Buffed Proc Chance & Lightning-Imbued Chalice

Yesterday I mentioned that the trinkets got a buff to proc chance.  Here is the official statement detailing the changes and the following is a quote showing the exact difference.

“Calculate the proc frequency as normal. Based on that, you can figure out the expected average proc interval. We also now keep track of time since the last successful proc (this is different from the time since last chance to proc), capped at 1000 sec. Multiply the proc chance by MAX(1, 1+((TimeSinceLastSuccessfulProc/AverageProcInterval)-1.5)*3). For example, if a proc has an average proc interval of 45 sec, and it’s been 72 sec since your last successful proc, you’ll get a 1.3x multiplier to your proc chance. If you’ve been out of combat for a few min, and it’s been 5 min since your last successful proc, you’ll get a whopping 16.5x multiplier to your proc chance.”

The proc chance is calculated in the same way:

Proc chance = PPM x ( 1+ H) x T/60PPM = constant, specific to trinket
H = haste (decimal)
T = time since last attack which has a chance to proc the attack

This value is not multiplied by a factor:

F = MAX(1, 1+((TL/API)-1.5)*3)
TL = time since last proc
API = average proc interval, previously calculated by this formula 60s / (PPM * (1 + H))

Lets put this in context of the trinket.  Lightning-Imbued Chalice is one of the new healing trinkets which drop in the newest Mists of Pandaria (MOP) raid Throne of Thunder.  The trinket has the following stats in the order of LFR/Normal/Normal Thunderforged/Heroic/Heroic Thunderforged*:

*All thunderforged items have simulated stats.  Values are not officially available on Wowhead.

The healing buff it gives is called “Restoration of the Infinite”. This trinket has been called “Holy Trinket of Overhealing” but I personally am extremely excited about it.  Firstly because of the high proc chance and secondly because it actually scaled with our spell power.  Finding data for this trinket was really hard since the trinket drops off Lei Shen only ~ 600 guilds have killed him and then I had to find all of the paladins.  I had to resort to accepting any fights and only ended up finding one paladin who was using it (and who appeared to stop using at the end of his attempts). He had ~ 27000 SP, ~12.29% crit, 2209 haste (21%)  and the normal version of it. Lets assume that Blizzard has already buffed the trinket procs. Here are some general observations:

  • Fight effects which increase healing such as Elegon will increase the healing from the trinket
  • Does not proc illuminated healing
  • Can crit, seems to be about same as your base crit level
Fight Fight Length Amount Healed Overhealing Procs Hit Crit Direct Heals Ticks Overall Ticks
Stone Guards 173 92974 0 1 1 0 521 181 702
Feng the Accursed 219 331331 23.8 2 1 1 1058 383 1441
Gara’jal the Spiritbinder 176 97687 100 1 1 0 608 295 903
Spirit Kings 366 604703 22 5 4 1 1654 571 2225
Elegon 277 293124 21.5 2 2 0 458 146 604
Will of the Emperor 684 803394 54.5 8 8 0 1251 501 1752
Feng the Accursed 219 331331 23.8 2 1 1 1058 383 1441
Gara’jal the Spiritbinder 156 196298 49.8 2 2 0 677 250 927
Spirit Kings 366 604703 22 5 4 1 1654 571 2225
Elegon 277 293124 21.5 2 2 0 459 146 605
Will of the Emperor 288 192157 100 2 2 0 298 141 439
Imperial Vizier Zor’lock 284 290073 32.3 3 3 0 853 307 1160
Blade Lord Ta’yak 317 191716 0 2 2 0 914 412 1326
Garalon 320 291252 25.3 3 3 0 994 230 1224
Wind Lord Mel’jarak 219 100261 0 1 1 0 526 80 606
Amber Shaper Un’sok 359 494137 34.8 4 3 1 1131 109 1240
Grand Empress Shek’zeer 346 286031 2.3 3 3 0 1037 105 1142
Jin’rokh the Breaker 285 194395 0 2 2 0 3770 1474 5244
Horridon 326 559480 7.1 4 3 1 747 243 990
Horridon 346 294044 32.1 3 3 0 927 299 1226
Horridon 335 299770 17.1 3 3 0 883 311 1194
Horridon 330 285698 22.4 3 3 0 770 262 1032

Here are some plots for reference.

lic_1

lic_2

The number of procs seems to scale approximately linearly with fight length.  The average time between procs is ~105 seconds.  This is disheartening.  Isn’t the RPPM supposed to be 3?  I would think this trinket should proc at least as often as the previous trinkets we looked at but it seems to be around the same number of procs when it should at least be quantifiably more. The amount of healing I observed never went above 3% for any fight.  The trinket does not appear to scale with ticks which is expected since the it is built into the equation.  The following is the proc chance (not calculating time since last proc) based on a PPM equal to 3.  The color is closer to purpoe when the proc chance is higher.

lic_3

The average time to proc according to the formula for this trinket is ~16 seconds wit 3506 haste (capped for EF).  This is a huge discrepancy with the actual average we see. Is this trinket worth switching out something like an upgraded 2x Relic which will give you back approximately 45K mana back on a 5 minute fight?  From these results absolutely not.  Why would I want to get a trinket that would randomly heal very little when I can get more mana to heal who I know is hurt? For this trinket to be useful, the proc chance needs to be fixed a lot.  It needs to heal more than the mana return of a 5.1 trinket would for people to even consider using it due to its random nature.  All of this has made me a sad panda.

Lets talk quickly about what the factor Blizzard added to increase the proc chance of these trinkets is doing.  What does this exactly mean for the trinkets?  Please see the plot below:

lic_4

This shows the factor multiplied based on the two variables in the above equation.  The scale goes from 10 to 50 with the majority of samples below 10.  What does this mean exactly?  Any trinket with an average proc interval above ~5 seconds will have nearly the same factor multipled to the proc chance.  This is (according to Blizzard’s formula) all of the new healing trinkets.  This really stumps me because why introduce such a factor unless it’s going to actually do something different to the trinkets?  If you’re doing this, why not just multiply the chance by a constant rather than an equation which affects none of the trinkets?  Unless I’ve calculated something wrong I fail to see the purpose of this factor.  As can be evidenced by the newest analysis considering the change has already been implemented, this has had very little impact if any.

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