How to Calculate your Maximum Damage

If you are interested its worthwhile reading the following stuff. The quick answer is:
Remember the formula for MAX:

[(Weapon Skill + STR)/100) * DMG] + Level Damage Bonus
We're talking about pre-20th levels, so Level Damage Bonus is zero.
DMG is the amount of damage your weapon does.

So figure the following formula:
[((Weapon Skill + STR)/100) * DMG] = 29

29 is the cap for damage for people under level 20. This was done to reduce the effect of twinking.  Twinking is giving your or someone else's low level character high level weapons in order to make them level quicker.

The max damage you will get under level 20 for your weapon is 29.  Strength and Weapon Skill directly affect the amount of damage you can do.  So if you are not getting 29 damage in a hit you have to increase strength, skill level, and the damage stat of your weapon.

BenJones
Station Member posted 01-11-2001 07:31 AM

But my 2H sword says its damage is 12. But I hit for a lot more damage than 12. I know my level and skill level in 2H slash have something to do with it. Does a high strength mean more damage or does it mean that the chances of you getting the max damage is more likely? How do I determing what my max damage will be?

BenJones
Station Member posted 01-12-2001 10:54 AM

Axterix
Station Member posted 01-12-2001 11:04 AM

Hi!

For those of you who haven't been reading the So, Stat Buffs Are Useless? thread, I'm Ruatha! I'm a 46th level Gnome Warriorette from the Brell Serilis server!

/wave

I'm also a big math geek, and I love to poke at the innards of the EQ Combat Engine with my +3 Sharp Stick of Poking and Annoyance(tm) to figure out how it works. As a Warrior, the EQ Combat Engine is REALLY important to me, because the more I know about how it works, the more I'll know about how to make myself a better warrior. And as a Gnome Warrior I have a vested interest in knowing how stats like STR and DEX and so on affect melee. This is because we Gnome Warriors, while being some of the brainiest Warriors around, don't have a real robust physique. (I'm a Warrior. With all my gear on, my STR is 110. My INT is 119. Think of me as the brainy little kid down the street, only heavily armed and armored.) So I need to know as much as I can about how stats affect combat so that I can buff up the important stats with gear and ignore the unimportant stats.

So in that thread I mention above, I've been having a blast talking about all kinds of math geekery and stuff. But there were some comments made and/or questions asked by some of the other posters in the thread that made me think that maybe it would be useful if I did a complete brain dump on what I know about how the EQ Combat Engine works, along with some spiffy graphs to provide visual aids. Then maybe the math geeks in the Shaman community could throw in THEIR knowledge, and we can push the "frappé" button and see what comes out! (If you already know all this stuff -- and I figure most Shamans do 'cause they wanna know how buffs work -- then you can just skip on to the next message or something.)

FIRST GRAPH
This is a Damage Profile for a Journeyman's Walking Stick (DMG 9, DLY 24) as wielded *mostly* in my primary hand.

I dual-wield 99% of the time. My other weapon is a Kunzar Ku'Juch (8/22). When I log a combat session, the hits from the Journeyman's Walking Stick are mixed up with the hits from the Kunzar Ku'Juch. However, since the JWS is a 1-hand Blunt weapon and the Kunzar is a 1-hand Slash weapon, I can go through my logs with a text editor and remove everything but the hits from the weapon I'm analyzing. Which is exactly what I did to get the graph above.

Before explaining the graph in detail, let's talk about the Level Damage Bonus. For those of you who don't know, Hybrid and Fighter Classes get a Level Damage Bonus. This bonus is different for 1-handed weapons vs. 2-handed weapons. For 1-handed weapons, the Level Damage Bonus is calculated by the following formula:

Level Damage Bonus = (Level - 25)/3

This bonus is added to every successful hit made by the primary hand starting at 28th level. The offhand doesn't get the bonus.
As a 46th level warrior, my Level Damage Bonus is (46 - 25)/3 == 21/3 = 7. So every successful hit done by my primary hand has 7 points of damage added to it.

