General Shield of the Righteous effective CD

[Shinela]

WARNING: ONLY LEVEL 42 - 99
(I'll just assume there's an artefact buff that works with the CD of either Judgment or Shield of the Righteous)

After hours of work (Literally. It wasn't easy. I swear to god. I had the formula after 7 hours and couldn't figure out why it was right. I took around 2 more hours just working out these formula's and reworking and checking and.. You get the picture. Speaking of pictures: Back and front)

Download

The link is safe, no problems when used or opened.

So what does this do?
The effective cooldown is the average cooldown on your Shield of the Righteous when you take in effect all the other numbers that lower the CD of SotR directly.

I have written these calculations down in Excel! All you have to do is add the numbers.
Add everything in full. 20.78% haste means you write down 20.78


NUMBERS
For the effective CD without the talent, it was relatively simple.

- Shield of the Righteous has a CD of 16 base. Add haste.
- Judgment has a CD base of 6. Add haste.
- Then every Judgment you use, the CD of SotR lowers by 2, 4 on crit.
​

You now have the value without using the talent Crusader's Judgment.

- The talent makes it so every Grand Crusader proc, you also proc Judgment.
- Hammer of the Righteous has a 15% chance to proc Grand Crusader. Base CD of 4.5. Add haste. Refresh Judgment, lower CD of SotR by 2, 4 on crit.
- Every time you avoid you have a 15% chance to proc Grand Crusader. Refresh Judgment, lower CD of SotR by 2, 4 on crit.

​

X = Haste
Y = Crit
T = CD SotR (16 / (1 + X / 100)
J = CD Judgment (6 / (1 + X / 100))
H = CD Hammer of the Righteous (4.5 / (1 + X / 100))
A = Avoidance ((Parry + haste) / 100)
J1 = Time Judgment removes from CD SotR (2 * (1 + Y / 100))
AS = Enemy's Attack Speed
T1 = Effective CD long term speaking (It's a limit, I just limit to infinity to avoid using odds which can't be calculated here)

No Talent
T1 = T - T / (J + J1) * J1

With Talent
T1 = [T - T / (J + J1) * J1] - (J1 / (H / 0.15)) - {T / [(AS / A / 0.15) * J1] * J1}

(0.15 comes from the 15% chance to proc Grand Crusader)

 

[Dreams]

Can't you just put the calculations in the thread, or maybe a pastebin if they're too long? Or at least post the conclusions in the thread?

I imagine the most relevant haste breakpoint is having a shield for every stomp on brutallus.

 

[Shinela]

Can't you just put the calculations in the thread, or maybe a pastebin if they're too long? Or at least post the conclusions in the thread?

I imagine the most relevant haste breakpoint is having a shield for every stomp on brutallus.

Not really a conclusion to bring. This is just here so you can enter your values and play around with them to see what the CD of SotR will be.

Though if you want the calculations written out (even though you can see them in Excel) I now wrote them down simplified in the main post

 

[Dreams]

Not really a conclusion to bring.

By conclusion I mean practical applications. For example specific crit/haste numbers for specific boss fights. I mean I get that people could just plug different values into the formula until they reached the desired cooldown, but let's be honest; the only people who are going to use this guide are people playing level 70 prot paladins in pve (there doesn't seem to be any other pve communities on this forum).
So perhaps a more focused guide would be helpful? just ideas

 

[Shinela]

By conclusion I mean practical applications. For example specific crit/haste numbers for specific boss fights. I mean I get that people could just plug different values into the formula until they reached the desired cooldown, but let's be honest; the only people who are going to use this guide are people playing level 70 prot paladins in pve (there doesn't seem to be any other pve communities on this forum).
So perhaps a more focused guide would be helpful? just ideas

Could probably get that going. I'll contact Fx and together we'll settle on the numbers which fit the best (to our perspective) for which encounters. I'll also add as to why we think those numbers would the best.

 

[Dreams]

Could probably get that going. I'll contact Fx and together we'll settle on the numbers which fit the best (to our perspective) for which encounters. I'll also add as to why we think those numbers would the best.

Nice.
I'm also curious if your formula is consistent with simcraft. Like, if you plug your stats into your formula and then also sim your character, do they get the same uptime on the buff? Or have you verified the formula ingame in some other way? You know in wow the theoretical often differs from the practical for no real reason

 

[Shinela]

Nice.
I'm also curious if your formula is consistent with simcraft. Like, if you plug your stats into your formula and then also sim your character, do they get the same uptime on the buff? Or have you verified the formula ingame in some other way? You know in wow the theoretical often differs from the practical for no real reason

I did compare them with simcraft. To save myself some time I did only use 10k itterations but the numbers were comparable. Simcraft was usually 0.2 behind or ahead in effective CD, which is probability just doing its job together with the chance that procs can overlap (though the chances of that happening aren't very big at all)

 

[Dreams]

I did compare them with simcraft. To save myself some time I did only use 10k itterations but the numbers were comparable. Simcraft was usually 0.2 behind or ahead in effective CD, which is probability just doing its job together with the chance that procs can overlap (though the chances of that happening aren't very big at all)

I'm actually kind of surprised simcraft got it right lol, but that's good

 

[Zoke]

soooo what youre saying is: i can just use simcraft and not actually do math for my self ?

 

[Blackberryy]

The link is safe, no problems when used or opened.

 

[Shinela]

soooo what youre saying is: i can just use simcraft and not actually do math for my self ?

That's where the download is for. Unless you want to wait 5 minutes every test.