Amplification Trinkets in 5.4

Healer Amplification Trinket

** Updated for new trinket behaviour in patch 5.4.8 (May 20, 2014) **

This is just a pretty quick post to talk briefly about the trinket drops collectively known as “Amplification trinkets” that we’ll see in 5.4. As usual in WoW, the tooltip doesn’t tell the whole story, so I’m here to fill in the blanks. I’ll try to keep the math to a minimum in this one, but some of it will be unavoidable, sorry 😉

The Amplification trinkets have two passive abilities, but the important/interesting one is the effect that improves your Spirit, Haste Rating, and Mastery Rating values and adds to your Critical Strike bonus.

Before I get into the nitty-gritty of how to evaluate the raw stats that this trinket grants you, I’d like to first address something that is a bit … flawed … about this trinket’s tooltip.

The relationship between item level and size of a proc or passive effect, P, can be found by:
P_(iLvl) = P₍₄₆₃₎*1.15^{((iLvl-463)/15)}
I learned this from watching Hamlet 😛

The tooltip rounds the % Amplification effect off to the nearest whole number, while the benefit you get from equipping the trinket is not rounded.

What this means is that you’re rarely going to see your in-game results match what the trinket’s tooltip claims. I’ve compiled a table, to the right here, of the various iLevels of this trinket, the benefit the tooltip states, and the approximate benefit you’ll get.

(Note: These numbers vary slightly from in-game data at the third decimal point, meaning they don’t show any differences at all until you have over 100,000 rating in one of the affected stats. Any variation you see in-game is due to the game’s rounding mechanism. Still, if you are worried you might hit that 100k mark, the item-budget-derived values can be found in this post on HowtoPriest. Note that neither this model nor my model can predict exactly how the game is going to round your final values, but in either case you should be off by no more than 1 rating.)

This information is really only important if you ever want to do your own calculations for things like, “How much larger will my Critical Strike heals be with my 2/2 upgraded Warforged trinket?”, but from an informational standpoint I think it’s pretty important to realise that the tooltip is a bit misleading, and I hope this helps at least someone! 🙂

The way this works is pretty simple – whatever Rating you have in Haste or Mastery, and whatever amount of Spirit you have, gets multiplied by (1 + whatever the “actual %” for your trinket’s iLvl is). So if you have the Normal mode Prismatic Prison of Pride, your Haste, Mastery, and Spirit all get multiplied by 1.07. Depending on how much of those you have already, this can be anywhere from a 100- to 1300-Rating boost to your secondary stats.

I’ll note here also that the Amplification trinket also increases the Spirit you receive from Mana Tide Totem. Even if the casting Shaman doesn’t have the trinket, players who have the Amplification trinket equipped will receive +214% of the casting Shaman’s Spirit, rather than 200%. (So if your Shaman has 100 Spirit, you will get 214 Spirit from their Mana Tide Totem. If your Shaman also has the Amplification trinket, you will get 228 Spirit from their Mana Tide Totem.) Similarly, the Amplification trinket also increases the amount of Spirit you get from trinket procs/on-use effects, even though this is not accurately reflected in the tooltip of the proc/on-use buff.

It’s a little more tricky for Crit, and I will have to walk you through some math to explain my point:

First of all, this trinket does not act like the “3% increased Critical effect” meta gem. This is tripping a lot of people up, and maybe it’s a mistake on Blizzard’s behalf in wording it this way, but what the trinket does is an additive 7% additional healing when your heal crits. It is not 2*(1.07X) = 2.14X. It is (2+0.07)*X = 2.07X. So if your heal normally hits for 100, and would normally crit for 200, then with the Amplification trinket, your heal will crit for 207.

Now then, with that out of the way, let’s talk about how to evaluate this effect in terms of secondary stat equivalencies!

Let’s say that you have a 25% chance to Crit in your gear. Without the trinket, your average heal throughout the course of a fight would be:

25% chance at 2X + 75% chance at X
0.25*2X + 0.75*X
0.5*X + 0.75*X
1.25*X

Which you’ll notice is (1+Crit chance)*Heal Size.

With the trinket, your average heal would be:

25% chance at 2.07*X + 75% chance at X
0.25*2.07*X + 0.75*X
0.5175*X + 0.75*X
1.2675*X

Which you’ll notice is (1+(1.07*Crit chance))*Heal Size.

