How expertise and hit influence Improved Mangle

A recent post made by Monedula at Omen of Clarity shows that when you have the Idol of the Corrupter Improved Mangle can be worth it again, his reasoning and math can be found here.

The ammount of misses and parries you get obviously has some influence on this all but how big this influence is was left unclear, therefore i decided to look into that using part of his math.

Below math is a shameless copy of the format Monedula used in said article, just with different numbers and a different approach to calculate the downtime because i used downtime percentage and not duration to compare in the end.

NOTE: I use the word hit here to mean not getting parried and not missing (hard cap expertise and hit).

Scenario 1 - 100% Hit, 68% Proc Chance and 6 Sec Mangle CD

Chance that the idol buff is not refreshed on a mangle:

1 time = 32%
2 times = 10,4%
3 times = 1,0%
4 times = 0,01%

The duration of the buff is 12 seconds so to have 6 second downtime of the buff you need to miss twice in a row (= 10,4%), continuing this path you get the following numbers:

18 seconds = 0,01% of the time
12 seconds = 1,0% of the time
6 seconds = 10,4% of the time

This means the chance to not lose the buff is 100 - (10,4 + 1 + 0,01) = 88,59% which relates to 11,41% downtime

Scenario 2 - 100% Hit, 68% Proc Chance and 4,5 Sec Mangle CD

Chance that the idol buff is not refreshed on a mangle:
1 time = 32%
2 times = 10,4%
3 times = 1,0%
4 times = 0,01%

The duration of the buff is 12 seconds so to have 1,5 second downtime of the buff you need to miss thrice in a row (= 1%), continuing this path you get the following numbers:

6 seconds = 0,01% of the time
1.5 seconds = 1% of the time

This means that the chance to not lose the buff is 100 - (1 + 0,01) = 98,99% which relates to 1,01% downtime

Comparison

The difference then is 11,41 - 1,01 = 10,4% uptime difference off the buff between both situations, to put this into perspective we first have to look at what the proc actually gives:

2.44% dodge and 1.98% crit

10,4% of this means that with the Improved Mangle talent you gain 0,25% dodge and 0,21% crit IF you have the idol of the corruptor and never get misses or parries.

Scenario 3 - 90% hit, 68% Proc chance and 6 sec Mangle CD

Chance that the idol buff is not refreshed on a mangle:
1 time = 35,5% (0,32 / 0,9)
2 times = 12,6% (35,5^2)
3 times = 1,6% (..)
4 times = 0,03% (..)

The duration of the buff is 12 seconds so to have 6 second downtime of the buff you need to miss twice in a row (= 12,6%), continuing this path you get the following numbers:

18 seconds = 0,03% of the time
12 seconds = 1,6% of the time
6 seconds = 12,6% of the time

This means the chance to not lose the buff is 100 - (12,6 + 1,6 + 0,03) = 85,77% which relates to 14,23% downtime

Scenario 4 - 90% hit, 68% Proc chance and 4,5 sec Mangle CD

Chance that the idol buff is not refreshed on a mangle:
1 time = 35,5% (0,32 / 0,9)
2 times = 12,6% (35,5^2)
3 times = 1,6% (..)
4 times = 0,03% (..)

The duration of the buff is 12 seconds so to have 1,5 second downtime of the buff you need to miss thrice in a row (= 1,6%), continuing this path you get the following numbers:

6 seconds = 0,03% of the time
1.5 seconds = 1,6% of the time

This means that the chance to not lose the buff is 100 - (1,6 + 0,03) = 98,37% which relates to 1,63% downtime

Comparison

The difference then is 14,23 - 1,63 = 12,6% uptime difference off the buff between both situations, to put this into perspective we first have to look at what the proc actually gives:

2.44% dodge and 1.98% crit

12,6% of this means that with the Improved Mangle talent you gain 0,31% dodge and 0,25% crit IF you have the idol of the corruptor and get 10% misses and/or parries.

Conclusion

Comparing the 100% Hit and 90% Hit situations shows that the more misses or parries you get the better Improved Mangle is for mitigation and threat IF you have the idol of the corruptor.
The actual effect of getting misses or parries is a lot bigger without the Improved Mangle talent then with it, a 10,4% difference (100% Hit rate -> 11,41% - 1,01%) versus a 12,6% difference (90% Hit rate -> 14.23% - 1,63%).
That itself means that by gaining 10% more hit you gained 2,2% (12,6% - 10,4%) uptime of the buff, which relates to 0,05% dodge and 0,04% crit.

For threat the talent Master Shapeshifter still outperforms Improved Mangle even if you have the idol because a flat 4% damage increase (4% * 2,07 ~ 8% threat) out performs a 0,25% - 0,20% critical strike chance increase, so in the end it's all about your situation....

Tarskin's case against improved mangle for a main tanking bear

First of all it’s important to notice that I do not run with the cookie cutter 0/60/11 build but with 0/55/16 because I believe the added dps/tps from master shape shifter is worth more then whatever you can throw at me from within the feral tree.

Pre-3.1 I used to go with 3/5 R&T as I wanted improved mangle which meant higher threat in my rotation but with the changes to the threat and damage done by faerie fire it is damn good, good enough to always use it whenever it pops off cool down.

This is where we run into a problem as faerie fire is on a 6 second cool down and mangle is on a 4.5 second cool down (if talented), for those who do not see this yet here below is a representation of 18 seconds worth of fighting.



As you can see on GCD 10 there’s a problem that both mangle and faerie fire come off the global cool down at the same time which means that you are losing threat as one of the moves will be not used while ready.
Therefore the threat offered by improved mangle talent is not as high as it was or as most people think it is, I therefore make the case to not take imp mangle so that mangle and faerie fire have the same cooldown which makes for a better rotation as follows.



Which is a rotation that makes perfect sense and frees up 3 points which can be put in 5/5 R&T and 1/1 primal gore which makes more threat then a 3/5 R&T build where 1 out of 3 improved mangle cool downs are wasted.

This would mean that the perfect build for 3.1 Main Tanking in my opinion would still be a 0/55/16 build and the defense of this build will be a seperate post as it goes beyond the scope of this post...

HOT OF THE PRESS!!!
Monedula from Omen of Clarity makes a case that improved mangle is worth it IF you have the Idol of the Corruptor and threat is not an issue, read his reasoning here.