Shamgarr

Well if Sapphiron's aura is a constant amount, all I need is a big pile of combat log entries of the resisted amount, as this will not be modified by any of the various damage reduction effects or absorbs people have. Divide by the appropriate amount for normal/heroic and there's the partial resist %.

The main issue is that the data really has to be completely uncorrupted to be meaningful - so no Frost Resist totems or auras at all, because there's always a chance someone was out of range, and I would need to be able to discard anyone like mages that might have put on mage armor, or a tank in polar gear. Everyone in the sample needs to have the same resistance (meaning probably just GOTW).

If anyone else has a combat log, or can get one, that meets these criteria, I'd love to work with it. Hoping to get one this weekend, but might not, and either way the more data, the better.

Based on my own most recent experience tanking Sartharion with 417 Fire Resist, I'm really starting to doubt the assumptions made so far about the level difference. I would strongly advise taking all the boss numbers up right now with a grain of salt until more data can be gathered. The level 80 numbers are solid (but not terribly useful except perhaps to PvPers), but the assumptions about 83 seem to not be matching some anecdotal experiences. My guess right now is that either the factor goes up higher than 415, bosses have a certain amount of spell penetration, or the formula is actually a simplification of a more general formula that incorporates both target level and caster level.

 

Shamgarr

Sapphiron Test

Got my first Sapphiron log (10-man), with some interesting results. Made sure everyone had just GotW, and weeded out pets. This left 1424 data points, not huge, but pretty significant and a higher sample than the individual cases that provided the level 80 data.

At 75 Resistance:

Partial Resist: Probability

0%: 0.1699
10%: 0.4305
20%: 0.3272
30%: 0.07233

Average Resist: 0.1302

First off, the individual percentages still agree very well with the triangular distribution about the mean. Thus the formula for the probability of each partial resist seems to hold (0.5 - 2.5*|x-AR|).

The "predicted" mean, which was already under some doubt, is

Resistance/(Resistance + 5*Level) = 75/(75+415) = 0.1531

For this sample size, this is well outside 99% confidence limits for the mean, so I'm pretty confident that there's something else going on.

Possibility 1:

The factor of 5*level holds, but the boss has some amount of spell penetration, reducing the player's effective amount of resist. If this were the case, the amount of effective resistance that fits the data is 62. Perhaps more appealing, if the constant is held at 400 instead of raised to 415, the effective resistance is 60. This would mean the boss had 15 spell penetration, 5 per level.

As tidy as this sounds, however, it does not agree with the observations of 30% partial resists at resistance values of 415 or higher, some of which will be mentioned below.

Possibility 2:

The constant is not simply 5*level, but takes some other value for bosses. If zero spell penetration is assumed, the value that fits the data is 501. A more rounded value of 500 yields a predicted mean of 0.1304, well within confidence bounds.

It is worth noting that increasing the constant from 400 to 500 is equivalent to multiplying it by 1.25. The same result is achieved by instead dividing the resistance by 1.25. Thus mathematically these two effects would be indistinguishable. Dividing 75 resist by 1.25 yields 60 resist, explaining the agreement with such an assumption above. Raising the effective constant, rather than reducing player resistance by a fixed percentage, seems a bit more intuitive.

Kel'Thuzad Test

For this I had 430 Frost Resist (with GotW), while everyone else had 75. The sample size is of course much smaller and harder to draw any precise conclusions from, but what is perhaps most important is the presence of 30% partial resists.

430 Resistance - 42 samples

30%: 0.095
40%: 0.40
50%: 0.31
60%: 0.19

Average Resist: 0.46

Predicted Resist from 430/(430+500): 0.462

There were also 10 hits that did 0 damage, and were classified as "Resist" (not Missed). I'm not sure what these mean, but it may have something to do with a binary check on the spell due to the snare component. It seems entirely independent of the partial resist check, and made up about 19% of the casts (again, with a very large confidence interval due to the small sample size). It's interesting that if this is the case, the chance for a spell to do zero damage is much higher simply due to it having a debuff accompanied with it - there were not separate checks for the damage or debuff, as these "Resists" did not simply deal damage but fail to apply the snare.

