Yes, this was another 10 man Sapphiron parse. Here is the link to the WWS of the more recent parse: Wow Web Stats

Originally I had thought that everyone except Mechenos was in full frost resist gear plus Improved MotW, but 4 of the other people in the raid had relatively large amounts of sub-30% resists, leading me to believe that they removed their frost resist gear before the pull (since I checked everyone's gear myself beforehand to make sure they had it on) or somehow lost their MotW buff. The parses that I deemed to be clean were myself, Azelle, Makeesh, Zant, and Zarrea. We had no shaman for totems and the only aura I can find in the logs is retribution aura. However, it's not impossible that I screwed up somewhere, either in parsing the log or in determining who exactly had which buffs and frost resist gear.

At the very least I can verify the accuracy of my numbers from that log (assuming no outside source of resistance, which appears to be the case from the combat log), which are:

30% resist: 39/171 = 22.8%
40% resist: 76/171 = 44.4%
50% resist: 51/171 = 29.8%
60% resist: 5/171 = 2.9%

Those numbers look much closer to what you got out of my original parse, so it's likely that one or more of the other people that I counted actually had more than 362 resistance, perhaps from the crafted ring or a flask.

Edit: Ok, after going back through it looks like Zarrea and possibly Zant had more than 362 resistance. Removing Zarrea's numbers gives

30% resist: 144/695 = 20.7%
40% resist: 303/695 = 43.6%
50% resist: 224/695 = 32.2%
60% resist: 24/695 = 3.5%

If we remove Zant's as well we get

30% resist: 111/527 = 21.1%
40% resist: 235/527 = 44.6%
50% resist: 164/527 = 31.1%
60% resist: 17/527 = 3.2%

Of course, it's not exactly rigorous to remove data just because it doesn't feel right or match our expectations, but Occam's Razor says it's more likely that they simply had more resistance than I thought.

Keep in mind that Sarth logs can be a bit complex.

Because damage reduction does not affect the "resisted" number, we can't simply divide resist amounts by the total. Without going through the math, the basic formula is actually:

x = Partial resist fraction (what we're looking for)
R = Resisted amount
D = Damage incoming: the sum of received damage and absorbed damage in the logs (ignoring resisted amount).
C = The net damage reduction of the tank

x = 1 / (D/RC +1)

For a feral druid for instance on a normal fight with no buffs, C = 0.88 (Protector of the Pack).

For Sartharion, the value of C changes throughout the fight. When the fight begins, if he has BoS and Grace active, it is 0.88*0.97*0.97*2. The 2 is from the double fire damage taken debuff. Gift of Twilight, the 50% damage increase buff, is not part of C, because it affects Sarth's damage dealt, thus both resisted and received amounts equally. C will change when Vesperon's Acolyte spawns, when Shadron dies, when Vesperon's acolyte dies, whenever the druid is affected by barkskin, pain suppression, divine guardian, or hand of sacrifice, and finally whenever the number of Grace stacks changes.

For instance for the case you have listed as 6%, it looks like it's actually a 10% resist before Shadron lands, with BoS and 1 stack of Grace up and no other CDs. The last entry looks like a 30% resist with Vesperon landed and Divine Guardian combined with Hand of Sacrifice.

These issues make any kind of "automatic" calculation from Sarth logs pretty rough, but the logs can still be informative when a particular partial resist is found that rules out certain constants.

Here are my numbers tanking Sarth last night at 210 resistance (not ideal, I know, but it was the best I could scrape together quickly):

10% resist: 1/81 = 1.2%
20% resist: 25/81 = 30.9%
30% resist: 41/81 = 50.6%
40% resist: 14/81 = 17.3%

Interestingly, the final breath was recorded as a miss. I don't recall seeing any misses from Sapphiron logs, does his aura work differently than Sarth's breath? Also, would it be more useful to gather some data on resists at 510 or 515? I can reach either one without much touble.

The "misses" are just a base % chance to be missed by spells that everyone has I think. I've seen a few as well, I don't believe it's affected by resistance. BEs for instance should see more. Frost Aura from Sapphiron is a debuff placed on the raid, which keeps ticking for periodic damage, hence the lack of any "misses" of this damage.

And yes, both 510 and 515 would be very helpful, though I somewhat hope you're talking about Sapphiron as tanking Sarth in that could be pretty risky...

Interestingly Grace actually does stack with BoS, despite some blue comments to the contrary. BoS and Vigilance don't stack however.

I've yet to see anything inconsistent about Sarth's breaths, I'm not sure what the rumors are other than the fact that most people expect the resisted portion to be some flat percent of the total. Every breath I've seen in a log though has some exact explanation consistent with the possibilities at the given FR.

I've just been working with Excel, I'm not proficient enough in any programming language to make something more automatic for Sarth logs, I typically either use a formula like the one above with 4 "basic" possibilities for the constant, or simply calculate the possible base breath amounts from the resisted amount, considering only the 1-2 that fall within Flame Breath's damage range. If I were to do anything more automated it would probably be in Matlab because that's what I know, but that wouldn't be terribly useful to others.

Narrowing down the constant

Did Sapph with 515 FrR, small sample size but got enough to narrow things further:

130 Samples at 515 FrR
Partial Resist: # of samples (percentage)

40%: 30 (23%)
50%: 67 (52%)
60%: 30 (23%)
70%: 2 (1.5%)

Average resist: 0.503

The presence of two 70% resists means the constant is lower than 515.

At present, the possible range for the constant is now 506-514. The only nice "rounded" value left is 510. It certainly doesn't have to be a multiple of 5, but as always simplicity is a decent assumption in the absence of further information.

