Assuming a 2 second swing timer and a 390 second long boss fight, we are looking at about 195 total swing over the course of the fight.
390 / 2 = 195
Assume the tank is superhuman, we can assume that Shield Block will be used 13 times.
390 / 30 = 13
(where 30 seconds represents the cooldown on shield wall)
If Shield Block is used 13 times, we can calculate then the uptime of it given the 10 second duration and length of the fight.
(13*10) / 390 = .3333 or 33.33%
Given the above figures we can look at some avoidance percentages and start figuring. I will re-list the given avoidance figures:
5% - Base miss chance (this will not change, ever.)
10.46% - Dodge chance
12.59% - Parry chance
51.52% - Block chance
31.06% - Critical Block chance (Note that the sum of Block chance +25% does not exceed 100% and thus will not change the critical block chance.)
If we sum the chance to avoid attacks entirely (all less block/critical block) then take the percentage of each we end up with what percentage of attacks are avoided, and what the percentage of avoided attacks are.
.05 * .1046 * .1259 = .2805 or 28.05% attacks are estimated to be avoided.
Of these avoided:
.5 / .2805 = .1783 or 17.83% are Miss
.1046 / .2805 = .3729 or 37.29% are Dodge
.1259 / .2805 = .4488 or 44.88% are Parry
Shield block is up for 10 seconds every use, and has a 30 second cooldown. Using the figures from above, we can estimate approximately how many hits you would take with shield block up, and how many of those are avoided, then how many are blocked (the remainder of hits after avoiding) as with shield block up and the above stats you are over 102.4% avoidance/block (commonly referred to as unhittable).
We have calculated that Shield Block is up for 130 seconds of the encounter, this is roughly 33.33% of said encounter. We have also stated that the maximum number of potential swings cannot exceed 195. So using these figures:
.3333 * 195 = ~65 swings while Shield block is active.
For simplicity, I intend to use avoidance as a straight percentages. PLEASE DO NOT ASSUME THIS IS THE ABSOLUTE TRUTH, AVOIDANCE (AND WINDMILLS) DO NOT WORK THAT WAY! In the law of averages, this is what you would expect to happen but as most of us have learned, this is not the way that avoidance works all the time in an encounter.
If our combined avoidance is 28.05%, we can use this to estimate the number of attacks avoided:
.2805 * 65 = ~18 avoided swings.
Using the percentages of that avoidance calculated earlier, we can estimate the number of parries give the avoided swings.
18 * .1783 = ~3 Miss
18 * .3729 = ~7 Dodge
18 * .4488 = ~8 Parry
This also allows us to calculate the remaining number of hits that are blocked, remember that with Shield Block up you would be 'unhittable'.
65 - 18 = 47 Blocked hits
Of these blocked hits we can calculate the critical blocks without having Hold the Line talented (again using the 'chance' as a flat percentage which is not entirely accurate).
47 * .3106 = ~15 critical blocks without Hold the Line.
Shield Block on CD:
******CD = Cool Down********
So Shield Block has been used at a super-human level, but what about the other 66.67% of the fight? Well first we need to calculate the number of hits in this section and then the avoided hits again.
195 - 65 = 130 Swings with Shield Block on CD.
130 * .2805 = ~36 Avoided swings
36 * .1783 = ~6 Miss
36 * .3729 = ~14 Dodge
36 * .4488 = ~16 Parry
Being that Shield Block is not up in this section, we only have a 51.52% chance to block, so using this we can estimate how many blocks we will have.
130 * .5152 = ~48 Blocked hits
130 - 48 - 36 = 46 Unblocked/avoided hits
Of the ~48 blocked hits, we still can estimate the critical blocks.
48 * .3106 = ~15 Critical Blocks
Hold The Line:
This talent increases your chance to critically block (what I am concerned with) and critical strike (threat) by 10% for 10 seconds following a successful parry once you have filled the talent out with 2/2 points. To calculate approximately how it affects the the results, I had to make some assumptions on how linear the fight would be. One such assumption is that all events would occur linearly over the course of a fight, ie. an even distribution. This is not the case in WoW, but for this purpose it will have to do as I do not have the means to appropriately simulate the events.