So! Let's look at the graph. The things that might immediately jump out at you and grab your attention are:
1) The prominent peak at 25.
2) The secondary peak at 8.
3) The smattering of hits along the range 1-7.
4) The smattering of hits along the range 35-73.

Let's take a look at these in turn:
The prominent peak at 25 is what we call the "Magic Number." When you're fighting blues, it is the number which will receive the largest number of hits. It turns out that if you're fighting blues, you will hit for the Magic Number approximately 12-13% of the time. It also turns out that the Magic Number can be precisely calculated by using this formula:

Magic Number = [(2 * DMG) + (Level Damage Bonus)]

For Fighter/Melee characters below 28th level, the Level Damage Bonus is zero. So the Magic Number for these characters is simply (2 * DMG).

The Journeyman's Walking Stick has a DMG of 9. According to this formula, and recalling from above that my Level Damage Bonus is 7, then my Magic Number will be [(2 * 9) + (7)] == (18 + 7) == 25.

And sure enough, the biggest peak falls on 25.

The second-highest peak on the graph falls at the Minimum Damage Number (aka MIN). MIN can be precisely calculated using the following formula:

MIN = 1 + Level Damage Bonus

According to this, my MIN should be 1 + 7 = 8. And sure enough, the second-highest peak on the graph falls at 8.

At this point, the quick-thinking among you will be wondering: "If your MIN is 8, why do you have a few hits along the range 1 to 7?"

Those hits happened during a few combats where, for tactical reasons, I switched my weapons around. So for a few combats, I had my JWS in the offhand. The offhand doesn't get the Level Damage Bonus, so the MIN for the offhand is always 1. Unfortunately, there wasn't an easy, consistent method of removing those few combats where the JWS was in my offhand. So I left 'em in. So just pretend that those few hits from 1 to 7 aren't there.

Next, you will notice that the majority of hits fall between these two peaks in a roughly (VERY roughly) even distribution. I say "even" because the lesser peaks between MIN and the Magic Number are almost always compensated by "valleys". In other words, there is a small peak at 12. But there's a "valley" at 9, which tends to even out the peak at 12. This becomes most evident when you use a weapon with a high DMG rating. There are prominent spikes along the graph from MIN to Magic Number, but between these spikes are relatively few hits.

Above the Magic Number are two types of hits, one type of which is exclusive to Warriors.

The hits above the Magic Number that are exclusive to Warriors are Critical Hits and Crippling Blows. According to Verant (so take with a grain of salt), the minimum value for a Critical Hit is [(2 * DMG) + 1 + Level Damage Bonus]. A Crippling Blow is a Critical Hit that occurs after the Warrior has gone berserk (which occurs when the warrior hits around 1/3rd of their total health). According to Verant (more grains of salt), the minimum value for a Crippling Blow is [(4 * DMG)+ Level Damage Bonus]. Crippling Blows also have a chance to stun the MOB.

They also don't occur very frequently. 1-3% of your total hits is the usual number given. You'll hear a lot of Warriors refer to Crits and Crips as "eye candy." The graph above shows why. All the hits from 36 to 73 on the graph are crits/crips. Some of the hits from 33 to 35 are also crits. Compare the scattering of crits and crips to the huge bulk of hits from 8 to 34 and you'll see that crits and crips don't affect a Warrior's average damage output to any significant degree.

The second type of hits that occur above the Magic Number are the hits that range from (Magic Number + 1) to the Maximum Damage (aka MAX). These are the hits that will be of the most interest to Shamans. Why? Because these hits (and these hits alone) are the ones that are affected by STR.

The value of MAX can be calculated by this formula:

MAX = [((Weapon Skill + Strength)/100) * (DMG)) + (Level Damage Bonus)]

My 1HBlunt skill is 200. My STR is 110. The JWS has a DMG of 9. My Level Damage Bonus is 7. So according to this formula, my max damage for the primary hand wielding a JWS should be:

[((200 + 110)/100) * (9)] + 7 == (3.1 * 9) + 7 == 27.9 + 7 == 34.9

Fractions are dropped, so my MAX with the JWS in my primary hand is 34 points of damage. You will notice that there is a small amount of hits at 35. This is because for some of these fights I had the 10-point Necro STR buff, which put my MAX at 35. But for the most part I was fighting at 110 STR, putting my MAX at 34.

