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Originally Posted by Tugurok and more importantly, Joimster
Restatement of model:
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The damage a mob does on a standard hit is DB + x*DI, where DB stands for Damage Bonus, DI stands for Damage Interval, and x is an integer between 1 and 20 (inclusive)
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Breakdowns:
Damage = DB + (x*DI)
DI (Damage Interval) = (max hit) - (min hit) / 19
DB (Damage Base) = (min hit) - DI
x = integer between 1 and 20, inclusive
min hit = DB + DI
max hit = DB + 20*DI
Modal damage = DB + 2*(Weapon damage).
The model is significant for various reasons:
1. It allows players to empirically evaluate ubermob encounters
2. It allows a means to evaluate the relative value of evasive vs. defensive disciplines
3. It suggests a means to evaluate the relative worth of weapon choice, such as that between 2-handers and 1-handers.
4. It suggests avenues for analyzing the mechanics of AC itself, including possibly the AC softcap
5. It suggests a means to consider mob ATK values.
Some or all of these points are followed up in some of the following quotes. After them, I'll present a condensation of further mob DI/DB values.
For example, Rani then drew out an important result of the finding, which is that it offers a way to evaluate the relative worth of tanking with defensive vs. evasive in specific encounters:
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Wow, an EQ mystery cracked open for all to see. Good job
Your theory holds true for Sontalak at least.
Maxhit = 425
Maxhit with def = 275
Minhit = 140
This gives:
Sontalak DI=15
Sontalak DB=125
One obvious conclusion one can draw from this is that the higher the DI value, the more beneficial it will be to tank the mob with defensive.
Edited by: rani at: 3/13/02 8:00:55 am
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Keple also noted this effect: "so if defensive really divide by 2 the DI (which seems to work with my logs as well), mobs with very low DI and high DB would perhaps be better tanked with evasive...". Besrikarle noted the difficulty in aggro maintenance when the tank is hitting less often (with evasive) as opposed to less effectively (with defensive).
Another inference to be drawn from the model is the effect of mitigation AC, again drawn out by Joimster:
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Mitigation AC should just determine the distribution of hits over the twenty different X values. The distribution would just be a probability for each X value, based on mitigation AC and the mob's attack rating in some way.
For a tank with high mitigation AC, the probabilities would be skewed such that, generally, there is a higher probability of being hit for a lower X value than a higher X value.
And it should also be noted that it is possible to mitigate hits into misses. Go tank a decaying skeleton and you'll see that this is true (you have high mitigation AC, it has a low attack rating).
- Joim
Edited by: Joimster at: 3/15/02 10:47:05 am
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The effect of level and AC on mob attack was discussed. Thresher offered the 3 following inferences:
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Fact: If we chart of AC versus damage we see a curve that always looks the same. Damage reduces slowly until some critical AC value is reached, then drops off sharply for a period of AC increases, then reduces even more slowly after some second AC point.
Fact: There are nearly always clusters in hit graphs at minimum (N = 1) and maximum (N = 20) damage.
Let's suppose that we can look at a hit as having a fixed component above (N = 20), below (N = 1) or in (1 < N < 20), plus a random component that smears some hits over a range that always includes (N = 1) and (N = 20).
Let's also suppose for a minute that Verants' algorithm makes the clusters by rounding hits below (N = 1) to minimum and above (N = 20) to maximum.
Let's lastly suppose that the random component of the hits isn't nearly as sensitive to AC change as the modal hit value.
Then we can infer that if your AC is high enough that the non-random part of hits is mostly BELOW N = 1, you will get the largest spike at minimum damage. This represents a ceiling on mitigation AC, since the random component will always put SOME hits over (N = 1) and reducing hits further below (N = 1) doesn't help. If the random component continues to be reduced even when the modal hit is far under (N = 1), this becomes a soft cap.
Secondly, we can infer that as the modal hit moves through the range (N = 1) to (N = 20), we see the 'sharp dropoff' effect that so many people have reported in the AC 700 to 1200 range.
Thirdly, we can infer that if the modal hit is often over (N = 20) most times, you see the big spike at max damage. This represents a floor on AC, which has been observed but never really commented on. Since at (N = 20) the random component will ALSO be large, we find that the floor is softer than the ceiling.
It's just a hypothesis. Have fun tearing it apart.
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Soru considered the distribution of probabilities of DI as a means to explain results found in charts of damage present by Axantur, which were not bell-curved shaped as might be thought:
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K1% chance of hitting for DB + DI (min hit)
K2% chance of hitting for DB + random(20) x DI (normal hit)
K3% chance of hitting for DB + 20 x DI (modal hit)
K4% chance of hitting for DB + random(20) x DI + random(20) x DI x SF (bonus hit)
Its the K4 region which is not present in MOB attacks. It forms a shallow bell curve on either side of the modal hit, implying it is formed from the sum of two random rolls. SF it the strength/level factor that accounts for high level ogres hitting harder than low level wood elves with the same weapon.
