This isn't going to be a structured post. Instead, It's going to be a cluttered, confusing piece of writing, since it's mostly a braindump. It's just meant to list key points that will affect our spell usage with the trinket. The goal is to eventually build an APL out of these observations and conclusions. I settled for a format that follows a cycle of "Claim -> Proof -> Observations".
Claim 1: When Arcane Power is not active, ToSW is worthless and equivalent to not having a second trinket.
Proof: Read the tooltip.
Observations: The key point to make here is that ToSW is a trinket that focuses all power gain within the duration of Arcane Power, which has a base uptime of 15/90 = 16.67%. This also means that our choice of spells during Arcane Power is very important, because every second of Arcane Power really counts. Another conclusion is that ToSW should increase the value of Overpowered relative to the other two talents. The damage gain isn't linear with Arcane Power's duration increase though, due to falling mana levels and reduced mastery benefits.
Claim 2: Assuming buffs stay constant, at 4 Arcane Charges and below 93% mana, the sequence "AM -> AB" always produces higher DPS than "AB -> AM".
Proof: AB4 costs 10% mana, 9% with the class trinket. AB->AM leads to the AM being casted at lower mana levels. On the other hand, casting AM first allows 3.6% mana regen over the duration, with AB casted at a higher mana level. Due to being <93% mana, we can guarantee that mana capping will not occur, which means that both options will end at the same mana level for remaining spells.
In addition, AM casted first allows a chance to trigger 4T18 for Temporal Power buffs.
Corollary: If Arcane Missiles is casted during the burn phase, then casting it as early as possible without mana capping will result in the best damage done.
Proof: By induction. If AM->AB is preferable to AB->AM, then AM->AB->AB is preferable to AB->AB->AM, and so on.
Observations: During a burn phase, if Arcane Missiles will be casted at some point, it is always better to cast it as soon as possible. This allows the remaining spells to be casted at a higher mana level and benefit from potential Temporal Power buffs, dealing more overall damage.
The significance of this is that it simplifies "how should I use AM" to "whether I should use AM". It's clear that IF you are casting AM, you want to cast it early. The remaining issue is determining when and when not to use it.
Claim 3: With Overpowered, the optimal strategy is to ALWAYS use Arcane Missiles as soon as possible without mana capping.
Proof: The key constraint of ToSW's optimal usage is the limited duration on AP. Arcane Missiles has a base cast time of 2.0 seconds, which is reduced by haste. Since it adds 2.0 seconds to Arcane Power, this means that Arcane Missiles always adds more time to Arcane Power than it spends. This means more time for Arcane Blasts, which feeds into additional gains from the trinket.
Observation: That this might not play well with the 15 second duration of Nithramus, since it dilutes the contribution from ToSW over a longer period of time.
Claim 4: Tome of Shifting Words leads to a (almost) strictly mana negative burn phase.
Proof: Default burn phase is mana negative already, and ToSW increases the cast speed of Arcane Blast without decreasing mana costs or increasing regen rate. Arcane Blast with normal Tome allows (1.8*1.8*(1-0.2744825)) ~= 2.35% mana regen over its cast. It would require at least 2AM casts before the cost of 1 AB4, which costs 9% mana with Arcane Power, would be regenerated. Since AB can only proc 1 AM per cast, beyond an initial dump of AMs, the mana curve during burn is strictly negative.
Observation: This is important to reaffirm and establish. Combining it with observation #2, this means we can make a rough assumption: Each additional spell will be casted at a lower mana level, doing less damage than before. This corresponds with a strictly decreasing DPS curve, which means we can use a greedy approach for rotation optimization, always choosing the spell that gives the highest DPET.
With those conclusions in place, we're starting to see an outline of what should be optimal.
1. AP starts.
2. Some form of conserve rotation involving a few ABs and AMs, keeping mana high and trigerring Temporal Power buffs.
3. At some point, begin AB spam for the rest of AP.
But when do we go from phase 2 to 3? Would it be possible that we just spend AMs as they come, and never purely spam AB? The main constraint here is AP's limited duration. Casting an additional AM at high mana comes at the cost of time spent casting additional ABs at the tail of AP with low mana. The strictly decreasing DPS curve means that any additional ABs are worth less and less, so the optimum DPS would be achieved when AM is equal in DPET to the final AB casted during AP. This is a question of "target mana level at the end of AP". Let's take a closer look at that.
Claim 5: With Tome of Shifting Words, for most "normal" levels of mastery, (DPET of AB4 at any mana level) > (DPET of AM4 at any mana level).
Proof: Spreadsheet time!
Let's start with some unhasted numbers. Luckily, both AB4 and AM4 scale similarly until 80% haste, when AB4 hits GCD cap. Tome has a 25% (technically 24.99981%) effect at base itemlevel of 695 (even if no version of the trinket exists in game at that itemlevel). We can build a damage and DPET table for Arcane Missiles and Arcane Blast at each trinket itemlevel.
For the next step, what we want to answer is "What is the mana level for a given amount of mastery, before casting AB4 is lower DPET than casting AM4 at a high level of mana?" Using the player mana regen rate of 1.8%/sec before haste, we can assume a 93%+1.8% ~= 95% average mana level for Arcane Missiles. What mana level for AB4 does that correspond to?
