Theorycraft 101: 5.4 Trinkets

Blizzard’s pattern of trying to make more interesting raid trinkets in MoP has provided a lot of interesting theorycraft material. As in past Theorycraft 101 posts, the goal is here both to give theorycrafters some useful conclusions and equations to save them the trouble of reinventing them independently, and to give everyone some general information that helps them evaluate these new bonuses when selecting items.

Item Budgets

In general, the amount of any stats budgeted to a certain slot scales like:

V \cdot Q^I

  • V is the budget value controlling how many stats that item slot gets compared to other slots.
  • Q is a constant equal to the 15th root of 1.15.
  • I is the item’s ilvl.

Often a more convenient way to think of this, especially when dealing with trinkets, is to use ilvl 463 as a baseline. The reason is that most trinket procs are coded into the spelldata with ilvl 463 values (which is the pre-raid baseline for MoP), and then scaled from there on any individual item based on its ilvl. The Int proc on Nazgrim’s Burnished Insignia, for example, is this this spell. So in general, since looking up the ilvl 463 value for any proc/bonus on Wowhead is easy, you can think of the value at higher ilvls as:

V_{463} \cdot Q^{(I-463)}

or

V_{463} \cdot 1.15^\frac{I-463}{15}

This explains, for example, how the 5084 Int on the proc linked above becomes 11761 Int (i.e. 5084*1.15^6, with a slight deviation due to rounding) when applied to an item that’s ilvl 553 (90 ilvls above 463). Sites like Wowhead will correct for those minor rounding issues so they can exactly match in-game values, but we don’t have to worry about them here.

A lot could be said about item budgets, but I wanted to give the overview here so you have the context on what you should expect from a trinket at various ilvls. A handy factoid is the amount of a passive stat a trinket has at normal budgeting: it’s 847 at ilvl 463, or 1959 at ilvl 553. In other words, the most vanilla possible ilvl 553 raid trinket would have 1959 of a primary stat and 1959 of a secondary stat (or 1959*1.5=2939 in the case of Stamina). Real trinkets will replace one or the other (or both) of those with special bonuses, but that 1959 (or whatever it is at the ilvl you’re looking at) is the basis for comparison.

To work a brief example, see Purified Bindings (553). Note that 11761 Int is just about 1959*6, so the trinket is exactly on-budget if the proc is active 1/6 of the time. Since it has a 20 second duration, you’d expect it to proc every 120 seconds. The 115 second ICD is intended to produce this result and have the trinket match the budget that a passive Int trinket would have.

But you came here to talk about more interesting bonuses than stat procs, so without further ado:

Amplification

Amplifies your Critical Strike damage and healing, Haste, Mastery, and Spirit by X%.” (3.03% at ilvl 463, 7% at ilvl 553, 9% at ilvl 580).

At first blush, this increases the value of all your secondary stats by X%. So if you have 30,000 secondary stats on your character sheet and wore an ilvl 553 Amp trinket, it would be very similar to a trinket with 2100 passive secondary stats (placing it slightly above the par of 1959 in this example). Two quirks:

  • It amplifies Spirit but not hit rating, which is a slight asymmetry across caster classes that I think is an oversight.
  • It increases crit bonus rather than crit chance, which makes things slightly more complicated.

Crit bonus effects have some odd stacking properties. The easiest way to think of it is is that when you crit for 200%, there are two components: the 100% “normal damage” and then 100% “critical damage.” Other than the crit meta, which obeys an idiosyncratic rule* but is irrelevant in T16 due to legendary metas, crit bonus effects all apply multiplicatively to the “critical damage” portion only (including Amp, Skull Banner, and Elemental Fury).

Long story short, the crit bonus provided by Amp causes you to do X% more “critical damage” overall. This does in fact increase the value of your crit rating by X%. But crit chance comes from sources other than rating, and the value of that other crit is also increased by X%. So the easiest way to evaluate this bonus is to:

  1. look at your total raid-buffed crit chance,
  2. imagine that it all came from rating (in most cases, multiply the % by 600), and
  3. take X% of that rating.

Putting it all together, say the total of my haste, mastery, and Spirit were 20,000, and my raid-buffed crit were 35% (16.7% from 10,000 crit rating, and 18.3% from other sources) and I had a 553 Amp trinket (7%). I’d evaluate this part of the trinket as being worth 1,400 stats from haste/mastery/Spirit, and 35*600*7% = 1470 from crit, for a total of 2870, significantly above the expected budget of 1959 secondary stats.

