Damage Formulas

[Conqueror]

Originally Posted by StormGuardian

** Note there is NO cap of x1.5 for archers

There has to be a cap.
Experimentally, the maximum hit does not increase indefinitely as S is increased. I am pretty sure about that. Without a cap, the damage of the maximum hit would increase indefinitely.

Originally Posted by StormGuardian

This will get you very close, but a few ppl that I'm getting numbers from are reporting only slightly higher numbers than this formula gives...which *might* mean that you take the higher of int or cnc, but i'm not sure. Obviously you can add in archer bonuses to max damage(as follows) and runes.

Two things:

(1) Glitchless has mentioned previously that the average of int + cnc is the quantity that is considered

and

(2) If the one that was higher was being considered, people with lets say 500 cnc and 100 int would be doing a lot more damage than people with 300 in each which does not appear to be the case.

Originally Posted by StormGuardian

z = y * ( 1 + (0.05+0.00025*CE)*(1 + 0.01*CS))

Either you left out sc or the y is a Y.

Originally Posted by beetdabrat

I'm still working on the archery formula and i'm not sure exactly how its done yet, but was testing and was getting higher hits than would be calculated with avg cnc and int. I also thing the arrow and bow are done seperately then added at the end.

Beet Da Brat

Is it possible that your results are higher than expected because you are not accounting for the archer class bonus properly ?

Archers receive a bonus to maximum ranged damage which, I think, should be considered in the non crit values at the beginning (your formulas don't seem to do so; they leave room for the class bonus at the end; it might be possible that the crit values are working on the class bonuses and not the other way around).

It might be best to test out the archery formulas with a vamp bow user or someone who does not have any ranged damage bonuses.

Just a hypothesis

Cheers

[StormGuardian]

Originally Posted by Conqueror

There has to be a cap.
Experimentally, the maximum hit does not increase indefinitely as S is increased. I am pretty sure about that. Without a cap, the damage of the maximum hit would increase indefinitely.

Believe me, I thought this as well for a VERY long time(and still think so to a degree), but from the numbers I've gotten the ONLY way to even come close to the max hits being reported is to throw out the cap. It's all still a theory, but hopefully we can find it soon!

Originally Posted by Conqueror

Two things:

(1) Glitchless has mentioned previously that the average of int + cnc is the quantity that is considered

and

(2) If the one that was higher was being considered, people with lets say 500 cnc and 100 int would be doing a lot more damage than people with 300 in each which does not appear to be the case.

I agree with number 1, this is why i said *might*, because that would be another way to increase maximum possible damage...still only a theory of course.

I also agree w/#2, I havent noticed a huge difference based on total, again, I dont have a 20+ lvl archer, so cant do too much testing on my own. Ergo Im having to have numbers reported.

Originally Posted by Conqueror

Either you left out sc or the y is a Y.

This was in reference to a NON-CRIT hit...sc is added in for the crits.

For crits, take that z(max non-crit for archer):

Z = * (1.5 * (1 + (sc / 1000)))

Z = max crit for archer

Originally Posted by Conqueror

It might be best to test out the archery formulas with a vamp bow user or someone who does not have any ranged damage bonuses.

Totally agree, that's why BdB didnt have archer bonus in his formula, and why I added it in as separate. My only archer atm is a rogue, so no worries there

Thanks for the input though, we'll nail this down soon enough

[Thomas Jordan]

I have been following this discussion with great interest. My observations about damage do not seem compatible with any of the formulas presented thus far.

Data set 1:
Level 47 Trapper (no archery bonuses).
Level 58 archery.
Level 58 bow and arrow (127 + 102 = 229 maximum damage).
All archery support skills level 47.
Intelligence 111
Concentration 329

Data set 2:
As above
Intelligence 106
Concentration ~ 135 (equipment stats and enchantments)

Data set 3:
As above
Intelligence 225
Concentration 224

Using all three data sets, my observable normal maximum damage against all mobs from the Traveler's Way to the Saltlands is approximately 470, with critical damage as high as 530. The data set testing occured this morning in the Snake River, when I redistributed my magic stats.

The observable maximum, mean and minimum damage did not change across these three data sets in the Snake River. The maximum remained around 470, and the mean (and median) remained around 235. Redistributing intelligence and concentration did not effect damage.

This would seem to eliminate any speculation that the damage formula is using either the minimum or maximum value of intelligence or concentration. If it is using anything, it is using the mean of the two values.