We can then translate our expected benefit from this additional Crit bonus into an equivalent Critical Strike Rating, and it’s much larger than what you’d expect. We had to do this math because we can’t just generalise directly to a 7% increase in the Crit Rating from our gear, like we can with Haste, Mastery, or Spirit. At our item levels, a fair portion of our Crit – around 10% Crit chance, in fact – arises from our Intellect-to-Crit conversion. Thus, while we have 25% Crit, only 15% of that comes from our gear, so a 7% boost to Critical Strike Rating from gear would only be worth 630 Rating.

What the trinket in fact provides is the equivalent of 0.07*25% = 1.7% additional Crit, and at a conversion of 600 Crit Rating to 1% Crit, this is the equivalent of 1050 Crit Rating. The more Crit chance you have, of course, the stronger this bonus is:

The Crit Rating equivalence of the Amplification trinket

Now of course, putting more of your secondary stats into Crit reduces the number of secondary stats you have in Mastery, Haste, or Spirit, so this isn’t completely cheaty. But in general, the Amplification trinket is budgeted a little higher than it seems, and the more Crit you typically run for your spec, the more valuable this Crit bonus inflation will be.

Just as a basic idea, the normal t16 4pc + Warforged offset gear profile I built for my Shaman calculations (see previous post) has around 33k secondary stats, so this trinket is worth at least 2310 secondary stats (but more like 2900 if I factor in the Crit rating equivalence as I did above). Remember, though, that this “extra Crit rating” is just a way of thinking about the trinket’s value. It is not fair to count it against certain on-crit mechanics like Resurgence or Mana Tea, but this does work adequately for other mechanics like Ancestral Awakening and Living Seed if you are trying to model those.

A Disc Priest Interlude

The healing Amplification trinket now procs from Atonement heals as well as direct heals, although as far as I could tell – after minutes of spamming PW:S and Spirit Shell – it doesn’t proc from pure absorb spells. This makes the trinket perhaps a little harder to proc as a Disc Priest than as any other healing class, although so long as you remember to Holy Fire/Solace, Penance, and PoM on CD, you should be able to proc it even in the midst of PW:S spam.

It can be difficult for you to evaluate whether the trinket is performing properly on the Crit bonus front, because of the funky way your Crits work. Let me just throw some numbers at you to reassure you that you are getting the benefit you should expect to see, even if it doesn’t seem that way.

Let’s say you were a Holy Priest, and you cast Renew, and it ticked for 8444 non-crit. With the Amplification trinket, the crit would be 17479, and 17479/8444 = 2.07. As expected.

Now you swap back to Disc spec, and you cast Renew – just because it does the same exact healing every time, so it’s much easier to test with. Let’s surmise that you have zero Mastery whatsoever, just because Mastery screws with the analysis so badly. (I’ll come back and add Mastery in a later step for extra convincing.)

Without the trinket, your Renew healing would look like:

Non-crit: 8444
Crit heal: 8444
Divine Aegis: 8444
Total crit healing: 16888

Now, equipping the trinket:

Non-crit: 8444
Crit heal: 8739 (8739/8444 = 1.035)
Divine Aegis: 8739 (8739/8444 = 1.035)
Total crit healing: 17478

Notice that 17478/8444 = 2.07, just like you got from the Holy thought experiment.

Mastery confounds this a fair bit, but let’s have a look again, taking it into effect and assuming 30% Mastery:

No-trinket numbers…

Non-crit: 8444
Crit heal: 8444
Divine Aegis: 10977
Total crit healing: 19421

Trinket numbers…

Non-crit: 8444
Crit heal: 8739 (8739/8444 = 1.035)
Divine Aegis: 11360 (11360/10977 = 1.035)
Total crit healing: 20099

So you can see you’re still getting the 3.5% benefit on both the Crit heal and the Divine Aegis amount, just as we did before. It’s just harder to compare the Crit healing total to the non-crit amount because Mastery slides in and wrecks all your numbers. But you’re getting the same exact benefit from it all, I promise 🙂

The Amplification trinket is very strong for Disc, partially because the other trinkets with cool effects this tier – Nazgrim’s Burnished Insignia (Multistrike) and Thok’s Acid-Grooved Tooth (Cleave) – do not interact with Divine Aegis at all. Meanwhile, the Amp trinket buffs the size of your DA shields in two ways – via the Critical Strike bonus buff and the Mastery you gain by equipping it.

Two Amps Better Than One?

