• Sservis

When is the optimal time for Rogues to Vanish, Mages to go Invisible, and Warlocks to Soulshatter? (ignoring Hunters as the cooldown is so short as to make the answer for them mostly moot)

The answer depends on any given fight mechanics, and how different classes threat over time occurs, but there is a specific answer for the abstracted case. If you don't like theorycrafting, look for the bold result in the Definitions and Solution section and move on.

Assumptions, Definitions, and Solution
There are two assumptions inherent in model.

Both threat(time) functions, tank and dps, are assumed to be strictly linear. In the expected case of average performance this should generally be the case with a notable exception. The biggest invalidation of this assumption is when the functions are not linear (piecewise linear due to phases or aggro resets, etc) Dps burst abilities have less of an impact as during any threat capped portion of the fight (when this argument matters), they have no value at all, threat would have been capped without them, added value = 0, hence ignoring their burst impact doesn't seem to be that bad of an assumption. (bursting and reaching a threat cap 60 seconds before the threat reducer is off cooldown is no better than reaching the cap 10 seconds before)

Also, the fight is assumed to be long enough to matter. If the fight is shorter than the "time when threat is unlimited" below, a different timing will be optimal. However, for situations where the dps barely exceeds the tank in tps, this time is 6-7 minutes or so (most fights of consequence).


w = tank tps, specifically the hard cap (if over tank but under the switch threshold is acceptable, use the switch threshold tps, but if under tank is required (Prince, etc), use the tank's actual tps.

r = dps tps (or any non tanking threat producing class)

c = cooldown of the threat reducing ability

time of first threat reduction, t = c * (r mod w) / w

time when threat is unlimited, u = r * c / w If the fight is shorter than this, the optimal timing of the abilities is different (or coincidental)


For abilities that don't reduce threat to 0 when used, but only reduce a portion of the threat use w' and r' as defined below instead of w and r. Essentially the fight can be modeled as a 100% threat reducer where both the warrior and rogue have (1 - p) * w tps subtracted out of their tps rates.

p = % that the ability reduces threat by (Vanish = 100%, Soul Shatter = 50%, etc)

w' = w - (1 - p) * w = p * w

r' = r - (1 - p) w


Examples (all threat rates made up)

A warrior produces 800 threat per second (tps), and a rogue produces 900 tps (after everything is considered). Furthermore, the rogue has to stay strictly under the tank (if not, 880 would be used as the tanks effective tps or 818 would be used for the rogue's threat to adjust for the 10% buffer).

w = 800 tps
r = 900 tps
c = 300 s

t = 37.5 s into fight
u = 337.5 s

Same as before except this time it's a warlock with 1100 tps and a 50% reducer.

w = 800 tps
r = 1100 tps
p = 50%

w' = 400 tps
r' = 700 tps
c = 300 s

t = 225 s into fight
u = 525 s


Proof
I'm going to find the change of total time spent threat capped as time of first vanish, t, changes. I'll show that the solution given above is at least as optimal as any other t (or it's 0 for all t in the case where r mod w = 0).

t0 = time of optimal first reduction as defined above, this is always < c as otherwise an earlier vanish could be done without disrupting later reductions and giving a short uncapped window earlier in the fight, producing more threat (and more dps) by the dpser.

g = the number of times the dps threat(time) function is capped by tankthreat(time) after a threat reduction. Every reduction at time t <= r * c / w comes from a capped situation, as more threat was done in the prior cooldown than the tank has done to date (w * t <= r * c).

Each second earlier that a reducer is used reduces the amount below the cap by w each time a threat reducer is used (reduce at time y means the amount below the cap is w * y, time y - 1 means the amount below the cap is w * (y - 1), difference w). There also is one additional second of uncapped time after the last reduction that comes from a capped threat as that specific reduction comes a second earlier. The gain of this extra time is (t0 - t) * (r - w).

The change in the total threat below the cap gained by the reducers is (t - t0) * g * w + (t0 - t) * (r - w).

If t < t0

g = Int(r/w)

In this case the gain is (t - t0) * Int(r/w) * w + (t0 - t) * (r - w), which by setting >= 0 we can solve for values of t that are better than t0

(t - t0) * Int (r/w) * w + (t0 - t) * (r - w) >= 0

reduces as

(t - t0) * Int (r/w) * w >= (t - t0) * (r - w)

Int (r/w) * w <= r - w (>= switches to <= as t < t0, and (t - t0) <0)

Int (r/w) * w <= Int(r/w)*w + r mod w - w

w <= r mod w

which never occurs.

