Duct Tape and a Prayer

The following is the current (datamined) Healing Priest Tier 10 4-piece set bonus:

• Your Flash Heal spell has a 15% chance to reset the cooldown on your Circle of Healing and Penance Spells.

With my current haste rating, Penance has a 1.64-second channel, leaving me 6.36 seconds to cast Flash Heals before Penance’s cooldown is up. (I’m glyphed and have Aspiration.) Since my Flash Heal’s cast time is 1.31 seconds, I can cast it 4 times before Penance cools down, with 1.12s left over.

The math for determining how likely a percentage-based proc will go off is 1-[(1-proc chance)^(number of opportunities)]. (It seems unnecessarily complicated, but that’s how probability works.) In this case our proc chance is 0.15 (15%), and our number of opportunities is 4.

If I’m just spamming Flash Heal until Penance cools down – which I rarely am, but let’s assume it for the sake of a best possible scenario – then my chance to reduce Penance’s cooldown by at least 1 second is 1-[(1-0.15)^4], or 47.8%. Given that, roughly every other Penance cooldown will be shortened by at least 1 second.

(Without going into the math, the increased number of casts from dropping Glyph of Penance and Aspiration don’t justify the extension of the cooldown.)

For the record, if you’re just spamming Flash Heal after you use Penance (which I hope you’re not) and assuming 0 Haste (I hope you have some), you have 15% chance to reduce Penance’s cooldown by 4.5 seconds, 27.8% to reduce the cooldown by at least 3 seconds, and 38.5% to reduce the cooldown by at least 1.5 seconds. (Remember, the proc doesn’t go off until the Flash Heal spellcast does, so you have to let Penance cool down by at least 3.5 seconds – 2 seconds channeling Penance and then 1.5 seconds casting Flash Heal – before you can trigger the bonus at all.)

Incidentally, due to the nature of the problem, there is no point at which you’re guaranteed a proc. You get to 99.9% chance of having triggered the bonus at some point at about 27 Flash Heal casts, but it’s possible to beat probability and go forever without having triggered the bonus proc. That said, with no Haste, on average you’ll reduce the cooldown of your Penances by about 0.6 seconds. (If you have Haste, the average reduction is [0.6 * (1 + Haste %)].)

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