Referring back to the So, Stat Buffs Are Useless? thread, a 67-point STR buff would have the following effect:

[((200 + 177)/100) * (9)] + 7 = (3.77 * 9) + 7 = 40.93

Again, the fractions are dropped, so the 67 point STR buff moves my MAX from 34 to 40.

What the 67-point STR buff doesn't do is affect any of the other hits from MIN to 34. Higher STR doesn't weight your hits towards the higher end of the spectrum. It simply extends the total range of your possible hits by increasing the value of MAX.

This is evident by the fact that graphs of weapons with the same DMG rating look more or less the same, with the exception that higher STR produces a higher MAX. In other words, let's say that I had the 67-point STR buff. As I mentioned earlier, that would put my MAX at 40 instead of 34.

If I were to log my combats with this buff, and if I then edited the log with a text editor to remove all the hits for 35 and higher, the Damage Profile that would result would look more-or-less identical to my Damage Profile above (except, of course, for the errant hits from 1 to 7).

This bears repeating, because it's crucial to understanding how STR affects melee. So consider another example:

Pretend I'm a 46th level Ogre Warrior with the same gear, but with 255 STR. 255 STR would put my MAX at 47. I go off and log my combat sessions. After I'm done, I go into the logs with a text editor and remove all the hits higher than 34. Then I create a Damage Profile.

If I did this, you would not be able to tell from looking at the resulting Damage Profile that my STR was really 255 and that I edited out the hits above 34. The graph would look more-or-less identical to a graph generated by a 110 STR warrior using the same weapons.

If you'd like proof, here's a Damage Profile taken by Copeland, a 52nd level Warrior with 203 STR using a Lamentation (DMG 9) in his primary hand:



Knock off the stuff on this graph at 35 and higher, knock off the hits from 1-7 and everything above 35 from my graph, and you'll have two graphs that look roughly the same.

Why is that important? Because what it means is that as a total percentage of your damage output, a STR buff only gets you the extra points above your unbuffed MAX. Look at my graph from 8 to 34. Note that if I were 52nd level, the whole graph would be shifted up 2 points. So pretend that the range runs from 10 to 36 instead of from 8 to 34. Now look at Copeland's graph from 37 to 46. Pretending for a moment that I'm 6 levels higher, the only thing Copeland's extra 93 points of STR gets him over and above the damage I put out are the points along the range from 37 to 46. His Damage Distribution from 10 to 36 will look more-or-less identical to mine.

SHAMAN MELEE
Thanks to the logs Arkand provided in the So, Stat Buffs Are Useless? thread, I was able to generate Damage Profiles for Arkand's 52nd level Shaman. They answered several questions I had. Thanks again to Arkand for putting them up.

When I first looked at them, I noticed that they all had huge, prominent peaks at 1. I was puzzled by this...until I saw a line in one of the logs that said "You bash a seafury cyclops for 1 point of damage!"

As a Shaman, Arkand's Slam skill will never increase. And it will never do more than 1 point of damage. Once I figured THAT out, I went into the logs and removed all the Bashes. After that, the logs made much more sense. =)

Here's his Damage Profile from his first test (where he cast "Strength" on himself):


Interesting things to note:
1) Shamans don't get a level damage bonus (which all of you probably knew, but I didn't )
2) The shape of this graph is roughly (very roughly) similar to the two graphs of my weapons and the graph of Copeland's Lamentation. The reason this particular graph is so "jagged" is because there are less data points overall. My first graph represents 3732 total hits. Copeland's graph probably represents around 5000 hits. This graph of Arkand's first test represents a total of 282 hits. As the number of hits increases, the graph becomes smoother and begins to look more like Copeland's.

Be that as it may, you can still see the rough outlines of the same shape that you see in my graphs and Copeland's graph.

In particular, there is a prominent peak at the Magic Number (16), a secondary peak at MIN (1), a distribution of points from MIN to Magic Number, and a smattering of hits from (Magic Number + 1) to MAX.