This testing also calls into question whether or not the damage formula is using intelligence or concentration at all. Data sets #1 and #3 each had a mean of 220 and 223 respectively. Data set #2 had a mean of approximately 120. The observed damage was the same for all three data sets. This implies that a mean of both 120 and 220 are either too low to have any effect on the damage calculation, or both values exceed some constant contained within the formula.

Since the observed maximum damage was around 470, this implies the formula is simply multiply maximum bow and arrow damage by a factor of approximately 2. Intelligence and concentration are not considered.

Nor does mob level appear to be considered in calculating maximum damage, although it does appear to be considered in calculating mean damage. The mean damage against level 44 through 54 mobs is approximately 235 (with slight variation between the higher and lower levels of this range). The maximum damage on the Traveler's Way remains at 470, but the mean damage is around 330. Mob level is clearly affecting the mean damage (and it clearly affects hit probability, which is outside the scope of this reply).

I have rarely fought mobs level 60 or higher primarily because I do not seem to hit them often enough. When I have, my mean damage is around 120. The low hit probabiity combined with the low damage renders such fights a waste of rested time.

While the mean damage against mobs level 44 through 54 is around 235, so too most of the damage is fairly close to that value. Extremes do occur, reaching close to 470, and as low as around 20, but the vast majority of damage is in a fairly tight range around 235. This implies the damage formula is using a standard distribution based upon the difference between character level and mob level, producing a bell-shaped distribution curve. Mobs well below the character level receive increased mean damage, and mobs well above the character level receive decreased mean damage.

If these observations are valid, then archery is either not using intelligence and concentration at all, or requires considerably more than I have.

TJ

Archers receive a bonus to maximum ranged damage which, I think, should be considered in the non crit values at the beginning (your formulas don't seem to do so; they leave room for the class bonus at the end; it might be possible that the crit values are working on the class bonuses and not the other way around).

Glitchless stated that class bonuses are multiplied at the end, for maximum effect.

interesting you seemed to have gotten approximately the same damage with very little conc/int

has any one considered the possibility that there is simply an unknown multiplier for the mean of the 2 values. it always seemed illogical to me that you would get the same % increase when you are using twice the stats even if it does let you use a gem or 2 more effectively it just didn't seem worth it.


maybe the unknown multiplier is dependent on lvl after all you dont see low lvls doing double there max dmg with stats just over 100 like TJ has

[StormGuardian]

thanks TJ for that info, could you answer 1 question for me. was your dex the same the whole time? aka your ~300?

if everything you say is accurate, and nothing else changed, then the only thing that comes to mind, is it's possible that dex determines max damage, and int/cnc the average damage.

still tho, there wouldnt be a x1.5 cap if you're hitting 470s instead of ~345 as you should.

[Thomas Jordan]

StormGuardian:

My dexterity remained constant during this experiment at 302.

I just played for a few minutes, hiking from Crella along the Snake River (level 50 & 51 mobs with a 52 boss) to the Saltlands (level 52 & 53 mobs, with a 54 boss).

My most frequent normal damage number was 236 against all of these mobs, with most other damage numbers within plus or minus about 30 of that. High damage right now was about 450. I didn't pay much attention to very low damage, and that gets hard to separate from my pets anyway. The second most frequent damage number was 235.

My most common critical hit damage was 476, almost exactly 1.5 + my serial criticality value times the 236 normal damage number.

I am wearing full 39 epic armor, which increases the probability of critical hits, and using the 58 bow set, which also increase the probability of critical hits. Additionally, I am using a critical rune, which further adds to critical hit probability. My other two runes are swiftarrow to increase bow attack speed and ironclad, to increase my armor class.

As I stated earlier today, the only thing that changed across the three data sets was the redistribution of my magic statistics. Data set #1 was my original, with a mean of 220. Data set #2 was while I was after I had zeroed out those stats (mean around 110), and data set #3 was after I redistributed the stats to obtain a balanced intelligence and concentration.

Oh, one slight change. I did gain a level in magic during these experiments, so data set #3 does have 3 more stat points than does data set #1 and #2.

TJ

[Conqueror]

Originally Posted by StormGuardian

z = y * ( 1 + (0.05+0.00025*CE)*(1 + 0.01*CS))
Z = z* (1.5 * (1 + (sc / 1000)))

These two formulas give results that are the closest to my actual values. Had a 2% error on the second formula. Not sure about the first but it was slightly off too.

And these formulas don't even account for int and cnc.