If t > t0

g = Int(r/w) - 1

In this case the gain is (t - t0) * (Int(r/w) - 1 )* w + (t0 - t) * (r - w), which by setting >= 0 we can solve for values of t that are better than t0.

(t - t0) * (Int(r/w) - 1) * w + (t0 - t) * (r - w) >= 0
(t - t0) * (Int(r/w) - 1) * w >= (t - t0) * (r - w)
Int (r/w) * w - w >= r - w (this time t - t0 > 0)
Int (r/w) * w >= Int(r/w)*w + r mod w
0 >= r mod w

There are other equally good solutions when r mod w = 0.

In this case all solutions are equally good as (t - t0) * (Int(r/w) - 1) * w + (t0 - t) * (r - w) can be rewritten as (t - t0) * (r - w) - (t - t0) * (r - w) = 0 as Int(r/w)*w = r.


Other comments
The maximum benefit a perfectly timed threat reduction versus the worst possible timing is b = c * (r mod w) * (w - r mod w) / w (using w' and r' if p != 100%). The worst time for a threat reduction effect is never, and the worst time to use it for the first time is t = 0 (or t = c). Between the optimal time and 0 (and 300) the cost curve is linear. By calculating b, the cost of an ill timed reduction can be found.

In the rogue example above the cost of the worst possible timing is 26,250 threat. If the rogue vanishes at 75s instead of 37.5s, the cost of the poor timing is 3,750 threat (26,250 * (75 - 37.5) / (300-37.5) as that delay is 37.5/262.5 of the way to the worst possible timing). Over the course of a 10 minute fight, that's 6.25 tps under optimal. The dps loss is depends on the specific threat reducers in play. (With only salvation and having to stay strictly under the tank, it's about 12.6 dps lost). Vanishing too early has a much steeper cost. Vanishing at 30s would cost 26,250 * (37.5 - 30) / 37.5 = 5,250 threat or 8.75 tps over the fight.

Overall, the first threat reduction should be done at such a time that the last important threat reduction will occur just as the threat reducer is coming off cooldown. (later ones the reducer is already off cooldown before the tank is caught).

(Pure speculation, this case could be nonexistent) It might make sense for shamans to drop Tranquil Air totems until the last meaningful reducer is used (this in the common case of dps tps slightly over tank tps is the first reducer), switching to dps totems afterwards as the extra reduction would effectively raise the threat ceiling until the reducers are used. If hard capped pre-reduction, dps totems may not help a portion of the party at all, while Tranquil Air might allow more damage in the same threat budget.

 

◊ Kolmar

Very much true on fights with tank transitions like Void Reaver or Bloodboil. Our enhancement shaman maintains Tranquil Air during all non-Fel Rage portions of the Bloodboil fight, switching to Windfury for when we have the Insignificance debuff. (Incidentally, saving group buff cooldowns for Rogue Fel Rages can be a great WTF inducer.) I can start a slam rotation and be next under our tanks in the first phase of the fight *without* Windfury, so it's a 25% DPS gain effectively. (Tranquil Air is -20% threat, so 80 threat per second per 100 damage per second; invert to find damage per threat of 100/80 = 1.25)

 

Koosai

While I appreciate your hard work, I don't see how it is hugely useful. Even with the same group/raid setup tps will vary from attempt to attempt. Atleast at my stage of progression, Working on Kael, there simply are not that many encounters with no threat wipes and sustained melee damage time. I can think of VR, Morogrim, Solarian and Gruuls. Though for Solarian we have a taunt rotation going so threat is meaningless and on Morogrim if I get too high on threat I can go dps the next wave of murlocs. Even for fights like VR and Gruul your optimal time to vanish will only be a guideline telling me not to vanish sooner. This is potentially useful, but typically I'm much too busy making sure I'm out of caveins and the like to watch the time since we started the boss.

On tranquil air, I know that since I raid with a ret pally in the melee group WF *will* be dropped since 2H dps is rather lacking without it. I don't ever see my enhance shammie running out of mana so if they feel inclinded they can just twist the totems and give you both.

Last note, I found your math annoying to follow as your variables seemed random to me. Personally I would have had tank tps be something like Ttps and Dps tps be Dtps, that way when I'm reading the math I don't have to scroll up and see what r is.