As seen from the data, while the sample size is extremely small, the average resist still agrees very well with the constant of 500. A constant of 415 is not possible, because 30% resists should be eliminated. This is true even if the boss had 15 spell penetration and the constant was 400, which would bring my resistance down to 415. As mentioned above, the amount of "penetration" which would make this data match with a constant of 400, is to divide the player resistance by 1.25 instead (bringing it down to 344), which is simply equivalent to raising the constant to 500.

The 75 resist data agreed reasonably well with the Sapphiron data, but with only 123 sample points doesn't really provide any additional information. Of frostbolts casts on people with 75 resistance, about 8% were fully resisted.

Conclusions

I need more data, preferably at a different resistance, to feel completely confident in this presumption, but right now, a constant of 500 for bosses looks quite likely. 415, or 5*Level, can pretty much thrown out at this point, so I'll update the first post. There still remain other, slightly more complicated possibilities which might produce the same results at a single resistance, such as combinations of a different constant, a smaller amount of penetration, or some more complex formula with caster and target level as variables, but at present there isn't any data prompting such characterizations.

I'll log our 25-man Sapphiron kill on Tuesday, and will probably wear my polar set and have a couple pallies put up frost resistance. I'll need to manually sift through the log and disregard any data from someone that gained or lost frost resistance aura during the fight, but this should yield a decent amount of data at 130 and 485 frost resist.

 

kalbear

If the 500 coefficient is correct, we should require 334 resistance (not 277) to get to the 30% always resisted barrier, which is where a druid can deal with Sarth's breaths with only their own cooldowns/pots to mitigate it.

 

Silverwind

Looks like the 75% cap on partial resists is gone too since WotLK. I've seen tons of 80% an 90% partial resists on the obviously bugged Twilight Shift you get hit by while inside the portals at sarth. (WWS Log)

 

Shamgarr

Now that's just plain weird... wonder what's going on there.

Thanks btw to Melthu for a nice chunk of Sapphiron data at 362 resist. I should reiterate that the formula and the 500 constant are still just educated guesses right now - really being sure of any of this is just going to take a lot more data.

I'd be happy to look through logs of anyone that can give *definite* resist amounts for even just a few of the players in a parse. Since I've got a lot of 75 resist data already, parses with some players wearing some resist gear would be nice. The raw .txt combat log is quickest to work with if you have it, though WWS links are fine too - unless I'm missing something I just have to copy/paste only 100 entries at a time.

Some particularly informative amounts to shoot for would be the "expected" thresholds given in the updated first post. At 125 resistance, for example, it should be impossible to get a 0% resist, and only 3 resist amounts should be possible due to being right on a 20% average. If a log where someone is positive their resist is 125 the entire fight shows this not to be the case, the 500 number would likely be inaccurate.

 

• frmorrison

This is for more data for your study.

This log has a 25-man Sarth 3D is in there with Orthogonal (Feral) using 330ish FR, I don't remember if that includes 130 FR Aura. He seemed to take less damage overall.

Wow Web Stats

DK - Ashbane Failure is the condiment that gives success its flavor.

 

Shamgarr

No new Sapphiron parse yet, but after doing a lot of OS3D last night with 337 FR and reviewing logs, I'm pretty sure I took some 20% breaths with the fire resistance totem still active, and I don't believe I ever got a 60% resist.

If accurate, this would indicate that 334 is not the threshold for eliminating 20% resists, and the constant is higher than 500. So as always, continue to take the posted thresholds with a grain of salt.

 

Rasmfrackn

All of the parses I used for my own crunching have expired, but here's one histogram from a 417 Frost Resist on Sapph25.



The bin labels are a bit off because of the way the base damage gets resisted and then the damage reductions apply, so instead of 40% resisted it actually looks like ~43% resisted, but every resist value was in a multiple of 160 (10%).

As you can see, at 417 he had about 40 out of 400 resists at the 30% level. (And about 5 out of 400 at the 70% level.) So while 415 looks like it should be the threshold to remove 30% resists, it's clearly not. Also his overall average damage resisted was right around 48%.

I'll get a fresh sapphiron on Sunday if you don't have more data by then. I'll be sure to collect resist values from other raid members as well.

 

Shamgarr

Well 415 was just the guess, based on 5*level before we had any boss data. The first Sapphiron parse indicated a constant closer to 500.