From TJ's post, it seems that int and cnc are increasing average damage, and not maximum damage.

[StormGuardian]

Thank you TJ and Conqueror for both your inputs. I think I've decided(after careful rereading of the descriptions of dex, int, and cnc, I'm gonna go with(for now at least) that indeed dex does determine the maximum damage, with (int+cnc)/2 being used in the equation to determine how likely you are to do maximum damage. Reasoning falls with TJ's data as well as 2 sets I have from ppl I've been getting numbers from ingame, and the descriptions of int/cnc which read, "int/cnc is also important to archers who rely on it and cnc/int to determine their chance of dealing full damage." Says nothing about increasing max possible damage(on this note, str says nothing about increasing max possible melee damage either...interesting ).

TJ's bow+arrow damage of 229 is getting roughly multiplied by 2 b/c his dex is twice (100+mob lvl)...~300 vs ~150, 229*2 = 458, which is very close to his observed max. So that makes me think that if anything, dex is the determining factor of maximum bow damage, which again, has no x1.5 cap. Then add in runes, class bonus for archer, etc to adjust for max damage.

I'm gonna ask both of you to continue watching your max damages, and to keep crits/non-crits separate, also keep mobs near your lvl and greys separate, and keep reporting anything unusual. We can nail this down

Btw, conqueror if you use a rune of pain, that 2% might be accounted for, just a thought.

Edit: ok just went over numbers with a ranger class...and the old formula, using (int+cnc)/2, WITH the cap of x1.5 seems to be holding with him. I asked him to watch numbers over the next few days and let me know how well that holds. There is a slight chance that formula could be different for archer/ranger/non-archer,non-ranger, but i highly doubt it, cause that would just be silly(besides archer/ranger class bonuses of course)

Reviving thread as im making some numbers... on accuracy for crush i dont see dex in anywhere.. is that correct?

[beetdabrat]

Ok try this.

bx = bow min
by = bow max
ax = arrow min
ay = arrow max
d = dex
m = mob level
sc = serial crit level
ce = class enhancement level
cs = class spec level
ab = archer bonus = 1 + ((1 + (ce / 200)) * (1 + (cs / 100)) * 0.05) = 1 if not archer
rb = ranger bonus = 1 + ((1 + (ce / 200)) * (1 + (cs / 100)) * 0.08) = 1 if not ranger
r = rune of pain = 1 if not linked

Weighted Bow Min = WBX = bx * rb * (1 + r / 100)
Weighted Bow Max = WBY = by * min(2, d / (m + 100)) * ab * (1 + r / 100)

Weighted Arrow Min = WAX = ax * rb * (1 + r / 100)
Weighted Arrow Max = WAY = ay * min(2, d / (m + 100)) * ab * (1 + r / 100)

Critical Bow Min = CBX = WBX * (1.5 * (1 + (sc *15) / 10000)
Critical Bow Max = CBY = WBY * (1.5 * (1 + (sc *15) / 10000)

Critical Bow Min = CAX = WAX * (1.5 * (1 + (sc *15) / 10000)
Critical Bow Max = CAY = WAY * (1.5 * (1 + (sc *15) / 10000)

Total Weighted Min = WBX + WAX
Total Weighted Max = WBY + WAY

Total Critical Min = CBX + CAX
Total Critical Max = CBY + CAY

Please let me know if these are accurate,
Beet Da Brat

but that is for bow users, i was actually referring to a CRUSHING accuracy.. is it ok that no dex is considered?

[beetdabrat]

Hehe sorry that wasn't in response to your post. Dex can be used in the accuracy for crushers but it isn't as important as it is for slashers.

Dex would be good for parries when using crushers.

Beet Da Brat

thx

[StormGuardian]

BdB, the only problem i see with you new post is the min(2, d/(m+100)) part...now...i dont use a bow very much, only have one that uses a bow atm, but i've never hit more than 1.5*(bow max + arrow max). Plus I'm still not sure why you're using dex instead. Someone(you may have already) should try only lvling dex to use with their bow and see if they can hit higher than max? With no CE/CS for archer class of course. I still feel like it's int/cnc average vs (100+ mob), but that's just me.

[Thomas Jordan]

I'm not archer class, so I don't receive the archer class enhancement and specialization bonuses.

The maximum printed damage on the 58 bow and arrow is 127 & 102. Add those together and multiply by 2 and you get 458. I have hit for exactly that numerous times (against lower level enemies), but I have never hit for more than that, leaving aside critical hits and when I'm using a pain rune.