Using the linear distribution, I can calculate the frequency with which Hold the Line can occur and approximately how many blocks occur while Hold the Line is up. First I needed to calculate the frequency of a parry (and this is the BEST imagineable condition where you parry the first swing and continue to parry in a linear fashion) which I took the number of occurances of Parry and divided the time by the occurances, it is a rough calculation.
390 / (8 + 16) = ~16.25 seconds a parry occurs.
Following the same logic, I estimate the block frequency.
390 / (47 + 48) = ~5.42 seconds a block occurs.
Knowing that hold the line can only last 10 seconds, the assumption is that it falls off for ~6.25 seconds before being renewed. If a block can occur every 5.42 seconds and a parry every 16.25 seconds, we can estimate how many blocks fall into the Hold the Line buff.
If a parry occurs, a block cannot, however it starts a timeline. Parry at 0 seconds starts a 10 second timer, so at 2 seconds the boss swings again and assuming BEST POSSIBLE SCENARIO that hit is blocked, the next swing is at 4 seconds, then 6, at ~7 seconds you would block again, but the swing hasn't happened so assume the swing at 8 seconds is blocked, and now no based on linear distribution no blocks would occur until after 10 seconds had passed. This would mean 2/3 of blocks are with hold the line up.
Unfortunately it isn't as easy as that, as we need to figure out how long Hold the Line is up during Shield Block, and when Shield Block is NOT up. To do this, I took at look at the number of parries, the time it could last, and what percentage of the total time that was for Shield Block being up and not being up.
With Shield Block:
8 * 10 = 80 seconds
80 / 130 = ~.6154 or 61.54%
Without Shield Block:
16 * 10 = 160 seconds
160 / 260 = ~.6154 or 61.54%
So when looking at how much it increases the critical blocks in this scenario, I calculate how many critical blocks I have with the Hold the Line talent using the blocked hits.
With Shield Block:
47 * .6154 = ~29
Using the logic where if Hold the Line is up you block 2 times, I can then estimate the number of hits with a higher critical chance and a lower.
29 / 3 = ~10 (For this I say it is 10 and 1 hit does not occur when Hold the Line is up).
So I can safely assume now that 19 blocks occur when Hold the Line is up.
19 * .4106 = ~8 critical blocks.
Now I can calculate the rest of the blocks with the regular crit chance:
(10 + 18) * .3106 = ~9 critical blocks.
8 + 9 = 17 Critical blocks with Hold the Line vs. 15 Critical blocks without Hold the Line.
Without Shield Block:
48 * .6154 = ~30
Using the 2/3 blocks:
30 / 3 = 10
I can now assume that 20 blocks occur with Hold the Line up:
20 * .4106 = ~8 critical blocks.
The remaining blocks are now calculated:
(10 + 18) * .3106 = ~9 critical blocks.
To sum this section:
8 + 9 = 17 Critical blocks while hold the line is up Vs. 15 while Hold the Line is not up.
This would give us an additional 4 critical blocks over the course of a fight, which is essentially the same as blocking 4 more times.
Conclusion (if it can be called that):
In looking at the results in this very simplified example, Hold the Line is roughly the equivalent of blocking 4 more times. This would be equal to an approximate 3% increase in block frequency when Shield Block is not active. Looking at some damage from a 100k hit:
Looking at damage without shield block up:
(100,000 * (48 - 17)) * .7 = 2,170,000
(100,000 * 17) * .4 = 680,000
2,170,000 + 680,000 = 2,850,000 Damage with Hold the Line
(100,000 * (48-15)) * .7 = 2,310,000
(100,000 * 15) * .4 = 600,000
2,310,000 + 600,000 = 2,910,000 Damage without Hold the Line
So the difference between Hold the Line and not is ~60,000 damage for this example which is about 2/3 of the encounter length stated.
Note: It's late and I've been at this for a while, I will review this tomorrow after I've had some sleep.
****Please keep in mind that as I said: This is NOT concrete and is a rough example only. Avoidance is very much less predictable than this example, and critical block/block is equally as unpredictable. *****