This suggests to me that the engine which drives the damage distribution of Shaman melee works just like the engine that drives the damage distribution for Fighter/Hybrid melee. This doesn't mean that Shamans can melee as well as Fighter/Hybrid classes. Shamans don't get Double Attack, nor Dual Wield, nor the Level Damage Bonus. All of these things will conspire to keep the total damage output of Shaman melee far below the damage output of Paladins and SKs, much less Warriors, Rogues, Monks and Rangers. It DOES mean, however, that when a Shaman makes a single successful hit, the mechanism which determines how much damage that hit causes to the MOB is the same mechanism (minus the Level Damage Bonus) that makes the same determination for Warriors, or Paladins, or whatever.
Here's the Damage Profile for Arkand's 2nd test:


This is the one that really got my attention.
Note that the primary peak is NOT the Magic Number. It's the MIN. Why? Because in this test, Arkand's 1-hand Blunt skill didn't get any higher than 150 *and* he didn't cast STR on himself to make up the difference. Note that the Damage Profile for Test 4 exhibits the same behavior -- which is also a test where he didn't cast the STR buff on himself.
Note that the damage distribution of a Warrior fighting red MOBs exhibits the same behavior.
Congratulations, Arkand. You've successfully proven that, at least in terms of Damage Distribution, fighting a blue with a low weapon skill does indeed simulate the damage distribution of fighting a red with a high weapon skill. =)
(However, since you didn't log your misses as well as your hits, we have no idea what your hit/swing ratio was, nor do we know how accurately it simulates fighting reds.)
Here's one last Damage Profile from Arkand. This is from his 3rd test, where his 1HB skill ranged from 154 to 160 and where he cast the 67-point STR buff on himself:



The conclusions that can be drawn from this graph are left as an exercise for the interested reader. =)

It seems that if you raise strength, it will increase your maximum damage primarily, but will leave the rest of the distribution pretty much the same. However, if you raise your ATK rating via a spell other than strength, it will greatly affect all parameters of combat, in your favor.

I think this is more easily explainable by the simple fact that the two ATK buffs essentially compensated for your 175 weapon skill.

Consider: We have a 39th level Warrior with a STR of 100 and a 1HSlash skill of 200. We also have a 39th level Warrior with a STR of 200 and a 1HSlash skill of 100. Assume that the Offense skill for both is maxed. This means that their MAX damage for the same 1HSlash weapon will be the same. Give these two Warriors the same 1HSlash weapon and throw them at the same blue-conning MOB. Who will be more effective against it?

The smart money will bet on the Warrior with 200 skill and 100 STR.

The graphs from Arkand's logs show two things:
1) Low weapon skill (for appropriate values of "Low") will produce a damage distribution where the MIN has a higher peak than the Magic Number.
2) A sufficiently large STR buff can compensate for low weapon skill. In other words, 140 Weapon Skill + 60-point STR buff seems to be equivalent to a 200 Weapon Skill and no STR buff.

Consider the Damage Profile of Arkand's 1st test compared with his 4th test:
FIRST TEST
FOURTH TEST

Things to note here: There is significant overlap of ATK values in both tests. In the first test, Arkand's ATK rating ranged from 770 to 780. In the fourth test, Arkand's ATK rating ranged from 767 to 788.

Note, however, that the Damage Profile of the first test has the prominent peak at Magic Number. The Damage Profile of the fourth test has the prominent peak at MIN. Why?

Because in the first test, Arkand cast STR on himself. His skill ranged from 141 to 143 in the first test, but the 67-point STR buff compensated for that low skill. In essence, the 67-point STR buff artificially boosted his weapon skill to 200.

In the fourth test, Arkand did not cast STR on himself. His ATK rating was simply a reflection of his Weapon Skill + unbuffed STR + Offense Skill. And during the fourth test, Arkand's weapon skill ranged from 161 to 168. But he had no buffs to compensate for this low Weapon Skill, so the Damage Profile has the big peak at MIN.

This suggests to me that STR buffs (and almost certainly ATK buffs as well) act primarily as a boost to Weapon Skill if the weapon skill is low. Once the weapon skill hits a value that is considered to be "not low" (and who knows how that value is calculated?), the effect of the buff diminishes.

