People posted trinket comparisons before, but none of them were complete, so I sat down and tried to come up with a complete set of numbers by spell from a mage's perspective. All numbers below assume ideal casting conditions (Edit: For numbers including lag, see a couple of posts below).


Fireball

Trinket Total damage DPS Spell power equivalent MQG equivalent
ToEP 875 9.72 29 1296
ZHC 104 8.725 26 1163
ToA 600 10 30 1333

Note that the tooltip for ZHC is incorrect. The above uses the accurate 204/-17 per spell numbers. Further, for ZHC I assumed that you would cast 6 fireballs then a scorch and a fireblast, since a 7th fireball would not fit into the 20 seconds without PoM. For the other trinkets I assumed chain cast fireball.

MQG (Mind Quickening Gem) equivalent is how hard your fireball would have to hit for MQG to add the same amount of damage. The math behind that number is as follows. With MQG you can cast 9 fireballs in 20.25 seconds. Without you can cast 7 fireballs in 21 seconds or 6.75 in 20.25 seconds. So you gain 2.25 fireballs per 300 seconds. So to get comparison numbers with for example ToA you do 10 / (2.25 / 300) = 3000 / 2.25 = 1333.

Spell power equivalent is DPS*3 since fireball is a 3 second cast that gets the full damage bonus from gear.

As you can see, for slow spells ToA (Talisman of Ascendance) actually adds the most damage. However, it is also backloaded making it arguably the worst for PvP. Note that Briarwood Reed performs just as well as all those purple trinkets for sustained damage (ignoring abilities like PoM or combustion).


Frostbolt


Trinket Total damage DPS Spell power equivalent MQG equivalent
ToEP 861 9.567 29 1076
ZHC 948 7.9 24 889
ToA 492 8.2 25 923

The assumed damage coefficient for frostbolt is 0.82. As you can see, with faster spells, ToEP pulls ahead.

Spell power equivalent is DPS*2.5/0.82.

Scorch

I did not run the numbers on scorch, but ToA, ZHC and MQG all perform horribly with scorch. MQG runs into the global cooldown so it is an obvious non-choice and ToA is also less than hot. Some people think that scorch works well with ZHC since it allows you to use up all charges. That is incorrect since using more charges with a spell that has a lower damage coefficient means that you get less overall damage bonus. So ToEP is the clear winner. However, you usually would not spam a low damage mana efficient spell while your trinkets are up.


Flamestrike

Conventional wisdom is that it is a bad idea to spam flamestrike since the dot component does not stack. Conventional wisdom is also that because of that improved flamestrike is not worth getting. I disagree with both. Completely ignoring the dot, theorycraft puts my flamestrike with the talent at 280 DPS. Even if I refresh flamestrike after just one dot tick, that is another 80 damage and 40 DPS right there. Blizzard can never match that kind of damage. And with improved flamestrike and master of elements, flamestrike effectively costs 30% less making it mana efficient as well.

With that said, here are the numbers for flamestrike vs ToA (the highest damage trinket for it).


Trinket Total damage DPS Spell power equivalent MQG equivalent
ToA 171 2.86 30 381

As you can see, the MQG equivalent damage is lower than the base damage of flamestrike, making MQG the ideal AoE trinket for a fire mage. Not to mention the tasty rolling ignites you get when casting a 2.25 second cast spell with a 40% chance to crit.


Threat

If you have 3 piece Netherwind there actually is a difference in threat reduction between the damage trinkets and MQG since the NW bonus is applied per spell. As it turns out, using fireball with burning soul MQG has a 0.65% higher effective threat reduction than ToA. I did not run the other spells and trinkets since the difference is so small.

would the overall outcome change when the mobs are debuffed. i.e. CoE, improved scorch, ect.

That is indeed true. Which is why I start off with "assume ideal casting conditions". Factoring in lag, the order of trinkets would change slightly. ZHC and ToA would benefit since ZHC has half a second of breathing room while ToA has 2 seconds. Thus, under realistic conditions ToA would perform as listed while ToEP would perform worse. ZHC is on the edge.

I can redo the math for different levels of lag if there is interest.

CoE is a debuff on the mob that is applied after everything else. Thus it would not change anything. Procs on the other hand get interestesting with MQG.

I think you did the math without +%damage talents. It'd be nice to consider the effective cast time .2s higher or something like that to account for lag. It'd also be nice if you could estimate the amount of time each trinket's cooldown was spent out of combat and remove that from the math, as well as account for the amount of time the trinket's full damage wasn't used because the mob died too soon. All that aside, I think there's something to be said for the regularity of ToEP over ToA/ZHC - adding resists into the thought process, they serve to make the average damage gain from ToA/ZHC more varied than the ToEP.