Since the other half of the Amp trinket is, in all cases, a primary stat proc that is right on budget, it is looking like a very strong trinket numerically. It will be even more so for classes with very high effective crit chances due to class mechanics, such as Elemental Shaman. The only important caveat is that is that Prismatic Prison loses a little value for healers because having all of the Int delivered as a high-value high-ICD proc is poor for healing purposes.

*The crit meta increases the “critical damage” in such a way that the total damage will have increased by 3%, before other crit bonuses. Now that every class has a 100% base crit bonus, the crit meta essentially works by increasing it to 106%.

Multistrike

Your heals have a X% chance to trigger Multistrike, which causes instant additional healing to your target equal to 33% of the original healing done.” (6.05% at ilvl 463, 14% at ilvl 553, 18% at ilvl 580)

This is the simplest new bonus. Aside from issues like pets, it’s a straightforward X/3% increase to your damage or healing output. I want to emphasize that this is not an RPPM or ICD effect, simply a plain fixed % chance to occur on any damage/healing event.

The only issue is comparing, for example, 4.67% damage/healing (14%/3) to 1959 secondary stats. I’ll leave that up to individual class modelers, but if you note that 1959 secondaries is, for example, 3.26% crit, you can see that Multistrike is generally looking to be in a good position.

Cleave

Your heals have a X% chance to Cleave, dealing the same healing to up to 5 other nearby targets.” (1.34% at ilvl 463, 3.11% at ilvl 553, 4% at ilvl 580)

Exactly the same as Multistrike, with the twist that output depends on the number of nearby targets other than your main target. The only important note is that it’s tuned so that, if it hits one added target, it’s 2/3 as strong as Multistrike. For example at ilvl 553, 3.11% is 2/3 the value of the 4.67% output you’d have gotten from Multistrike.

So this trinket is dead even with Multistrike when it hits, on average, 1.5 added targets. In situations where it can regularly hit 5 targets, it is far above budget, and in situations where you are attacking a lone target it is useless. The ramifications of this are obvious, but the rule of thumb that it surpasses a “normal” trinket at around 1.5 splash targets should help you decide when to use it. For 25-man raid healers, I suspect you are very often going to be healing targets who have more than 1.5 other people nearby, except at enforced spread fights.

Cooldown Reduction

Increases the cooldown recovery rate of six of your major abilities by X%.

(17% at ilvl 463, 39% at ilvl 553, 50% at ilvl 580, in each case reduced by half on the tank version)

There’s not too much to say about this in terms of item budgeting, since its benefits are based on the vagaries of each particular class rotation, and I imagine the tuning was done ad hoc. Consult your class’s spreadsheet expert. I just want to correct a common misconception about how the bonus works.

50% CDR does not mean you can use the ability twice as often. It’s exactly analogous to the way haste works, it reduces the cooldown to 1/1.5 = 67% of where it started. So in the end, you can use the ability 1.5 times as often over the course of a fight, not twice as often. Since X% CDR means you can use the effect X% more times in the long run, the benefit is generally linear as the budget increases, as it should be.

This chart lists the affected abilities for each class, in case you need. The trinket doesn’t exist for Int users in this tier.

Other Tanking Effects

I’m not going to say too much about Juggernaut’s Focusing Crystal and Rook’s Unlucky Talisman. They have unique effects that can’t be compared in an apples-to-apples way against 1959 primary or secondary stats. I simply want to note that their inherent % bonuses follow the usual item budget rules just like everything else discussed here. As you upgrade through ilvls, these effects will increase in same way that any stat allocation would (because, as discussed above, all trinket procs/effects are built into the ilvl scaling mechanism now).

This does raise an interesting issue I want to touch on, but a full analysis will be for another post. For a bonus like Juggernaut’s, which is based on a flat % of your overall damage output, there’s a question of whether the overall benefit the trinket gives is actually scaling quadratically with your stat growth. Scaling is inherently confusing and I do want to make a post about it overall, but the basic thrust is that normally as you go up in ilvl, each item has more stat points, and each stat point is worth more because your totals of other stats have increased. It’s left as an exercise to the reader how this logic applies to effects that are based on a % of your other stats such as Juggernaut’s and Amplification.