It would take at least 85% mastery with 705 ToSW, and over 100% mastery with 720 ToSW, before AB4 casted at ~10% mana (the minimum) would have lower DPET than AM4 casted at high mana. These mastery figures are pretty unrealistic, which means we can assume the observation is true. With Unstable Magic, AB gains even more ground relative to AM, giving this observation even more secure ground.
Observations: As long as Arcane Power is up and mana is enough to last through the rest of it, using AB would do more DPS than AM for the duration of Arcane Power.
Note: This conclusion does not account for what happens outside of AP. This is strictly about "How to do the most damage for the duration of Arcane Power" - which is extremely relevant for the ring, but not necssarily what would provide maximum player DPS.
Additional Note: Without ToSW, the spreadsheet indicates that there is no mana level that would give AB4 higher DPET than AM. This corroborates with our original understanding of burn phases without ToSW: Use AMs ASAP, unless it causes disruptive delays to overall burn/evocation cycles.
Observation #5 tells us this: "The optimal amount of damage done during AP would involve spamming AB at the tail to very low mana." There are some simplifications being made here; we're not fully accounting for midway AM procs that might cap at 3 charges, potential Temporal Power gains, or Prophecy of Fear. Those would complicate things a lot.
The biggest problem we have though, is that damage done during AP isn't a "closed system". The amount of mana you finish at the end of the burn affects the amount of time you spend evocation outside of AP, which is also damage lost. Making a simplified assumption that evocation gives mana steadily instead of in large chunks, we can estimate the amount of time lost to these "extra evo ticks". Evocation grants 20%*(1+haste) mana per tick, with one tick happening immediately, and each additional tick 2/(1+haste) seconds later. We usually gain between 25% to 35% per tick, depending on haste buffs such as Mark of Warsong and Bloodlust. Using 30% as a median, we can adjust DPET estimates in our earlier spreadsheet, and compute new mastery and mana levels for DPET parity between AB4 and AM4.
Claim 6: Ignoring external factors such as Prismatic Crystal, Nithramus and Unstable magic, reaching 0% mana during burn phases with ANY trinket does not give optimal overall player damage.
Proof: Spreadsheets.
After adjusting for the extra At any reasonable mastery level and with any itemlevel trinket, AM4 at high mana is more desirable than ToSW ABs casted at around zero mana.
Observations: This should answer a lot of questions for why a lot of players, especially with normal ToSW and lower levels of gear, didn't feel the same strength from the spec trinket that mythic players do. Most of them did not have the legendary ring, were using the normal 705 version of the trinket, and mindlessly spammed Arcane Blast during AP until they reached 0% mana. This is especially penalizing with old T17 gear, which was heavier on mastery relative to current T18 items. In the end, they lost most of the gains from the trinket due to the extra amount of time they spent evocating.
Notably, this has implications for Prophecy of Fear openers. This is supportive of the strategy that begins a burn phase with dumping Arcane Missiles into the boss after putting up Prismatic Crystal, at the cost of spending less time Arcane Blast spamming.
Note that this is a simplified conclusion that doesn't take into account multiplcative effects such as Prismatic Crystal+Unstable Magic, Nithramus, or other multiplicative effects. Nithramus is especially important as a skewing effect.
Claim 7: Haste has heavy effects on usage of Tome of Shifting Words, due to both reduction in cast time, and increased mana regeneration rate from evocation.
Proof: With a "target mana level at the end of AP" strategy, it always requries a fixed number of Arcane Blasts to reach from ~93% to the the target mana level. Haste reduces the amount of time taken to get there, which leaves more Arcane Power time for staying in conserve mode and using Arcane Missiles. On the other hand, Nether Attunement means that Evocation gains more mana per tick. This means we want to set a lower target mana level, and spend more time spamming ABs.
Observations: The biggest implication of this is that Bloodlust heavily affects the pacing of 15 second burn phases. What happens when it pushes us past the 80% haste soft cap is also a question that will take a lot of effort to answer.
Unfortunately, the two different effects of haste are a little conflicting. Does it mean spending more time It will take more detailed math to figure out whether we really spend much more time AB spamming, or does it mean we should spend more of AP casting AMs? I don't know, so maybe you should do the math and tell me!
Alright, enough of a wall of text. To close this post, I'm just going to include some key figures and formulas for analysing this topic.
Code: Select all
mana_regen = 1.8% * (1 + haste) per second
cast_time = base_cast_time / (1 + haste)
evocation: 20% * (1 + haste) mana per tick, 1 tick on cast, 3 ticks spaced 2 / (1 + haste) seconds after
Arcane Blast:
mana_cost = 2% * (1 + arcane_charges) * (1 - 0.1 * arcane_power_active)
damage = 121% * (1 + 0.5 * arcane_charges) spellpower
base_cast_time = 2.25 * (1 - 0.05 * arcane_charges) seconds
Arcane Missiles:
damage = 5 * 28.5% * (1 + 0.5 * arcane_charges) spellpower
base_cast_time = 2.0 seconds
Tome of Shifting Words:
base_itemlevel = 695
base_effect_percentage = 24.99981%
effect_percentage = base_effect_percentage *1.15 ^( (itemlevel - base_itemlevel) / 15 )
