doubt FDCL gives a damage benefit great enough vs Mindbender to be worth even 1 reapplication in a fight. (Especially, as you said, if it happens to wipe DP)