One simple explanation for 510 would be that up to level 82, the constant continues to work on a 5*level system. Thus it would be 410 vs. an 82 mob. When moving to boss level, a special amount is added. This would be similar to the hit mechanics, where the hit cap goes up 0.5% per level up to level 82, then jumps up 2% when moving to boss level. I'm not really sure how such a system would work out though for an arbitrary level difference (i.e. a level 70 fighting a level 80), as adding 100 per level beyond 2 is pretty steep... It may simply be that there is a harsh nonlinear increase in the constant as a function of level difference, which yields some value in the range of 106-114 for a 3-level difference.

I think of this as a "low-priority" concern, but I'd be interested to see some numbers vs. an 82 heroic boss. Some that come to mind are the Maiden of Grief's void zone, Novos' arcane field before you engage him, Kerisrasza's intense cold. If anyone can think of others let me know, if i can put together a cutoff amount of the appropriate resist, and it's a boss I can clear to with just a healer without spending forever on it, I may do that sometime. It has to be something with a pretty fast damage component.

Also, I wore this set vs. KT. Very few samples, but what's unique about KT is the presence of the binary resists on Frostbolts. I had 11 resists out of 30 casts, or about 37%. This is compared to the roughly 19% at 430 FrR. While resistance is clearly fairly powerful for mitigation vs. spells with a binary component, finding out the exact formula for this is pretty hard right now due to the extremely small sample size, and it's not nearly as useful. If there are fights in Ulduar where wearing resist vs. a binary spell is helpful, it's already intuitive that the more you wear, the more you'll resist, and there are no useful cut-offs to find like there are for partial resists.

Summary

The constant appears to be between 506 and 514. This yields 10% and 20% cutoffs at

10%: 217 to 221
20%: 338 to 343

If the constant is 510, the cutoffs are

10%: 219
20%: 340

If anyone gets any data on Sapphiron or Sartharion with a resistance in the range of 217-221, 338-343, or 506-514, I would love to get a copy of the log or WWS.

I got a wicked cold shortly after collecting the last set of data I promised, but it looks like it probably wouldn't have been relevant anyway. I think I can try to get into the 338-343 range this week, though we've started doing our 100 club achievements so the rest of the raid may not like that.

To be clear... by "cutoff" you mean "resistance value at which that partial resistance amount no longer appears", right? I.e. 221 or 222 resistance guarantees at least a 20% partial resistance value? If that's the amount required to guarantee a 10% partial resist, that seems rather extreme. If it guarantees a 20%, though, is there an even lower resistance value range to test for the guaranteed 10% resists?

Did Sapph/KT tonight with 340 FrR, 181 samples altogether.

In these I did not see a 20% or a 60% resist; all 30%, 40%, and 50%. If the constant is 510, only these three resists would be possible.

Unfortunately, while promising, this isn't quite "conclusive", as if the constant is slightly more or less than 510, the probability of one of these resists is very small, and quite reasonably would not be seen in just 181 samples.

If the constant were 509 for instance (for whatever reason...) there is an 80% chance of not seeing a 60% resist, despite it being possible.

That said, the more samples that are gathered at this resist, the more confident we can be that 510 is the constant. Alternatively, the first time a 20% or 60% resist appears, it cuts the range of possibilities in half, leaving only 4.

Still, for the time being, I think it's plenty safe to treat 510 as the constant, and for the only fight where this really matters, treat 340 FR as the cutoff for eliminating 20% resists on Sartharion. If this is incorrect, and you still receive and log a 20% resist wearing 340 FR, at least you have the immense consolation of contributing to this pool of knowledge.

Updated the main post with the current data, and fancy pictures.

I'd rather see something besides a constant. Let's look at post #53

Using 510 as the constant. Resist should be 50.2439% Yet we clearly see 2 70% partial resists. There needs to be a cutoff here somewhere that makes us jump to the next 10% interval. So was it because the resist total exceeded 50.1%? I come up with these values for 1 70% resist.

50.10%=1 in 1,000
50.25%=1 in 400
50.50%=1 in 200
50.75%=1 in 133
51.00%=1 in 100

There were 2 partial resists though. The only way i can see the possibility of the 2 70% resists was if the assumed 510 constant is incorrect. If you lower the constant to say 498 it works out a to be 50.84%. Which makes a 70% resist chance become a 1 in 116 chance. Which models a bit closer to the 2 in 133 in the results. Now the reason i use 498 is because i don't like a constant. It would require 83 tables. I'd rather do this instead.

player resistance / ( (caster level + (caster level * 5)) + player resistance )

I'm confused here - in the case in post 53, if the 510 constant is correct, then wearing 515 resistance, 70% partial resists are possible. The sample size of 133 is fairly small - the fact that 2 occurred instead of 1 or 3 is just a matter of chance. If you're saying there should have been no more than 1 partial resist if the constant is 510, keep in mind the probability of seeing 2 or more over 133 samples is roughly 20%, so nothing terribly uncommon.

Either way it seems you're trying to find a formula that better matches this small set of 133 points. Keep in mind that there's a lot data throughout this thread, and cases with much larger sample sizes. More importantly though is that the appearance of certain partial resists at all wearing certain amounts of resistance has narrowed the constant to 506-514 already.

As Mijae said, whether we call it a "constant" or not, there is some single number that goes in the formula for an 83 boss, and a different number that goes in the formula for an 80 mob. It's 400 for an 80, and between 506-514 for an 83 - I don't know of any simple formula based on caster level that will yield these two numbers, other than to say it is 5*level until 83, when 100 is added. How this affects greater level differences or non-boss mobs, I have no clue, but it has no terribly important applications.