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....