So for archery at least, potential maximum damage is twice the printed bow & arrow maximum damage.

Intelligence (Int) and Concentration (Cnc) influence the probability that each hit does high damage. The higher your combined Int + Cnc, the greater the chances of doing higher damage. Personally, I have found that keeping Int & Cnc about the same provides consistent results (all the hits do similar damage) as compared to high Int / low Cnc or high Cnc / low Int, which produces erratic results. Some hits with the high / low combination are quite high, while others are quite low. The median results from the high / low combination are about the same as the median results from the even (or nearly even) combination.

Mob level compared to your level also influences damage. Up to about +6 the negative effect isn't too bad. Beyond that, and damage really falls off rapidly. I have killed bosses at +10, and regular mobs at +20, but it took forever. My perception was that flaming arrow and poison arrow were doing more total damage to the mob than the actual arrow damage was inflicting. I haven't fought too many fights against mobs that much higher than myself, so that perception may not be very accurate.

I do not have a feeling for how much Dexterity (Dex) influences accuracy. Mine is currently 350, with excellent weapon accuracy and Level 57 Trained Eye. My accuracy begins to suffer at about +8 or +9 mobs. For those I have to add an 4++ Rune of Accuracy to have much hope of hitting enough times to cause serious damage.

These observations are based on PVE. Against PVP, it appears to be enemy armor class that influences damage inflicted, and nearly every shot hits (discounting parry, block, etc by the opponent).

TJ

[StormGuardian]

Good to know TJ, perhaps once the average of cnc/int is double that of mob+100, that's where the max is then.

Weird tho, that every time I hunt with lvl 0 bow/arrow(max damage 6), I never seem to hit for more than 9 when killing mob unless i crit(proc from epic legs as crit shot/serial crit is 0), I've hit as high as 14. Fighting in Tway with 200+ int/cnc...interesting indeed. I'll keep watching it

[Conqueror]

458 seems really low TJ.

It has been a long time since I used the 58 set but I remember that I could almost crit around 600 with the 58 archery set without any runes.

I also remember that I was critting above 600 with the 48 bow and the 58 arrow. Again, I can not give exact numbers because I do not remember them.

EDIT: Nvm. You meant non crits. I didn't see that. But how can you have a 458 non crit with the 58 set without the rune of pain.
Seems a bit high to me. Especially for a non archer.

At some point when I have spare gold, I will redistribute dex and give this a shot. I have a hunch that dex does not have much of an impact on damage.

[lankas]

ok, I am archer, so I need write some tests here which I did weeks ago.
first, stats:
CE 92, CS 86, SC 87, atm int+cnc=750. using rune of pain 4++
Best crit 1084
using 99 rare archery set.
I tryed everything to increase my max crit dmg, cause I knew that ghosttamer did 1k+ crits too, but she is vampire, no archer bonus.
I maxed my cnc, didnt worked, maxed int - same result, average cnc and int - same result, dex over 500 - same result. Increased cnc + int almost to 900 - same result.
cant figured out why I am lack in dmg, I farmed like 500 hours of rrt, I did like 10 times 1084, but no more.

maybe you guys can tell me what I am doing wrong

[Thomas Jordan]

Conqueror:

I'm too lazy to take screen shots, but yes, I do 458 non-crits against low level mobs without a rune of pain. On rare occasions I've done almost that well against mobs around my level. So I am very confident that potential maximum damage is twice the maximum damage of the bow plus the arrow.

Stormguardian:

My combined Int & Cnc is 664, or 332 median. That is already more than double a level 116 mob +100, so I seriously doubt there is any upper limit on Int and Cnc. Every time I add a few points to Int or Cnc median damage against the same level mob does show a slight increase. I'm currently fighting mobs ranging between level 66 (+3) to level 69 (+6), with an occasional venture into a much higher area just for some variety.

Since posting earlier this morning I've really been paying attention to my median damage against this range of enemies. As simplistic as this sounds, it almost appears that every level increase in mob level reduces median damage by 10% for a maximum penalty of 95% (sound like a familiar formula to anyone?). I ran over to Mt. Whitecap for one quick (well, not really so quick) fight and did about 24 median damage when I managed to obtain a hit (with rune of pain). That's right around the expected value of 0.05 X (458 X 0.06), or 95% penalty. It's also consistent with the results Destruction noted in his topic about fighting +15 bosses. He noted typical non-magic damage was in the 20s.

TJ