Drape of Shame (Math incoming)

[badewaxter]

http://www.wowhead.com/item=142170/drape-of-shame

I've seen a few posts of people asking about how to value the static buff provided by Drape of Shame (linked above) and was curious myself. I'd like to submit the following for community approval.

So the math here isn't crazy difficult, but I wanted to make this post b/c I wasn't able to find anything concrete while searching.

I've run a few in game tests and was able to show a few critical things
- The people on forums stating this only increases heals done on the cape wearer are INCORRECT. I spam healed a few people in my class hall and recorded the exact same heals coming off of soothing mist as I saw when channeled on myself.

- The increase to healing is on the full value of a crit heal, changing the crit multiplier from 2 to 2.1.

In order to try to quantify the value of this buff, consider the following situation;

Over a time period "t" you cast "n" heals. Based on your character stats C (Crit% Chance), for large values of t and n, C/100*n heals will be crits and (100-C)/100 * n heals will be normal heals.

that is to say

H = C/100 * n * B * CM + (100-C)/100 * n * B = (C/100 *CM + (100-C)/100) * n * B

Where the symbols are as follows

H = Total Amount Healed

C = Crit % chance

n = number of heals

B = Base heal value

CM = Crit Multiplier

(Obviously this is a simplified example since different heals will have different base heal values. If you wanted to, you could write a system of equations including one equation for each individual heal, but barring differences in individual spell chance to crit, you should arrive at the same conclusions)

From here, a simple ratio can determine the benefit of the proc based on scenarios where CM = CM0 (original Crit Multiplier) and CM = 1.05*CM0 (crit multiplier increases from 2 to 2.1)

Benefit = ((C/100 * 1.05 * CM0 + (100-C)/100) * n * B) / (C/100 * CM0 + (100-C/100) * n * B)

Simplify

Benefit = (C/100 * 1.05 * CM0 + (100-C)/100) / (C/100 * CM0 + (100-C)/100)


CM0 = 2


Benefit = (C/100 * 2.1 + (100-C)/100) / (C/100 * 2 + (100-C)/100)

Simplify

Benefit = (2.1*C - C + 100) / (2 * C - C + 100)

Simplify

Benefit = (1.1*C + 100) / (C + 100)

The above expression varies between 1 and 1.05 when C ranges between 0 and 100. Which is consistent with what you would expect since if all heals are crits then the cloak should give you a flat 10% bonus to the crit (or 5% increase to overall healing)

inverting the formula provides the following cutoffs for the benefits provided:

1% increased healing at 11.11% crit

2% increased healing at 25.00% crit

3% increased healing at 42.86% crit

4% increased healing at 66.66% crit

5% increased healing at 100.00% crit

I hope this has been helpful, feel free to comment and correct/critique.

If unclear, the point of this post is that although the Ilvl of DoS is only 855 base, the 2% flat increase to healing is not insignificant and is worth quite a bit of stats on its own. Take this into account with stat weights when determining whether a higher Ilvl cloak is a better piece.

Thanks

[Deleted]

Nice to see some math on it But Cloak also increases the stat values from other items with crit rating. So would be kinda nice to get some understanding on how the bonus it self adds to the state value. Forexample the stat values geting from Geodudes sheet.

[badewaxter]

Nice to see some math on it But Cloak also increases the stat values from other items with crit rating. So would be kinda nice to get some understanding on how the bonus it self adds to the state value. Forexample the stat values geting from Geodudes sheet.

I'm not as familiar with all the intricacies of Geodew's sheet, and I believe that math would be quite a bit more involved than I'm ready to look into. Perhaps he'd be willing to chime in? TAKE THE FOLLOWING WITH A GRAIN OF SALT.

My initial gut reaction is that the effect on the overall stat weights would be somewhat negligible. Taking the derivative of the "Benefit" function with respect to overall crit rating provides the following expression

d(benefit)/d(C) = 10/(C+100)^2

So for an example, I'm currently crit heavy (happenstance, lots of verse gear has crit on it) and I have 31% crit. In my case, d(benefit)/d(C) = 10/(31+100)^2 = 0.000582. The interpretation of this data is that a good estimate for the observed benefit of the drape proc will increase by 0.000582 for every 1% increase to my overall crit. that's 0.05% which isn't nothing, but i would imagine isnt significant enough to shift the balance of the overall stat weights. note that since the derivative is decreasing as C increases, the .05% estimate is also an overestimation.

[badewaxter]

Updating this thread since I just saw the DoS nerf:

Math below

From here, a simple ratio can determine the benefit of the proc based on scenarios where CM = CM0 (original Crit Multiplier) and CM = 1.025*CM0 (crit multiplier increases from 2 to 2.05)

Benefit = ((C/100 * 1.025 * CM0 + (100-C)/100) * n * B) / (C/100 * CM0 + (100-C/100) * n * B)

Simplify

Benefit = (C/100 * 1.025 * CM0 + (100-C)/100) / (C/100 * CM0 + (100-C)/100)


CM0 = 2


Benefit = (C/100 * 2.05 + (100-C)/100) / (C/100 * 2 + (100-C)/100)

Simplify

Benefit = (2.05*C - C + 100) / (2 * C - C + 100)

Simplify

Benefit = (1.05*C + 100) / (C + 100)

The above expression varies between 1 and 1.025 when C ranges between 0 and 100. Which is consistent with what you would expect since if all heals are crits then the cloak should give you a flat 5% bonus to the crit (or 2.5% increase to overall healing)

inverting the formula provides the following cutoffs for the benefits provided:

0.5% increased healing at 11.11% crit

1% increased healing at 25.00% crit

1.5% increased healing at 42.86% crit

2% increased healing at 66.66% crit

2.5% increased healing at 100.00% crit

I hope this has been helpful, feel free to comment and correct/critique.

In my particular case, at around 20% crit, this translates to ~.83% increased healing which is worth ~350 intellect.

[Deleted]

Math is already done on it, and already in a nice spreadsheet

https://docs.google.com/spreadsheets...XY4jaE/sharing

[Name]

Let's imagine comparing this cloak to cloak 'X' that has desirable stats. Can someone approximate - how much higher ilvl cloak 'X' gotta be to become better than the subject?

[Name]

That's pretty damn precise, thank you!

Of course, there is also a factor of actual stats, which the drape's are tailored for raiding, rather than m+, so one has to consider that when comparing it to other m+ choices.