TL;DR - Gross Takeaway: In current group content 1 point of AC is worth about 1.5 points of damage prevention on average from armor classes 6000 to 13000 for a level 120 warrior with max AA. I got too lazy to get much data below 6000, because I had to slow the mobs to survive and the parses started taking forever to get. Also, I was almost out of armor to remove.
Maybe this is the appropriate place to ask: Any else with maxed / 8 trophies curious about the impact of dropping the 100, 150 AC old ones in favor of the 0 AC new ones with more heroic stats ? Specifically these two: Replica of the Qeynos Claymore https://everquest.allakhazam.com/db/item.html?item=117193 Trophy of Duality https://everquest.allakhazam.com/db/item.html?item=124221 I don't have much issue subbing the Replica out for the NOS trophy but it looks like it will be a much more difficult choice come next trophy vs Trophy of Duality (because it has more AC and HP and some other stats as well). It kinda like feels like subbing out a type 7 AC aug for a type 5 heroic stat aug and maybe it's not the best decision for a tank?
I can't answer this question with hard data, since I didn't record it but I will say that in the course of this experiment my evasion AC also went down. Presumably from loss of heroic agility and I saw a corresponding increase in enemy hit rate. My feeling is that this effect (along with the decreased hp pool) had a larger impact on survivability than the 9k ish difference in average hit.
It's very difficult to tell from your takeaway above. As mentioned there are a few factors. HAgil/Evasion AC was already mentioned. This can be a fairly large different in being hit (not so much highest hit) The top 4 you also used a shield. Shield AC is pre soft-cap so is calculated differently than other AC. In addition there is also shield block. Any type 18/19 defense augs?
In answering the trophies, I have changed to heroic ones but I may go and have a look again at some of the trophies
No, calculated differently means nothing. The mitigation jumped from 6-7-8-9-10k to 11-12-12.5-13k. the "calculated differently" is over and done with when those numbers are displayed. Equipping a shield may have changed Maym's *Proficiency buff*, if he wasn't clicking it off for each test (it appears to me he wasn't doing so, and the proficiency buff lowered hits by 6% spa168 for the four shielded data points) but the AC calc thing is a complete red herring.
pardon the crayon, I'm guessing the graph would have a shape something like this if that had been taken into account:
Good catch Szilent. It didn't even cross my mind to click off the buff. Slope should be the same, just shifted by 6% for those data points. Regarding Lubianx point's - for this specific analysis, I didn't engage with those possibilities. This is literally just an analysis of the impact on damage values when hit. So yes, absolutely heroics and other items buff can impact hit rate, but I didn't look at this and just looked at damage per hit as a function of armor class. All the misses, and miss rates don't matter, since the parsed data only uses successful hits to generate the average values. I guess my biggest surprise is that AC is still behaving in a linear fashion at higher armor classes. The conventional wisdom I had absorbed was that AC had diminishing returns in today's game, but that doesn't seem to be the case. I know Dawnwall isn't close to maxing AC, so I'd be curious if better equipped tanks see this trend continue at 14k and 15k mitigation AC.
I always thought of the thing about diminishing returns was based more on the change of increase vs percentage of total. Simply meaning, replacing a 73ac aug with an 83ac aug. The 10ac addition is very little when armor slots can have over 1000ac in some items. 5 or 6 expansions ago, if you picked up 10ac from an aug replacement, it was a nice pickup because armor slots were 300-600ac per item. Now it just moves the aug one or two slots away from being next to replace. I'm also using augs as my example because there are not many armor slots in game with different AC values. When you make visable armor, the stats are already set for your class. Now, along with the back evolving item, and including the tank face slot and tank shield as 'normal choices'. It only leaves 3 slots which have an 'option' to choose a lower AC value - Charm, Neck, Range -.
I would be surprised if we saw the opposite. I.e. the break point where AC >= NPC ATK and most hits are mitigated to minimum damage (DB + DI1). Clearly mob ATK is very very high and has been for the past several expacs. This means there is a lot of room to continue to raise AC. It would be interesting to see the same data graphed but rather counting minimum damage hits instead of maximum. As AVG DMG approaches MIN DMG, with more and more AC, the graph will eventually flatten out and then one has plenty of AC. How far back into old expacs do we have to test where we see e.g. 10k AC have this result?
I don't believe the underlying mechanics have changed with the weighted distributions since I was last familiar with them, other than a dev post further explaining how some things were calculated. Assuming level parity, when Real Mit AC = Mob ATK, Min % = Max % = 12.5% (or whatever the number was, it's been many years). Then you would have a gradual bell curve towards the middle where DI 10 and 11 would be about the same, and the distribution would mirror at the mid point. It was not a uniform distribution. As you shifted towards one end or the other, the curve would move but otherwise hold a similar general shape. What changed more was as more hits got shoved past a tail end (min or max), they'd be mapped onto that tail end. That's where we see Min % increasing further with more AC/less mob attack, Max % increasing with the opposite. What we observed during the peak of the research was DI obsolesence where AC past a point would break the DI distribution and not only could you never see DI 20 hits (Max), but you could also never observe all the way down to DI 14. This showed that there was a further benefit beyond average damage intake due to the sheer change in incoming spike damage. A max round was now considerably less, and it's why it's important to look beyond averages alone. I'd imagine, as AC tends to infinity or ATK tends to 0, that we'd see this go further and further until Min %, or DI 1 = 100%, similarly also when ATK tends to infinity and the first few DI values could never happen. At the time we were never able to prove what happens at the extremes, but we were able to prove DI obsolescence in current (raid) content at the time (PoR+). It'd be interesting to compare the distributions nowadays with the crazy AC values that have been achieved.