Simple average effects are never the right way to compare passive trinkets with activated trinkets.
If the encounter lasts 45 seconds, how much damage does ToeP add? Does the BWR still perform just as well? Clearly not.
What if the encounter lasts 2 minutes (two full ToeP activations)?
In the real world (well, in the real-virtual world of WoW), the ToeP almost always outperforms BWR on boss encounters provided the player doesn't lag the activation too much. This is because trinket activations are discrete values. You don't get half an activation if the encounter only lasts 45 seconds, you get a full activation, making the ToeP twice as powerful as your average would imply. You don't get 1.3 activations over a 2 minute encounter, you get 2.

The average is only the floor value of the ToeP (and other activated trinkets).

For fire spamming mages, Eye of the Beast is probably the best out of all the options unless it's a very burst happy fight.

+ damage talents do not affect the math since they work on everything equally. The only exception are talents that are applied before +damage gear.

I will redo the math for 0.1, 0.2 and 0.3s latency.

Time out of combat is difficult. However, DPS matters most on bosses, so your choice of trinkets should be affected by the length of the boss fight. A one minute fight favors MQG since you get to use it just as often as other trinkets. A 5 minute fight is bad for MQG since you get only one use and are stuck with a long cooldown for nothing.

That is true. However, there is also the counter argument that if you get for example stunned/punted/have to move/whatever while the trinket is up you lose part of the bonus. How that works out depends completely on the boss as you noted, so it is very difficult to capture in a simple formula.

Ideally a mage should have all trinkets since each is optimal in a different situation. Even ZHC which is mathematically the worst shines in PvP where frontloading is everthing.

Correct. Three specific examples from my raid last night include:

-Pop ToEP; Battleguard Sartura immediately comes flying across the room at you and you are forced to run away and eventually blink, losing the entire buff duration.

-Pop ToEP with huhuran at 31%; You are immediatly silenced with no ice block up, and lose half of the buff.

-Pop ToEP; Vek'lor decides that your elite sniping position on the stairs is an excellent place to cast blizzard; you blink, strafe to narrowly miss an exploding bug, and are forced to sit on the stairs and bandage, losing the entire buff duration.

There are situations in which Briarwood Reed is better, and situations in which ToEP is better, some within the same fight. Neither is optimal 100% of the time; you just need to take all the variables of a given fight into account beforehand and go from there.

Here are the numbers factoring in lag.


Fire

I assume that you are trying to maximize trinket usage. That is, cast a fireball if there is enough time. If not, cast scorch and then a fireblast (fireblast is frontloaded and thus the spell of choice if the trinket is running out). Doing this boosts the damage trinkets over MQG and ToEP over ZHC. However, if you wanted to be completely accurate you would have to factor in the reduced DPS from casting a scorch over a fireball, which would again favor MQG. But scorch has other benefits (debuff, mana efficiency) so I left that out.

ToA is sitting pretty because it does not take any reduction since it has the most cast time buffer.

Spell power equivalent takes the extra cast time into account as well.

0.1 second latency

Trinket Total damage DPS Spell power equivalent MQG equivalent
ToEP 850 9.44 29 1301
ZHC 1013 8.44 26 1163
ToA 600 10 31 1378

0.2 second latency

Trinket Total damage DPS Spell power equivalent MQG equivalent
ToEP 875 9.44 30 1343
ZHC 1013 8.44 27 1201
ToA 600 10 32 1422

0.3 second latency

Trinket Total damage DPS Spell power equivalent MQG equivalent
ToEP 775 8.61 28 1421
ZHC 1013 8.44 28 1393
ToA 600 10 33 1650

With increasing lag, the damage trinkets perform increasingly well against Briarwood Reed and MQG - at least at low levels of latency; at high levels all bets are off.


Frost

Frost is a little bit different since the tree has no spells like scorch and fireblast. Assuming that you are out of cone of cold range (that spell doesnt scale well anyway) and that a scorch with trinket is less efficient for a frost mage than a frostbolt without trinket, the frost mage has no choice but to eat the lag and cast one spell less.

As it turns out, at 0.1-0.3 second lag, ZHC an ToEP lose exactly one spell while ToA loses nothing. Thus, at lower latency, MQG and ToA pull ahead of the other two.


0.1 second latency

Trinket Total damage DPS Spell power equivalent MQG equivalent
ToEP 716 7.96 25 903
ZHC 878 7.32 23 830
ToA 492 8.2 26 930


0.2 second latency

Trinket Total damage DPS Spell power equivalent MQG equivalent
ToEP 716 7.96 26 1031
ZHC 878 7.32 24 948
ToA 492 8.2 27 1063


0.3 second latency

Trinket Total damage DPS Spell power equivalent MQG equivalent
ToEP 716 7.96 27 1069
ZHC 878 7.32 25 983
ToA 492 8.2 28 1102


In conclusion, ToA is surprisingly powerful given that is the most accessible trinket. ZHC is probably a little bit underpowered given its ilvl (it was overnerfed - they should have lowered its PvP effectiveness without reducing its PvE power). MQG is situational but where it shines it really shines. In the long run (level 70) it will surpass all the other trinkets since it scales. And finally, the little blue reed can hang with all the big purple boys.