Blessing of Salvation, the paladin's current form of reducing threat provides a flat, 30% threat reduction on all generated threat (without affecting the threat accumulated before that). It is being removed in the WotLK and being replaced with a spell called Hand of Salvation (HoS).

**** As a disclaimer, this is still Beta, so Hand of Salvation is subject to change.

The current implementation of Hand of Salvation:

Hand of Salvation

6% of base mana

30 yd range

Instant cast

2 min cooldown

Places a Hand on the party or raid member, reducing their total threat by 2% every 1 sec. for 10 sec. Players may only have one Hand on them per Paladin at any one time.

Now at first glance, one might think "oh 2% every second for 10 seconds, so that is 20% threat reduction". Well that isn't the case. It's incremental so the effects of the last threat reduction affect the effects of the next one. Further more, once the buff runs out it no longer affects threat generated after it. So the idea behind this Hand spell is a bit different than the old Blessing of Salvation that we are all familiar with.

Now Blessing of Salvation reduces threat by 30%, which can be modeled by the equation:

Code:

Threat_With_BoSalv = (1-percent_reduction)*Threat_Without_BoSalv

Rearranging that gives:

Code:

Threat_With_BoSalv
percent_reduction = 1 - ---------------------
Threat_Without_BoSalv

Now one my think it silly to even model BoSalv since we already know that it is a 30% reduction, but I wanted to set up the stage to show how we are going to tackle HoS. HoS will be a different beast because it reduces threat in a recursive manner. Not to mention, it affects all the previous threat you have already generated before the buff was placed (unlike BoSalv).

Still, I am going to try to emulate the same model to get an equivalent percent_reduction value for HoS. Using this value, you can look at your threat and get a good general idea of how it will look after HoS is done. The new equation will look like:

Code:

Threat_With_HoSalv
percent_reduction = 1 - ---------------------
Threat_Without_HoSalv

Now we just need to calculate the quantities Threat_With_HoSalv and Threat_Without_HoSalv.

Let's look at Threat_With_HoSalv first since it is the harder part.

Say you have some amount of threat you have generated. We will call it AT for Accumulated Threat. We will assume at least some type of semi stable tps over the 10 second period of Hand of Salvation. Hand of Salvation will work like this:

+1 seconds: Threat = (AT + TPS)*0.98

+2 seconds: Threat = ((AT + TPS)*0.98 + TPS)*0.98

+3 seconds: Threat = (((AT + TPS)*0.98 + TPS)*0.98 + TPS)*0.98

and so on down to +10 seconds.

If you run the numbers you will find that it isn't going to come out to 0.8*(AT+10TPS), which is what you would expect from a flat 20% reduction after 10 seconds.

Actually what you end up getting is more like:

(0.98^10)*AT + TPS*[0.98 + 0.98^2 + 0.98^3 + ... + 0.98^10]

One thing to note from this equation is that if AT is sufficiently big enough (I.E. A huge threat lead or perhaps a really really long time), then it will swamp out the second part, leaving only (0.98^10)*AT = 0.817073*AT, or an 18.2927% reduction in threat (well while this number is true, using this equation to get it as is is a bit wrong, but I will go into that later). This is also true if the person affected by Hand of Salvation stops generating threat while it is active (so TPS=0).

************************************************** *******

ASIDE: [0.98 + 0.98^2 + 0.98^3 + ... + 0.98^10] is a geometric series, which reduces down to the equation:

Code:

(0.98 - 0.98^11)
----------------
(1 - 0.98)

I won't go into how this is calculated unless someone really really wants to know.

************************************************** *******

So the equation we have thus far is:

Code:

(0.98 - 0.98^11)
Threat = (0.98^10)*AT + TPS * ----------------
(1 - 0.98)

Now that we have Threat_With_HoSalv ready to go, let's look at Threat_Without_HoSalv:

Threat_With_HoSalv = AT + TPS*10

Pretty simple. That is the threat you will generate if HoSalv wasn't there.

To get the actual threat reduction, we need to simply divide the two:

Code:

AT*(0.98^10)+TPS*(0.98 - 0.98^11)/(1 - 0.98)
--------------------------------------------
AT + 10*TPS

This leaves a function of two variables, AT and TPS. If we assume (for a moment) that TPS was constant the whole time, then we can say that AT = TPS*time and the equation simplifies down to one variable, time:

Code:

time*(0.98^10)+(0.98 - 0.98^11)/(1 - 0.98)
--------------------------------------------
time + 10

The characteristic for this is

There is something else to consider: We really don't care about the spikes/degradations of TPS during AT as it happens before we use Hand of Salvation (HoS from now on). During HoS, however, it is important to watch the TPS. The TPS generated might not be the same as the average TPS used to generate AT. That might be due to fight mechanics, threat dumps, etc., but for whatever reason it is possible that the DPS'er won't be doing the same TPS when HoS is up versus their average TPS up until AT was accumulated.

In order to combat this, I simply multiplied the 10 second HoS portion of both the numerator and denominator by a value m, which is simply a relative multiplier (I.E. is the TPS during HoS twice the TPS before, m=2, or is it the same as before, m=1, etc.).

The equation will now look like this:

Code:

time*(0.98^10) + m*(0.98 - 0.98^11)/(1 - 0.98)
-----------------------------------------------
time + 10*m

So now it is back to being a two variable equation, using time to represent the various combinations of accumulated threat and m to identify how the TPS during HoS looks like compared to when the initial threat was accumulated (is it more, less, or the same).

There are two ways to view this data in a 2D graph. You can hold either m or time constant and plot against the other variable. Here is how it looks in both formats:

Here you can see some trends:

1. Increasing relative TPS during the duration of HoS gives a lower threat reduction in terms of percentage. This doesn't mean your total threat is lower, just that the comparison of your threat with HoS to threat without HoS is lower as m gets larger.

2. Increasing time gives a higher threat reduction in terms of percentage. The longer you wait to use HoS, the better the threat reduction percentage is.

3. The characteristics all converge to a TPS value of 18.2927% as time increases towards infinity. Consequently, if m=0 (dps is stopped during HoS), then the characteristic is a constant value of 18.2927% as well.

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