It overlaps with the K2 hits, which explains the sawtooth pattern on the left side of the modal hit.
Open questions:
what causes K1, K2, K3 and K4 to vary? Strength, level, buffs, AC, disciplines, debuffs, etc?
what is the formula for SF?
horrible thought: is the fact that mobs don't get bonus hits a bug?
Soru
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Another important contribution came from Gjin LoL, in extending Joimster's model to consider mob ATK values:
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See if this makes sense to yall.
First assume NPC's act in most ways like PC's except they aren't level restricted and have some AI behind them.
Second assume that the equation given for damage: DB + x*DI, where DB stands for Damage Bonus, DI stands for Damage Interval, and x is an integer between 1 and 20 (inclusive), is the same for NPC's as it is for PC's.
The mystery is X. Lets assume that X is a function of:
- Class
- a mitigation factor (ac)
- attack value
Lets assume class is some constant, the money question of course is, how do Mitigation AC and ATK relate? This is what has been asked since the dawn of time.
Lets assume that Z = (1 - AC/Atk).
AC = players Mitigation AC (best case right now is about 1200, which would be about 1750 displayed in inventory)
Atk = Mobs Attack (assume 2000 is max)
Z indicates how well (or badly) a PC can tank.
Example 1:
Best Mitigation AC = 1200
Best Mob Atk = 2000
Z = (1 - 0.6) = 0.4
Take Z times the range, Z*20 = 8. Assume this value is your modal on the bell curve of X probability, you get the following modal hits using the equation provided by Steel Warriors:
Cazic: 360 Damage per hit
Yelinak: 300 damage per hit
This indicates the best case tanking of the mobs above (no defensive).
If Mitigation falls off, lets say to 1000, the modal values become:
Cazic: 400
Yelinak: 350
Now take the monk class which probably has about 800 Mitigation AC with stellar gear, you have the following modals:
Cazic: 440
Yelinak: 400
This is of course assuming both CT and Yelinak have 2000 attack. Those numbers are per hit modal values. Whats really cool is that you can figure out exactly what CT / Yelinak etc, atk rating is:
Atk = MitAC / ((1 - (ModalHit - DB)/20*DI))
Where MitAC is your mitigation AC
Modal Hit is the modal damage done to you by the mob, from a log file
DB is already provided for CT, Yelinak, and mobs in the thread
DI is already provided for CT, Yelinak and the mobs in the thread
Now whats really really interesting is you can use this exact same formula to determine what damage you do to mobs.
Assume that Creator has 2000 mitigation AC and the best player character (while cursed) has 1200 ATK. Also assume that Z can never be less than 1, and you get:
Z = 1, which means PC damage to Creator will be modal around the dmg bonus + DI which is 13 dmg (1hndr - main - 20 delay). Which means 50% (bell curve) of hits are 13 damage.
This is verifiable with a log parse. But this seems true based on our fights with him.
By the same token you can determine what the Creator's AC is by:
Atk(1 - ((ModalHit - DB)/20*DI)) = AC
Where Atk is your atk,
Modal hit is your modal hit
and AC is the Mobs Mitigation AC.
Would be interesting to plug these into a few log parses and see what comes out.
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I'm not sure if this part has been followed up on, but perhaps that would be useful.
Gjin followed that up with:
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I'll throw out my last supporting factor for my equation, and I think this might sway you guys.
You remember when we had Broca's thread on ac, and in the discussion we mentioned a warrior tanking Yelinak. Anyway, he got between 3-4% AC effectiveness for 100 ac added.
Also you remember many many posts that say that only after adding an incremental amount of AC (usually 100) that a difference was made in actual effectiveness?
Allright here we go ....
Example Cazic:
Warrior 1 Goes from a 440 (800 mitAC) to a 400 (1000 mitAC) modal hit on Cazic. This is an increase of 200 AC: which is 4.5% tanking increase per 100AC added. Ref. Yelinak post.
The big scary last point:
To go from a modal 8 to a modal 7 in X probability, use the following formula for Cazic:
Modal 8 was shown to be 1200 Mitigation AC in my above post. To be a better tank and get your Modal to Modal 7, you need:
(1 - AC/2000)*20 = 7
Solving for AC yeilds ...... 1300.
The step difference between Modals (8 to 7, 7 to 6) are in 100 AC increments.
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The following is an alphabetical list of mobs with DB and DI values collated from various posts (with thanks to the authors, who will not all be cited here, though special props to Fulorian Cavestomper):
SNIP VERY LARGE AND VERY THOROUGH LIST OF UBER MOBS
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