RPPM

I’ve reviewed the math of RPPM in two prior posts, but this is a good time to note the updates for 5.4.

Every 5.4 RPPM trinket is 0.92 RPPM with a 10-second ICD (except that Ticking Ebon Detonator is 1.00).

Also, for reasons described by Blizzard in this post, haste no longer increases the RPPM of most trinkets, with the only T16 exception being Dysmorphic Samophlange.

A 10-second ICD produces an interesting player-favorable quirk. Since the procs are all 10 seconds long, it prevents overlaps that waste uptime. But since RPPM chance “pools” for 10 seconds (as described in earlier posts), blocking out procs for a 10 second period actually does not impair your overall proc chance in any way. In this case you do get the best of both worlds–the same number of procs you’d have normally, but arranged so that there are no overlaps.

To be on-budget, these trinkets whose procs are all 6 times the value a passive stat trinket would need to have 1/6 uptime. With a 10 second proc duration, you’d think all you need is 1.00 RPPM on all trinkets to be on par. The only quirk to this is that the “bad luck protection” system adds about 13% to proc rates in reality (as discussed in the previous post). Blizzard, slightly generously, has started discounting RPPM rates by around 9% to account for this. This results in a proc rate of 0.92 on all trinkets. Except that for some reason on Ticking Ebon Detonator, the they reduced the proc value by 9% instead (1069 per stack at ilvl 553, instead of 1176).*

Given this information–0.92 RPPM, no haste, 10s duration and no overlaps, uptime for most T16 trinkets is much simpler than it used to be. It will always be simply 1.13*0.92*10/60, or 17.33%. In the case of Samophlange, multiply further by your haste factor to get your final uptime.

Long story short, all RPPM trinkets in 5.4 have an average value that’s very close to equivalent to the passive budget. Essentially always, it’s a proc with 6 times the stats a passive trinket would have and an uptime of around 1/6. The only important exception is Samophlange, which gets a haste multiplier on top of the usual budget.**

*Note that Detonator, Samophlange, and Talisman all have per-stack values that are 1/10 of what a “big” RPPM proc values at the same ilvl would be. However, the actual mean stack height over the course of the proc is 10.5, not 10. The same is true for Black Blood, which has a mean stack of 5.5. This amounts to a free 5% added value to the first three trinkets, and 10% on Black Blood.

**I just want to note since the question is posed so often: just as Samophlange is pegged pretty close to its correct budget + haste, the same was true for Horridon’s Last Gasp. Any nontrivial ilvl jump from Horridon’s to Samophlange is likely to be a clear upgrade.

RPPM on the Pull

Starting in 5.4, for purposes of the “bad luck protection” described in earlier RPPM posts, the moment a raid encounter starts, your RPPM procs all behave as though 120 seconds have passed since the last proc.

Given the formula at the end of this post, any trinket or other RPPM effect with a mean proc time of 45 seconds or less will be guaranteed proc on the pull. This corresponds to RPPM of 1.33 or higher (including haste if it applies). Procs that are close to that value will be very likely to proc within the first few seconds.

A 0.92 RPPM trinket will begin each fight with a significant bonus (just about double it’s usual proc rate). It will have a 31%* chance to proc on your first attack, and if that fails, roughly a 35% chance to proc within the first 10 seconds of combat.

25 thoughts on “Theorycraft 101: 5.4 Trinkets

  1. As a Holy Pally, I’d love to have seen a healer CD reduction one. I’m already cycling through four throughput CDs on a regular basis.

    Of course, considering how raid cooldowns affect so much right now, I can understand why Blizzard avoided it.

  2. You sure about HLG? It seemed to me that it wasn’t working as intended, and most people theorycraft it wrong on the first go unless they know it works strangely. You’d think a proc while it’s already active would extend the duration by 10 seconds, but that’s not the case. When it procs while active, it doesn’t just extend the duration; it also stacks.

    That is, if it procs once, and then procs again immediately, over those 20 seconds that the buff was active, you gain more 1656*5*4 mana, not 1656*5*2.

    At least that is my understanding.

      • I guessed HLG stacking was unintended because the stacking effect was not mentioned in the tooltip, and it made it way overbudget to the point where LFR HLG almost gave more regen than Soothing Talisman, which was already pretty good compared to the Spirit Chunk trinkets. We can only speculate.