The damage formula is somewhat linear until you get above the mobs attack power and it starts to level off, here's a simulation with a million hits per run against a mob with 10,000 attack power when the players ac varies between 0 and 20k. It starts to level out a lot after this point. vertical axis is total damage taken, horizontal axis is your ac.
What modelling/data is this sim based off of? Afaik the devs have never disclosed how ATK vs AC computes into the histogram, but I could be incorrect there. The total damage curve's shape against AC is going to be subject to whatever values the DB and DI are. e.g. Txevu Aneuks would be essentially a flat line because their DB was so high and their DI was very low. AC does work on the histogram. It just hardly matters for reducing average inc DPS. Powered up Valik would have been much steeper until it asymptotes given that his DI ballooned. Ghost in Razorthorn would have been a less steep line asymptoting sooner because while the gap between its DB and DI were not that out of the ordinary, its attack was pants. These are old examples because I don't have that kind of data for contemporary things and I'm going off of memory. With an understanding of the general nature of ATK vs AC, you can extrapolate the expected damage taken for any DB and DI values, then multiply that against average swings per round and then knowing how fast the rounds are, convert that into expected inc DPS from melee. You could make a good guess of what a given NPC's real ATK is and work from there. I don't know if we ever came close to achieving that.
Still awaiting an answer! Apologies for some thread necromancy, but I forgot to post some older findings. Sometime in ToL or NoS I was bored and decided to push extremes and see what the limits are, if anything. So I returned to my old friends the Aneuks in Txevu on my SK. They still swing fast and flurry enough to get a reasonable sample despite NPC vs PC level difference hitting the 10% hit rate floor even with your back turned. At some point a ceiling is hit. You will never achieve 100% minimum hits, but it will peak at what I am confident would settle to 75% minimums. The highest DI value that can connect on you will be DI 12 and as it is the very tail end of the distribution we're looking at <1% of the time. We would need a very large sample to get a more concrete %, but it could be 0.5%. What this means is DIs 13-20 are never seen, or in other words, the top 8 hits cannot happen. We can say the same applies in reverse when ATK dwarfs mitAC meaning max hits will peak at 75% and the lowest 8 DIs don't happen. However, short of being blessed with JT buff and tanking raid bosses naked on a caster for hours this isn't feasible to test. Translating this to player damage distributions against mobs, it is messier but the underlying mechanic is still the same. I am skeptical player ATK is so high against NPC mitAC that we have hit that point, but due to the noise, distribution shifts from further ATK gains are harder to observe and so people may think nothing is happening with more attack in current content. I don't believe said limits have been hit. Log examples: 11606 mitAC. 5016 crush swings in 3h 5m. Max DI 12 4194 mitAC. 5030 crush swings in 2h 52m. Max DI 14 I had one at 9349rAC but the log became corrupted and after 9 hours of trying not to kill the Aneuks I went to do something else. It showed similar distribution results to the 11606 mitAC parse. Kicks show a similar distribution to the above with the same max DI roll taken. If my mitAC at level parity was the same I don't believe the distributions would be any different, so I do not believe there is a level difference factor on the final distribution in my experience, just what benefits levels (and skill increases) give you for extra mitAC. What I wanted to glean was at what mitAC vs that mob's ATK the threshold was hit. Given how close even wearing hardly any gear was to as much mitAC as I could muster at the time, I doubt it would have taken much more. Unfortunately I don't have my old posts on TSW anymore where I looked at mitAC increments of 10s and 100s, so I can't relate how much the distribution curve would move and give an estimate of at what mitAC would the Aneuk be at its weakest. Similarly, it would have been interesting to find what mitAC equals its ATK, take samples throughout and then apply that universally so the real value of mitAC at various increments against any mob could be properly given since then it's all about plugging in a given mob's DB and DI and adjusting a distribution based on what your mitAC is. I think my SK's naked mitAC is still higher than the Aneuk's attack, but I would need to check. I do think it's similar to the buffed mitigation raid tanks had in-era, if perhaps a bit weaker. What this shows is that the above "sim" seems off with the claim of a difference happening at a 10k mitAC difference vs ATK when limits appear to be hit much sooner. That chart would significantly plateau at both ends. I may revisit this if I have time.
I wonder if you have the logs still? I'd be interested in looking at the histograms. While they are smaller samples, they're a good starting point to get a decent idea. For example, your 9411 mitAC log should be the closest to where the mob's ATK is close enough to parity with your mitigation given that the max hit is close to 12.5%.
The information for what people believe the damage formula is exists, people are running private servers of EQ, they have what they think the code is. Discussion of this on the forums isn't allowed as far as i can tell though. I am not saying they are dead on accurate, or that they all agree on exactly what it is, but I am using the formula some of them are. The assumptions i made are what I've noticed is roughly common on live current content, db = x, di = x/10. for instance, db = 50k, di = 5k if the mob had 1k attack power, then the peak would happen much earlier of course than when they have 10k attack power. With the parse you showed, in order to get those numbers with 11606 mitigation ac that mob would have somewhere around 1250 attack power. EDIT: you already tested this i didn't look at the second graph, with 1 million hits, you get 0.18% 15's and 0.62% 14's at 4194 AC EDIT: this is at 1250 attack power, which is an assumption on my part of course, the only real point is that the formula is reasonably accurate to what we see on live.
severs are not relevant. They are just a "best guess" at how things might work. There is no way to know if they have it right, they just do their best to make the resulting numbers look similar to live