 

Gimpy

Slightly off topic but this seemed like a good place to ask. I am trying to find out about if healing threat is different if self healing or if healing others. I understand that healing others generates .5 threat per point of healing done. Now there appears to be some confusion if self healing is still .5 or 1 or 2 pts of threat per point of self healing done. Any answers or links to other threads on this discussion would be greatly appreciated.

 

Malan

You don't see the connection there? Obviously the TPS is going to by dynamic but come on man, you can surely see how to apply this? If you estimate your tank as doing 900 TPS and you throw an estimate for yourself on there, you can find a good idea of 'burn vanish at X point' and then kind of adjust from there based on actual conditions.

Shitting up every single thread on EJ since '06

 

Koosai

Yes I understand when you would use it, but mostly what I meant by it not being particularly useful is the fact that for most fights it simply does not apply. Honestly the other reason that I don't find it very useful is that I don't have a good idea of how much tps my tanks will put out as that vaires from boss to boss based upon armor, and other circumstances. I will try to make a not of checking their average tps after kills during tonight's raid.

 

Prinsesa

Joe McHealer is at 800/1000 HP.
John McWarrior is at 500/1000 HP.
They are currently engaging one mob.

Joe heals John for 5000 HP. Joe creates 250 threat on the one mob engaged. 250 because he only did an effective 500 healing, the other 4500 was overhealing and thus does not count towards threat.

Joe heals himself for 5000 HP. Joe creates another 100 threat (200 effective healing * 0.5 threat per healing) on the one mob being engaged.

If Joe and John were engaging two mobs, the latter scenario of Joe healing himself for 5000 would create 50 threat per mob, since healing threat is divided by all mobs aware of the healer.

Basically, healing threat is always generated on the healer's part regardless of who he is healing. The three exceptions to this are Earthshield, Prayer of Mending and Lifebloom.

If Joe places an Earthshield/Prayer of Mending on John and it triggers for 200 HP. John creates 100 threat towards the mob. The healing threat of ES/PROM counts towards the person it healed, not the Shaman/Priest that cast it.

If Joe places a Lifebloom on John and it ticks for 10 HP for 7 seconds, then blooms for 100 HP, Joe will create 35 threat on the mob and John will create 50 threat on the mob. The threat of the normal HOT ticks of Lifebloom count towards the Druid that cast it, while the threat of the final Bloom effect of a dispelled/expired Lifebloom counts toward the person it healed.

"We do want Sanctuary to be the tanking seal"

- Ghostcrawler

 

Koosai

Hmm, I was pretty sure that self healing was 100% damaged healed as threat. So in your example Joe healing himself would generate 200 threat. Though I recall reading this in Working Theories of 2.3 but my quick glance in there had nothing about healing threat. I'm also pretty sure that I recall pallies having 50% threat reduction to all heals and that stacked with the 50% for healing other, this was supposed to stop them from heal tanking... I don't think I'm misremembering all this, but I can't find it anywhere currently.

 

Apate

Did you test this, or perhaps investigate it? LB does not appear to operate like Earth Shield and PoM. http://elitistjerks.com/f40/t12192-d...fferent_heals/ and http://elitistjerks.com/297244-post129.html

It's pretty common misinformation (unless you come back with some conclusive testing, which would be awesome), so please do your part not to spread it.

Also, I've never heard of self-healing generating extra threat, and that ought to be pretty easy to test.

See you, auntie.

 

Prinsesa

This is correct. Assuming no Salvation and no Righteous Fury, a Paladin generates 0.25 threat per point of effective healing.

The other three healers generate 0.5 threat per point of effective healing when untalented.

Priests have a talent that reduces the threat generated by their healing spells by 20%. This causes them to generate 0.4 threat per point of effective healing.

If a Paladin casts Improved Righteous Fury on himself, a Paladin generates 0.45 threat per point of effective healing.

Shaman have a talent that reduces the threat generated by their healing spells by 15%. This causes them to generate 0.425 threat per point of effective healing.

Druids have a talent that reduces the threat generated by their healing spells by 30%. This causes them to generate 0.35 threat per point of effective healing.

"We do want Sanctuary to be the tanking seal"

- Ghostcrawler

 

Borodin

Self-healing and healing others generate the same threat and that is 0.5 threat per actual health restored. That threat is then divided among the mobs who are aware of the heal.

The Paladin threat reduction was created in the very early days of WoW because it had otherwise been discovered that Paladins could AoE tank pretty much just by self-healing.