If resisted amounts in that chart were based off damage taken, I'm guessing the 70% values were actually another resisted amount but with some damage reduction CD active. On Sapphiron all you have to do is take the resisted amount divided by 1600 (1200 in the 10 man). There are only 4 possible partial resists at a given amount of resistance.

Tonight I got 2090 samples at 130 Frost Resist. The distribution was:

10%: 0.2397
20%: 0.4943
30%: 0.2555
40%: 0.0105

Average: 0.2037

Sticking with the assumption that the formula is correct and there is 0 spell penetration involved, the presence of the 40% resists means the constant is below 520. The Sartharion numbers I have, while harder to work with and not terribly conclusive, do seem to indicate a constant above 505.

This at least puts some limits on the required resistance thresholds.

For a minimum resist of 30%, for instance, it looks like the required resistance is between 338 and 346.

As far as the unknown constant, the only multiple of 5 possibilities left are 510 and 515. While it certainly doesn't "have" to be a multiple of 5 it's a place to start. As mentioned earlier, the closest thing to a "conclusive" answer on the constant is finding a resistance that only produces 3 possibilities over a large sample size, or simply eliminating enough possible values until only 1 is left.

Having a resistance equal to the predicted constant would always produce such a situation, though it can be harder to hit precise resist values that high right now for testing.

If the constant is 510, 340 should be such a resistance. If it is 515, there are no such resistances other than 515. In 10 man Sapph this week I'll try to get some values to narrow it further.

 

Schnappi

If bosses work with a certain constant then 515 sounds like a nice arbitrary value because it is exactly 100 more than bosslevel*5.

 

Rasmfrackn

Ah yes, sorry. I made those before I knew what I was looking for. I won't paste in the whole data set, which would just be evil, but this is the consolidation:

38x (360 resisted, 720 taken) (33.33%)
8x (360 resisted, 504 taken) (41.66%)

135x (480 resisted, 617 taken) (43.76%)
32x (480 resisted, 432 taken (52.63%)

119x (600 resisted, 514 taken) (53.86%)
28x (600 resisted, 360 taken) (62.5%)

35x (720 resisted, 411 taken) (63.66%)
5x (720 resisted, 288 taken) (71.43%)

Total points: 400 exactly
Total 30% resists: 46 (11.5%)
Total 40% resists: 167 (41.75%)
Total 50% resists: 147 (36.75%)
Total 60% resists: 43 (10.75%)

I stripped out the text so I can't account for the two different taken values per resisted amount, but the smaller values are all 70% of the larger ones, so I'm betting it's Divine Guardian or something similar.

Rasm

 

Mijae

Those numbers also look like they should be for 10 man, not 25. The 360, 600, and 720 resists would not be possible in 25 man, but they would for 10 (based on 1600/1200 damage and 10% resist intervals). Perhaps this data was taken during the time before the damage values were fixed and set to current?

Feral DruidStats spreadsheet
v3.2.0.0.xls - updated 8/4/2009

 

Erusdruidum

On the 60% resists, you had 35 and 5, so it should be 40 total for 10%, not 43 for 10.75%. I assume this is from the same 417 resist set as the above post?

 

Rasmfrackn

You're right. I'm not sure how hard it is to add 35 and 5, but it explains why my total-sum double check was 0.75% over.

It was a 10-man sapph kill... the resist rates and such should all be the same though, with just the damage values being 75% of the 25-man version.

 

Melthu

Here are a few more numbers for 362 resistance:

30% resist: 173/878 = 19.7%
40% resist: 369/878 = 42.0%
50% resist: 294/878 = 33.5%
60% resist: 42/878 = 4.8%

 

Douglas

Do we know this for sure? Certainly pumping up the raw damage is one way they tune 25-man higher than 10-man, but different values for hidden formulas (eg. resists) would be another way they could do that -- do we know enough to rule that out for certain?

 

corveroth

I'm capable of running some super-high resist numbers against Sapphiron (756 unbuffed). Is there some end resist value that would be particularly useful to gather data at? I'm thinking 773 would guarantee minimum 50% resists if the 515 constant is correct, but to be honest, I'm having trouble following this math.