It is known that a 67-point STR buff on a Warrior with maxed Weapon and Offense skill for her level won't have a significant effect on her damage output aside from moving the value for MAX up the appropriate number of points. Compare the peaks at MIN and Magic Number on my first Damage Profile vs. the peaks at MIN and Magic Number for Copeland's Damage Profile. If STR did more than move the MAX and compensate for low weapon skill, then Copeland (with 93 more points of STR than me) would (in theory) have less hits at MIN compared to his hits at Magic Number than myself. We would see a shift of his hit distribution away from MIN and towards Magic Number.

But he doesn't. The total number of his hits for MIN is 80% of his total number of hits for Magic Number. The total number of my hits for MIN is 78% of my total number of hits for Magic Number. They're roughly equal, despite Copeland having 93 more points of STR than I do. Which suggests that if you were to somehow buff my STR by 93 points, it wouldn't somehow give me a weapon skill of 293. So there appears to be a point at which a STR buff stops acting like a boost to Weapon Skill. My guess is that it's around 200.


Are the lower strength buffs just added 2-3 extra points on max which may only hit a few times in a night?

Unfortunately, it certainly looks that way. The 5-point 1st level STR buff that Shamans get is completely, utterly ineffective for any purpose at all that I can tell except for giving you five more pounds of carrying capacity.

As the buffs add more to STR, their value becomes highly dependent on the DMG rating of the weapon. See my post named Some Preliminary Analysis on How STR + DMG Affects Combat for more details.

allow me to quote ye a moment.

"Congratulations, Arkand. You've successfully proven that, at least in terms of Damage Distribution, fighting a blue with a low weapon skill does indeed simulate the damage distribution of fighting a red with a high weapon skill."

So we can assume that fighting a red with a high level skill and a 67 point strength buff will simulate me fighting a blue yes?

You shoulda quoted the very next line, Valantor, 'cause I answered that very question.

Here it is:
"(However, since you didn't log your misses as well as your hits, we have no idea what your hit/swing ratio was, nor do we know how accurately it simulates fighting reds.)"

All I can say about how accurately "low weapon skill vs. blue MOB" simulates "high weapon skill vs. red MOB" is that the damage distribution for both situations is similar. Note that "damage distribution" does not equate to "overall effectiveness." If the hit/swing ratio for the "high weapon skill + red MOB" scenario is 50%, while the hit/swing ratio for "low weapon skill vs. blue MOB" is 60%, then no, the "low weapon skill vs. blue MOB" scenario will not be an accurate simulation of the "high weapon skill vs. red MOB" scenario, even if their graphs look identical down to the last point value.

Before we can say that it's an accurate simulation, we would need to know (A) the average hit ratio for a low-skill, blue MOB scenario; and (B) the average hit ratio for a high-skill, red MOB scenario.

Until then, all we can say is "The graphs look more-or-less the same."


Nowhere in your post did you mention the bonus damage Verant added to two handed weapons a few months ago. Are these tests from before that change? Or are the charts up to date and there never was a bonus damage added to 2hand at all? I wouldnt put that past Big Brother Verant.

Nah, no conspiracy. I just forgot.

The new Level Damage Bonus for 2-handers is calculated by:

2-handed Level Damage Bonus up to 50th level = (Level - 25)/2

At 51st level or higher, it's calculated by:

2-handed Level Damage Bonus post-50th = (Level - 7)/3

BUT!

Not only did they adjust the Level Damage Bonus for 2-handers, but they seem to have snuck in a hidden bonus for 2-handers that nobody can yet account for.

Look back up top at the graph of Qualtar's Damage Profile with the Polyphenomenal Axe.

Qualtar was 54th level during the time the Profile was taken. So his Level Damage Bonus would be (54 -7)/3 == 47/3 == 15.

The Polyphenomenal Axe is a DMG 37 weapon. So his Magic Number would be (2 * 37) + 15 == 74 + 15 == 89. And sure enough, the big peak of the graph is at 89.