        However I see from your math that with Haste, Samophlange is also way overbudget, so that answers my question. I can only wonder if Blizzard did that on purpose because they messed up last tier, to purposefully make it a significant upgrade over HLG.

        Or it’s just intended for these trinkets to be overbudget, which I find kind of strange.

        • The “overbudget” appearance isn’t due to stacking, it’s due to RPPM increasing with haste. The idea is that RPPM mimics the effect of old-fashioned %-on-hit procs by increasing in value as you get more haste (with RPPM having the added effect of being balanced across classes with different attack profiles).

          • I’m aware of how RPPM works. I meant that with 10% haste and no stacking, HLG is right on budget. If they expected the average healer to have 20% spell haste, then it’s still close to budget with no stacking, but a good trinket, and making raid trinkets slightly better than valor trinkets is nothing new. Instead, with stacking, for haste-stacking healers it’s ~40% overbudget. It just seems like an oversight to me, like someone copied the code from another trinket and forgot to set max stacks to one. And of course they’re very hesitant to nerf things once they go live because as GC has said before they don’t want you to wipefest on a boss you previously had on farm.

  3. For most math about trinkets, it seems the 522 Soothing Talisman of the Shado-Pan Assault still has the upper hand against 535 Contemplation of Chi-Ji, even with 190 less intellect when both are fully valor upgraded. How does this work? Is Bliz just relying too much on the automatic scaling without working out it manually, or is the math just wrong?

    • The main reason is that Contemplation gets penalized by 1/6 for being a on-use effect. I know this rule reaches a kind of a silly result in the case of a Spirit effect since there’s no advantage from using it at a certain time (Spirit doesn’t even interact with any class abilities). But that’s how it’s always been with on-use trinkets. So the end result is that this trinket with 1/6 uptime gets a proc value of 5x what the passive stat would be at this ilvl (compare 8282 proc value to the 1657 Int).

      That said, I’m not sure that the 522 is better. Mean Spirit value of Contemplation is 8282/6 = 1380. Mean Spirit value of Soothing is 28905/180*5/0.564 = 1424 Spi equivalent. So Contemplation gives up the equivalent of 44 Spi in order to gain 190 Int, which is clearly better.

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  5. I’m curious if you use weak auras and if there’s a way to calculate the proc chance of an rppm trinket using your equations. I’d ultimately like to have two progress bars, one for when the buff is active and a second showing the proc chance over time.

    • I don’t see why you couldn’t, as long as you can know your current haste and the time since the last proc (and that WA can track these things). Your current “proc chance” isn’t precisely what you want since that fluctuates constantly as you attack–what you’d want to track is whether Bad Luck Protection has kicked in to provide any kind of a boost.

  6. Do other slots use the same V*Q^I scaling? The trinket data matches to within essentially roundoff, but 1.15^(1/15) doesn’t seem to explain the other slots as accurately.

    In the table below, the first column is iLevel, the next columns are primary stat values for: trinket, head, boots, belt, wrist, ring. For reference, this was item lookups on wowhead.

    572 2339 2243 1765 1685 1384 1304
    566 2211 2108 1664 1584 1308 1228
    559 2072 1960 1554 1474 1226 1146
    553 1959 1840 1466 1386 1159 1079
    540 1735 1603 1289 1209 1027 947
    528 1552 1408 1144 1064 918 838

      • D’oh, yes! I think that explains why wrist items and trinkets matched the model while none of the other slots did…

        Do you happen to have the scaling worked out for slots when they include sockets?

          • Yup, that worked perfectly on at least two of the slots (it’ll most likely work on the others).

            Here’s an example from a leg item with two sockets:

            572 2323
            566 2188
            559 2040
            553 1920
            540 1683
            528 1488

            If you normalize iLevels to 463 as you did above, you get V463 = 899, which explains the data to within roundoff.

            Thank you, the discrepancy was driving me crazy!

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  8. How do you deal with itemization on non-trinkets, more specifically secondary stats, I can’t get the model of V_463*1.15*((ilvl-463)/15) to work for them.

    If you have, say Akolik’s acid-soaked Robes, it has 1664 of mastery and crit on it @ 580 itemlevel(480@463) and three sockets. As you pointed out elsewhere sockets might matter, but even adding three times 80 it doesn’t math out.

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