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New Data on FoF Pooling

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Good morning, day or evening ladies and gentlemen of Icy Vein
There have been a number of discussions concerning FoF pooling and why it should or should not be done.
Here i shall try to convey to you my take on it while also describing the two practises that evolve from this concept. 

Important Gameplay Concepts

Fingers of Frost: Your successful Frostbolts, Frostfire Bolts and Frozen Orb hits have a 15% chance, and your Blizzard ticks have a 5% chance to grant you the Fingers of Frost effect. The Fingers of Frost effect causes your next Ice Lance or Deep Freeze to act as if your target were frozen, and increases Ice Lance damage by 25% for 15 sec.  a.k.a FoF
Brain Freeze: Your most recently applied Nether Tempest, Living Bomb, or Frost Bomb spell has a chance when it deals damage to grant you the Brain Freeze effect. The Brain Freeze effect causes your next Frostfire Bolt to be instant cast, cost no mana, and act as if your target were frozen for 15 sec.
Shatter: Doubles the critical strike chance of all your spells against frozen targets plus an additional 50%.
Icelance: Deals 306 to 392 (+ 33.5% of Spell power) Frost damage to an enemy target. Ice Lance damage is quadrupled against frozen targets.
Frozen Thoughts: Consuming Brain Freeze increases the damage of your next Ice Lance, Frostbolt, Frostfire Bolt, or Cone of Cold by 20%.   This is our 2set bonus

Step 1: Sketching the situation

1. Cast procs as soon as they come up
This practice is pretty straightforward. Cast your procs in the exact order that the come up with the following priority: Brain Freeze > Icelance. This practice is pretty straightforward and results in a react-to-procs gameplay. 
So if you are in the middle of casting a Frostbolt, and your previous Frostbolt procs an Finger of Frost, whenever you are finished with your cast you use Icelance. If you do not react in time, and you are in the midst of casting a next Frostbolt and during that time a bomb tick procs Brain Freeze then you use the next 2 GCD casting Frostfire Bolt first and Icelance second only to continue as normal. 
There is nothing complicated concerning this tactic, and it all fundamentally comes down to reacting in time.
2. FoF Pool
This practice revolves around the idea of maximizing the damage bonus out of your 2set bonus. Instead of casting all procs as they come up, you always try to keep 1 FoF Charge. This changes our rotation in a slight way.
-Apply Living Bomb
-Cast Frostbolt (Frostbolt procs FoF.)
-Cast Frostbolt (Doesn't proc FoF)
!Brain Freeze proc!.. You are in the middle of casting next Frostbolt that doesn't proc FoF.
-Cast Frostfire Bolt
-Cast Icelance
If the second Frostbolt that was cast did proc FoF, you would use Icelance. During FoF pooling you shouldn't cap your FoF Charges except if Brain Freeze procs constantly.
The priority is once again BF > FoF > FB but it requires you to always have a FoF to use. 
Keep in mind you might want to use this weakaura in order to see how long you have till FoF falls off (if you are extremely unlucky with BF procs). What is this basically does is that it replaces the standard FoF Blizzard animation by the exact same only the opacity goes down related to it's remaining time. Remember to go to interface->Combat-> Alerts and disable spell Alerts.



Damage Gain of FoF Pooling

First we will determine the damage of Frostbolt and Icelance pre crit and pre crit amplification.
Gear profile: Average mage unable to reach the 18960 Haste Breakpoint.
So Haste to 14242> Masteru> Crit> Haste post 14242
With my profile this results in:
Haste: 50%
Mastery: 84%
Crit: 24%
Spellpower: 52.000
Frostbolt DPET:
We can not use Lhivera's library wholly due to having PBoI messing with our crit Amp.
So let's figure out our own function.
With 0 Crit using Lhivera's Library: 126.263
Having 24% Crit: As such 123906*0,24*1,097 = 33.242
Total DPET = 159.505
Frozen Thoughts buffs the damage by 20%. So the TotallyTotalDPET is multiplied by 1,20. There is no need to bother with the difference between damage and DPET because (Damage)*1,20/(Cast Time) is the same thing as DPET*1,20.
So TotallyTotalDPET: 159.505*1,20 = 191.406
Icelance DPET:
For Icelance we can not use Lhivera's library except to calculate Icelance at 0% Crit and without FoF and then procede with calculating the total damage by ourselves.
Icelance DPET at 50% Haste = 24521
FoF Icelance at 0% Crit: (245.21+0,50*24521*1,097)*1,25*4 = 189.852
FoF Icelance at 24% Crit: (24.521+(2*0,24+0,50)*24.521*1,097)*1,25*4 = 254.412
So TotallyToalDPET with 2pac = 254412*1,20 = 305.294
Conclusion: Every one time you do FoF Pool instead of using Brain Freeze + Frostbolt you gain a potential:
(305.294 - 254.412) - (191.406 - 159.505) = 18.981 Damage. This value compares the damage gain of Icelance with the damage gain of Frostbolt.
As you can see the damage gain from pooling FoF is not that significant. 
My conclusion here is that it is not worth pooling FoF (at least during the 14242 rest to mastery period). I do not know how to work out this result further one, but the munching of one Fof Charge seems to me would provide a more significant dps loss than the 19k gain.
I would love if anyone can review this
Edit: With kind input of Struntcantor
loss of one FoF charge can be roughly modeled by replacing 1 FoF IL with 1 Frostbolt. So take 254,412 - 159,505 = 94,907 DPET lost per FoF overwritten. 

In order for pooling to be a gain, you need to accurately pool >5 IL for each FoF you overwrite.

Additional Case: Trinket Proc

With a 588 Bindings proc up, you gain 7.09% crit (16296 int * 1.05 * 1.05 /2533.66 int/crit = 7.09% crit) and 19762 spell power. Recalculating your numbers with those increases you get FB DPET at 232,415 and 278,898 with 2pc and IL DPET at 352,894 and 423,472 with 2pc. 

Gain is therefore (352,894 - 232,415) * 0.2 = 24,096 DPET, an absolute gain. But where with no trinket proc you had 4.26% dmg gain over the FB/IL pair by pooling now you have only a 3.8% dmg gain. Ratio of pooling to overwritten procs stays the same. So trinket procs don't influence whether to pool or not.
Edited by Berlinia
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