So! His MIN should be 1 + 15 = 16. And his MAX should be 155.

But they ain't.

His MIN is 19. His MAX is 158.

Something shifted the two ends of his damage spectrum upwards by 3 points, while leaving his Magic Number unaffected. And so far we have no clue what that "something" might be.


Finally, where can i get a good log parser that will allow me to log tests with and without strength/cripple lines?

http://kqp.mpog.com/EQParse

It'll even make the spiffy Damage Profiles I've been using in my posts.

And thanks to all the nice people who enjoyed my post! I was worried that it'd be boring or something. Glad to see that some folks enjoyed it!


------------------
Ruatha Kneeslasher <Wings of Honor>
46th Level Gnome Warriorette
Some day we'll look back on all of this, laugh nervously, and change the subject...

Ruatha, I'm interested in some hit percentage and damage graphs of SK and necro pets compared to PCs of the same level. Happen to know of any?

Nope! Sorry...
Also, there isn't a hard damage cap of 29 for 19th level characters. With sufficient strength buffs my retired 19th level paladin on Bert can hit for 31 damage. Would be glad to show you if you would like 8)

Correct! It's not a hard cap. The reason why is because the 29-point "damage" cap is really a 14-point cap on the DMG rating of your weapons.

As part of their efforts to minimize the effects of twinking, Verant has made it so that the DMG value for any weapon used by Fighter/Hybrid characters from 10th to 19th level will have a DMG of no more than 14.

Got a twinked warrior with an Exe Axe? That's a 14/50 weapon from 10th to 19th, not a 25/50 weapon. (From 1st to 9th level, it's a 10/50 weapon because there's another DMG cap before 10th level.)

Got a twinked warrior with a Mith 2-hander? That's a 14/32 weapon (factoring in the haste) from 10th to 19th level, not a 21/32 weapon. And from 1st to 9th level, it's a 10/32 weapon.

My favorite one so far has been the twinked Ogre I saw running around with a Weighted Axe. At 20th level and up, it's a 45/150 weapon. From 10th to 19th, it's a 14/150 weapon. From 1st to 9th, it's a 10/150 weapon. He kept dying and couldn't figure out why since he was using this huge, bruising weapon.

So if your DMG is capped at 14, then your MAX below 20th level (2 * DMG) + 1 = 29.

However, if you have a high enough STR, then your MAX will increase before you break the cap.

Remember the formula for MAX:

[((Weapon Skill + STR)/100) * DMG] + Level Damage Bonus
We're talking about pre-20th levels, so Level Damage Bonus is zero.
DMG is 14.

So figure the following formula:
[((Weapon Skill + STR)/100) * 14] = 30

We pick 30 since that's obviously the next step after 29.

If you solve this for (Weapon Skill + STR), you'll discover that your Weapon Skill + STR need to combine in SOME way to make 215. So if your STR is 130, then once you max out your Weapon Skill for 16th level (which maxes out at 85 for Fighter/Hybrid types), your MAX goes up to 30.

If that's your theory, then if I take the same druid, and perform the same test, raising ATK by the same value (only with strength this time instead of ATK), I should get the same results. My suspicion, though, is that the results will NOT be the same, considering the tests I performed in the past.

I suspect that they will, given the results of Arkand's tests. BUT! I don't know. I'm interested in seeing the tests, though! No matter WHO ends up being right, we'll still have learned a little bit more about how EQ combat works.

Also, I hope you can comment on the skill-raising issue I pointed out. If the tester's SKILL went up DURING the tests, that would have a significant effect of the results (more damage on later tests). That could explain the reason why the later test revealed better results than the earlier test.

Well, I know from the logs that Arkand's skill during Test 4 was higher than it was during the three prior tests. The graph for Test 4 looks like the graph for Test 2 (STR buff was not cast in either test). So even though Arkand's skill was higher in Test 4, it's clear that the EQ combat engine still considered his skill to be "low".

So I suspect that the effect of his increased skill isn't huge. (Until, presumably, the skill reaches the point where the EQ combat engine says "Okay, your skill is no longer low. Your skill is now adequate for this MOB.")