First off, congrats to Fire and Blood, who downed Sarth3D for the first time last night! Really nice job by everyone, and a very smooth first kill.
I think in the future I'll cover the strategy we used and the general fight - that sort of thing is kinda fun - but for now I'd like to go over something that's really changed: how resistance works in WotLK. All thanks go to Shamgarr at the EJ forums for his excellent research and testing on this; while I helped with data, he did all the heavy lifting.
In the era of BC land, resistance had a hard cap and only resisted chunks in 25/50/75/100% intervals. There were breakpoints where it was more likely to resist 75% than 50 (and 50 than 25) but if you had maxed out your resistance, you could guarantee a 75% resist, every time. The formula for this was pretty simple:
Damage reduction percentage = 75 % * effective resistance rating / ( caster level * 5 )
If you want 75%, this means that effective resistance rating had to be equal to the caster level (mob level) *5. For the flames of azzinoth, that meant 73*5, or 365.
And if that formula worked in WotLK, that would mean a level 83 mob like Sartharion would need 415. 415 FR doesn't sound like that much compared to 365, does it? 50 more points isn't so bad, and could be easily covered by the Fire Resist fur lining from leatherworking. And 75% FR would certainly make taking 70k fire breaths easier.
Except all of that is totally wrong. WotLK introduced diminishing returns and a much more granular scaling for resistance. Yay, more diminishing return math! This time it's a bit easier to digest. :)
Unlike BC , partial resists come in 10% packets. This means that smaller amounts of resistance are more likely, over time, to be meaningful - so having that 130 Frost Resist Aura on Sapphiron actually helps quite a bit.
The range of resists that you can get are also much smaller. There's no 0/25/50 resist spot any more. Instead, the average resistance is calculated fairly simply:
average resistance (damage prevented) = resistance level / ((special value) + resistance level)
Because this formula uses the resistance level as a divisor, it's naturally diminishing. Which means that at 415 resistance against a level 83 mob, your average damage taken is this:
ADT = 415/(83*5+415) = 50%. (ETA: this is incorrect; against a level 83 mob the 83*5 number is actually 500. So you need 500 resistance to get 50%, and higher values to get to the no less than 30% and 40% resists.
Now, how do we figure out what values we can take? That's the important part, as average damage doesn't tell us what the worst case scenario is. This appears to either use a two-roll system or something very similar to a two-roll system (probably a one-roll, but using this methodology) based on the average damage taken.
For the first roll, use the average damage taken number.
50% of the time, you'll use that number.
25% of the time, you'll use that number - 10%.
25% of the time, you'll use that number + 10%.
Then whatever that number is, figure out a percentage chance based on where it falls between the two 10% barriers, and roll again using the distance from the 10% barriers as the chance.
If you're on a boundary point (like we are with 500) this math is easy:
50% of the time, you'll get to 50%. There's 100% rounding to 50%, so it's always 50%
25% of the time, you'll get to 40%. There's 100% rounding to 40%, so it's always 40%
25% of the time, you'll get to 60%. There's 100% rounding to 60%, so it's always 60%.
If you're not, though, it's a bit trickier. Let's take what my Fire Resistance was against Sartharion last night - 310.
Average Resistance = 310/(500 + 310) = 38.27%
50% of the time, we'll go to 38.27%.
25% of the time, we'll go to 28.27%.
25% of the time, we'll go to 48.27%.
In the 38.27% case, we have a 17.3% chance to get to 30% (rounding down, (10-8.27)/10) and a 82.7% chance to get to 40% (round up, (10-1.73)/10).
In the 28.27% case, we have a 17.3% chance to get to 20% (rounding down, (10-8.27)/10) and a 82.7% chance to get to 30% (round up, (10-1.73)/10).
In the 48.27% case, we have a 17.3% chance to get to 40% (rounding down, (10-8.27)/10) and a 82.7% chance to get to 50% (round up, (10-1.73)/10).
So the total chances for all values are:
20%: 17.3%*25% = 4.32%
30%: 17.3%*50% + 82.7%*25% = 29.3%
40%: 17.3%*25% + 82.7%*50% = 45.7%
50%:82.7%*25% = 20.67%
This also reduces to the following formula: the chance to get a given resist x against a level 83 mob is
Probability (x) = .5 - 2.5* abs(x - (resistance/(500 + resistance)))
and ignore negative probabilities.
That's the basic math, but as a tank that's not what you care about. You care about what the most damage you will take given a specific resistance - and more importantly, what resistance you need to eliminate certain values. And this appears to be pretty easy too:
|Resistance||Minimum Possible Resist|
So at 334 resistance, the worst that can happen is that you'll take a 30% hit. The best is that you'll take a 50% hit.
So what does this mean for resistance fights? Well, as you can see you need a huge amount of resistance to get 50% removed from the table and an average resistance of 60% - 750. You need 1167 resistance to get 70% average resistance. And 1500 resistance for an average resistance of 75%, which will still get you hit with 60% resists some of the time.
Practically, this is unobtainable given current itemization patterns. In order to get the same level of resistance that you needed (in theory) for Mother Shahraz and assuming similar gear to the Polar set, you would need at least 15 pieces of armor to get that high. Yikes. On the flip side - hey, it's not likely we'll be facing any resistance fights like Mother any time soon...
For Sarth3D main tanking this has some nice benefits. The maximum breath damage that you can take is 73825 damage, with all the bonuses up and 0 resistance. Assuming protector of the pack and blessing of sanctuary/grace, at 30% resistance you need 44112 effective HP to survive a worst-case breath.
With barkskin, you need 35289 health (or 47053 without the 25% buff).
With Survival Instincts you need 45243 health without the 25% buff).
With nightmare seed and a mighty fire protect potion, you need 50549 health.
And the awesome thing is, this is totally doable with current gear. It's easier with being a leatherworker, but it's not impossible for others to reach 334 FR. And if you can do that, it means you can survive the breaths by using your own cooldowns for a while and not rely on any external cooldown, making the fight as easy for druids as it is for DKs.
I'll go into the gearing choices for Sarth3D in a later post. :)