 

Erusdruidum

Yeah, for a constant of 515, 773 guarantees at least a 50% resist. If the constant is 510, you need 765 to do the same. (At least, assuming what we have so far is accurate)

 

Melthu

If Shamgarr is right and the value is between 505 and 520, trying values in between there will be beneficial. Specifically, if the constant is either 510 or 515, trying those two exact amounts will help narrow it down. There's no need to test numbers upwards of 700+ unless you believe that our current knowledge of resistance mechanics is either incorrect or incomplete.

 

Shamgarr

Data at any value between 506-519 would be helpful as mentioned, though one problem with testing higher resistances like this is inevitably the sample size is smaller (only you, vs. 24 other people at some other FrR), so it's slightly harder to "prove" that a particular partial resist is impossible, though the presence of one would be extremely informative.

I got distracted and failed to get a set in this range before this week's 25-man Sapph, but I did get about 3k samples of plain old 75 FrR at least. Mean worked out to 0.1261. This predicts a constant of around 520. Keep in mind the confidence interval on the constant, even at 3k samples, is still significant - everything in that 506-519 range is still fairly probable.

Now Melthu your last set of numbers are fairly interesting. Just to verify, I assume it's the same as your last parse, and it was a 10 man where no one had any aura/totems? Also you got all the numbers just by taking the resisted amount from the combat log for the members with 362 and dividing by 1200?

I ask because the breakdown of your last parse was

30%: 23.9%
40%: 44.7%
50%: 27.7%
60%: 3.7%

With a predicted constant of 518. Your more recent numbers have a definite preference for the higher resist amounts, yielding a predicted constant of 493. At 878 samples, if the constant were 515, the odds of seeing a case with a prediction of 493 or lower are extremely low - difficult to quantify exactly but something less than 0.2%. If the constant were 510, the odds are on the order of 1% - possible, but still fairly unlikely. As my predicted constant from my 10-man data was around 501, it did make me wonder if the 10 man / 25 man values are different - though under this assumption the likelihood of a case like your first parse becomes quite low (though not as low).

In other words it's hard to make the two parses mesh with a single constant. It's not out of the question, but simply interesting enough that I wanted to check how sure you are about everyone's exact resistance each time, and the logging/calculations. It's hard to get this much detail out of the 75 and 130 data I have, because the spread of possible constants is simply larger for these resist amounts than at 362, even with higher sample size.

The next set I'd like to get data for is:

3-piece Polar set: 287 FrR
Titanium Frostguard Ring: 68 FrR
AV insignia: 10 FrR
Arcanum of the Frosty Soul (on junk helm): 25 FrR
Lesser Flask of Resistance: 50 FrR
Imp MotW: 75 FrR

Total: 515 FrR

Though it may take some weeks to get much data with this myself, the first appearance of a 30% or 70% resist would knock out everything above or below 515. The lack of one, over enough samples, would yield 515 as the constant with increasing certainty. If I can find a failed pug or something that still has Sapph 10 up, I could probably talk a healer into doing a few pulls til enrage and getting a lot of data fast.

TLDR VERSION:

After all this I swear to god if Ulduar has no resist fights I'm going to be more than a little annoyed...

 

Melthu

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.

 

FalseMyrmidon

Here's a 3D parse. Our tank didn't have any FR past 130 from a totem.
Wow Web Stats

Thought it looked like the resists were really high so I did the math on the first 12 in excel and it came out to 10-20% resists overall which sounds right.
Wow Web Stats

Damage Taken	Resisted	Absorbed	Total (approx)	Percentage of Total Resisted
9214	2386	6591	18191	0.131163762
16531	2517	140	19188	0.131175735
15567	2530		18097	0.139802177
17318	2614		19932	0.131145896
14649	1337	5723	21709	0.06158736
20312	3281	1424	25017	0.131150817
19214	5358	1488	26060	0.205602456
21483	1795	5273	28551	0.062869952
18041	5154	1875	25070	0.205584364
33579	5244	1879	40702	0.128838878
102973	2084	5332	110389	0.018878693
14447	5840	5296	25583	0.22827659

The 6% resist is kind of weird though and I can't figure out what happened there but the rest falls in line with the theories outlined so far.

 

Shamgarr

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.

 

Melthu

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.

 

Shamgarr

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...