Caster DPS Amplification Trinket

As of a hotfix to patch 5.4.7 sometime last week, the Amplification trinkets are now stacking multiplicatively rather than additively. This is a buff to wearing two of these trinkets, and makes the second trinket more valuable than the first, which is a mistake in my opinion, but I am not yet Queen of WoW 🙂

To determine what benefit you will get from wearing two Amplification trinkets, first refer to the table above to identify the benefit your particular item-level trinkets will grant separately. Divide that percentage by 100 (to convert to ‘decimal’) and add 1. Then multiply the two percentages together. Since many reforging programs or websites may not be aware of this change yet, you may need to do this math for yourself to work out your optimal reforging.

I’ll do an example for you – I have two 588 iLvl trinkets, so individually each grants 9.7003% bonus. 9.7003/100 + 1 = 1.097003. So to work out how much secondary-stat-boosting benefit I’m getting from my two trinkets equipped together, I simply multiply 1.097003 x 1.097003 to get 1.20342. The two trinkets combined give me a ~20.34% boost to my secondary stats. Previously, the secondary stat boost had been additive, so I would have gotten 9.7003 + 9.7003 = 19.4006% increase from equipping the two trinkets, so this is a 0.94% increase overall in the amount of stats I get from wearing both trinkets.

For me, this works out to 332 extra stats (Spirit, Haste, and Mastery) compared to what I was getting before this change. For players who divest all of their resources into one stat – say, Selfless Healer Paladins with a very heavy Mastery build – the 0.94% boost here may be worth as much as 427 extra stats (using one of my guildmates’ stat breakdowns), 210 of which are in Mastery alone. This is less than the value of one additional Mastery gem or switching two Spirit/Mastery or Int/Mastery gems to full Mastery gems instead.

I’ll also note that right now, the increased Critical Strike bonus function of these trinkets, when worn together, is a bit weird. Previously, it had been additive – a crit while using both trinkets would heal for 2.1703 times a non-crit. If the crit bonus was working the way the stat-boosting function is, then now, under the new multiplicative regime we’d expect to see crits at 2.1775 times a non-crit. Instead, I’m getting crits at 2.1739 times a non-crit, exactly halfway between the two models. Nobody really knows what is up with this – I’m trying to get developer confirmation, but this is probably a very small deal for them.

I’ve tabulated what I expect the results to be for equipping two Amplification trinkets of the same ilvl, below, showing what you used to get from doing this, and what you get now, and an estimate of the Critical Strike bonus function:

The secondary stat boost and estimated critical strike bonus from wearing two identical-iLvl Amplification trinkets.

Currently, Mistweaver Monks are the only healer class that is able to proc the Intellect effect on both the healer and caster Amplification trinket through their usual healing mechanics. The caster Amp trinket (shown, right) will proc for Mistweavers from their melee spells (Jab, Tiger Palm, Blackout Kick), Crackling Jade Lightning, Level 30 Talents, Spinning Crane Kick/Rushing Jade Wind, and Chi Torpedo. Since Mistweavers frequently use at least some subset of these spells during the course of a fight, double Amp trinket is quite strong for them.

All other healers may only proc the Purified Bindings of Immerseus with auto-attacks (and for Druids, special abilities from Cat or Bear form, including Faerie Fire). While you could in theory use these rarely-used abilities to force the trinket to proc when you want it, giving you a large Intellect boost on-demand for your throughput CDs, you’re most definitely sacrificing positional and responsiveness advantages in order to be able to get the proc, and I’m not sure it’s strictly worth it, especially when the trinket could go to a caster DPS instead. For most classes, the second Amplification trinket’s passive effect is probably not going to contribute more to your throughput than a trinket for which both the passive and proc effects are useful.

Double Amplification trinkets probably are the best-in-slot combination for Mistwweavers, though. While both the Cleave and Multistrike trinkets have a nice proc rate for Monks due to the sheer volume of eligible healing events the Monk creates every second, they are lackluster compared to larger Critical heals since Monks typically run very high Crit chance builds. The pair of trinkets can also help ease the burden of reaching the 50% Haste breakpoint – if you so desire, of course, which I am iffy on (see here for why, although I think there are a few extra factors that we could consider to expand the analysis).

Unfortunately, Monks are not able to coin the caster DPS Amplification trinket. It doesn’t show up on the loot table for any of the 3 Monk specs in the Dungeon Journal filter, so you’ll be ineligible for LFR/Flex versions, and will probably have to wait until all your casters have their trinkets before you’ll get a chance to play with the double-Amp setup. 

If you were not already using two Amplification trinkets, the additional benefit you now get from this change to how they stack is probably not worth giving up the trinket you’re already using. Even at the highest iLvl, 0.94% additional secondary stats is unlikely to tip the scales. However, you can use this information to make your own informed decision. 🙂