This does indeed give the exact same results, as the "two-roll" description was basically three triangles, the superposition of which yields the one triangle you describe.

This also means there's an even simpler way to put this. I'm going to keep things in terms of damage "resisted" rather than taken:

L = Level
R = Resistance
AR = Average Resist

AR = R/(5L+R)

x = possible resist. As noted, x must take the values 0.1*n, for integer n. Thus the probability of any particular x is simply

P(x) = 0.5 - 2.5*|x - AR|

or putting it all together,

P(x) = 0.5 - 2.5*|x - R/(5L+R)|

Negative probabilities are simply treated as zero. This is the same as wrapping the whole thing in the "theta" function you describe, but the meaning of that might not be as apparent to people as the fact that negative probabilities are meaningless.

It would likely take quite a long time, but a dedicated group of folks could go kill the 3 drakes in 10-man OS and then just let Sarth smack their FR tank down for several hours to collect data. I'm sure that healers could develop a mana regen rotation to prevent going oom over a very long period of time. You could cycle MOTW, FR Aura, and neither to get several different FR values tests without having to leave combat to change gear. Maybe you could get even faster fire damage attacks per minute by having your "tank" stand outside the central platform and get pelted by Pyrobuffet? That might be a binary spell though.

If this idea would work (I've never done this kind of thing before, but I'm very interested in helping to perfect the new resistance formulas) I'll propose this to my guild today, to see if anyone's interested. What's a good way to record all this data accurately?

A group of 10 will probably get more data by running a partial clear of BWL up to the drakes. Then get into combat with the one with FR pulses, and collect data on resists for each character. Ideally, each character has a different amount of FR (that you recorded beforehand) so you can collect as many resist sample points at a time as you have volunteers (up to 40).

Alternately, you could get a group up to tackle Hydross, testing resists on his melee swings.

Or you could try soloing/2-manning Baron Geddon, which is possible from all reports.

I think clearing OS10 and holding it open is clearly a waste of everyone's time.

Sarth has an enrage timer. I think it was at 15 minutes. So you would need to reset him a number of times for that much data.

I'm going to take logs of a 10-man Sapphiron this week, where everyone just has GotW, as a start. I'm not sure what a good program is to parse all that text into taken/resisted amounts, might have to do something cumbersome with Excel if I can't find anything else. As far as I can tell WWS is still trying to convert the damage into the old 25/50/75 resist system.

For looking at higher resists, I typically tank KT in polar set anyways so will get a bit of data there. One thing I have no clue about is the phenomenon of "misses", and how that is or isn't affected by resist. I've seen a handful of full misses of Sarth's breath and KT's frostbolt, and I have no idea how that fits into the partial resist math worked out so far.

NPC spell misses against you are just like player misses against NPCS. They are not at all affected by resist values, and only affected by a pre-set hit rate. Level 80 NPCs are going to miss you roughly 4% of the time just like you would them, and a boss level NPC will probably miss you 1-2% of the time.

Any boss-level "??" mob counts as player level + 3, so you should be able to go to any of the older raid bosses that do elemental damage and get some useful test data.

For instance, I think pretty much everything Baron Geddon does is fire damage (not sure about his melee), so he could make for a decent test subject. If memory serves, his Living Bomb ability is the only thing that's not resistable.

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.

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.

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.

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.