Proposed new melee equation

[a_Guest03]

I know I'm cranking out a lot of equations, but I think eqemu is to the point where we can have accurate spawns, aggro, and equations. I keep hearing that it's off, and I can't understand why some of the variables in the current equations exist in their locations... Why would level have anything to do with damage?? Skill has to do with level, so use that variable to replace all references to level. Characters with advanced skill benefits (some monk skills) shouldn't be hampered by their levels.

Anyway, another proposed equation: standard melee equation

Maxdamage = 3 + damagebonus (from weapon) + weapondmg * CUBEROOT(STR^2)*meleeskill)*.05
EDIT: this equation isn't cutting it :P We'll work it out some more and post an update.

I'll keep cramming numbers in to get max damage, and assorted damage sets. The reason I put STR^2 is to punish all wussy casters in melee. No matter how high the skill, they will never succeed. I need data to test this with, and complaints about situations where this data doesn't work.

If anyone thinks there should be a class modifier for the groups, I think that can be arranged. I think basic weapon sets are just more effective for each group. While rogues may not have much strength, they have much faster weapons with good damage.

Give me feedback!!

[Graypaint]

While rogues may not have much strength, they have much faster weapons with good damage.

No to mention they can backstab, although that equation may be off as well, havn't tested it.

Hrmm
So Max dam with a Dmg 12 weapon, using 100 str and 100 skill would be 281.5?
That seems resonable.
958 damage with 252 str and skill(forgot caps)
That looks good to me, considering most times you see a 12 damage weapons it has a decent delay.
Yep yep
(calculations may be wrong, did them as I was going to the doctors office =)

[a_Guest03]

Graypaint, I think your equations are off... I'm seeing 100 str, 100 skill, 12 damage weapon does 63 max damage. Does this seem unreasonable? Assume that's a level 19 guy, with a decent weapon. 63 damage at 19? I think that's fair.

[vetoeq]

Where is attack rating in this? Is it only used to see if you land a hit?

Your damage seems a bit high for a 19th lvl with a 12 dmg weapon, he should see a max hit of around 25 (2xdmg+1) until around 40th level or so (been a couple years since I was that lvl).

I do distinctly remember that each time leveled from around 25-40 my max hit increased by 2 (or was it ever other level it increased by 2?...bah, don't remember)

--
VetoEQ

[Graypaint]

lol I had wrong time for appointment.
Yeah, lemme took at what I did for those equations hehe =)

[a_Guest03]

Would 39 be too high for a level 19 with a 12 damage weapon? I can adjust the equation a bit.

Also, what's the highest hit anyone has seen dealt with a melee weapon without a crit, and what weapon damage was it?

[vetoeq]

I looked at some old logs:

60th level SK with 41dmg weapon and 255str (avatar) max hit for 302. (post 2h dmg upgrade)

Actual weapon in question was rocksmasher.

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VetoEQ

[a_Guest03]

Alright, I didn't know there was a 2hand damage bonus. I'll have to figure that out. Anyway, give me more feedback. I'm changing the equation still... I'm not satisfied that it captures all circumstances. The CUBEROOT and STR squared seem wrong. Caster classes are punished by caps on skills. I need more advice.

[vetoeq]

I never was an expert on combat stats, I left that to the monks/rogues/rangers, they seem very in tune with those stats and their effect. You might try on the Safehouse, Monkly Business or Ranger Glade for some insight, I would think you might get some interesting info from those folks between the spam.

I'll be happy to give as much input as I can from old logs and what feels right, however, my info will be based off when I actually looked at people hitting during groups/raids and those logs.

--
VetoEQ

[a_Guest03]

I DID NOT SOLVE THIS. This was calculated very meticulously by people in the know. Very special thanks to Graypaint for finding this link!

I'm quoting most of it because I don't think many of you will go there to read it. It's very impressive.

http://pub14.ezboard.com/fthesteelwa...cID=1656.topic

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

If you read lower in the responses, you learn that the list is slightly off. I think the DB value needs to have one DI value subtracted to get the correct values.

Can we use this data?

We can redo the database again (yeah, pain in the ass), and use these formulae. Most of the uber mobs already exist here. If we can figure out minimum damage levels for BASIC mobs, then we can resolve the minimum, and if we can figure out maximum, we apply that to the npc_types table. We may have to guess ATK ratings of NPCs.

[vetoeq]

This is VERY good stuff...this is exactly the type of info I was suggesting to go fishing for as I know there are some folks out there that are 'in the know'.

It seems like a very good starting point, if nothing else.

/cheer's to you guys for hunting it down.

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VetoEQ

[a_Guest03]

Jeggred made me a driver to test values. Whatever is missing in the DB, I think we can solve using test values from his driver and logs of real data.

Just an update to what's going on with the equations.

The equation we use to test damage values is:

Roundint(DB + (1-AC/ATK)*randint(1,20)*DI)

DI is a float value truncated to 1 decimal place, loaded from database for NPCs. It is the damage interval. For each of 20 rolls of the "dice", you can multiply that by the damage interval.

DB + (1-AC/ATK) * 1 * DI

will be different than:

DB + (1-AC/ATK) * 20 * DI.

randint(1,20) will give 20 different integers to multiply the damage intervals by, meaning that assuming AC, ATK, DI and DB don't change, attacks have 20 damage outcomes.

DB is an integer, loaded from the database for NPCs. It is a damage bonus, which is should be able to be evaluated using an equation from currently existing values in the database. The NPC will always deal this much damage ON TOP OF what it can get out of the 1-20 roll described above. If Cazic Thule hits you, it won't be for 200, but his DB is 200. His DI is 20. You might get hit for 220 or 240 or 210, but never for DB, always above.

AC is the target's AC. That's pretty self-explanatory. I don't know how we'll solve these for the database yet... It may be interesting. This will apply to PCs and NPCs.

ATK is the attacker's ATK. We'll also have to put these values into the database if they don't exist yet. NPCs will need to have them for this equation to work.

If the equation comes out negative, the hit becomes a miss: Damage won't heal, so negative damage becomes 0.

More to come as we uncover it.

[a_Guest03]

Here is more information we can use to figure out the database values for much of Norrath.

Originally Posted by Serack Doushi of Steel Warriors forum

I am trying to fit this in with some observations of my own.

Soloing through my levels as a monk (just got 150 days played) I found that I could determine what level most of the mob's I soloed were by how hard they hit. The formula for most lower level mobs is

(Max damage - DB)/2 = level

Almost all mobs below 40 have a DB of 2. Several old world mob's that are 40 to 47 have a DB of 27 (giant critters in Perma, Stone spider and Nox in Sol b, and Shady Swashbuckler in EC *117 max hit level 45*)

Untill I read this topic I never had cause to look at minimum damage of these mobs or to figure out a DI. I will start looking at this to determine if I can come up with anything interesting to add to the conversation as it pertains to lower level mobs.

There may be a way to determine the DI of certain types of spawns according to level and type. Like if a drake in ToV is X level it will have this DI and this Max hit. And Veterans in Kael will do such and such...

This should give us much of the values of early level mobs. We can adjust as necessary.

[vetoeq]

Originally Posted by a_Guest03

AC is the target's AC. That's pretty self-explanatory. I don't know how we'll solve these for the database yet... It may be interesting. This will apply to PCs and NPCs.

ATK is the target's ATK. We'll also have to put these values into the database if they don't exist yet. NPCs will need to have them for this equation to work.

Thats supposed to be Target's AC vs. Attackers Attack I believe.

[vetoeq]

GN,

I found this URL that has DB values for delays and level...might be useful:

http://lucy.fnord.net/dmgbonus.html