One of the most important posts you have never seen

[Kailyn]

moderator note - as pointed out below, these tables do not scale 100% accurately beyond level 50.

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This an excellent posts that prooves all the stuff we have been taking as gosple for the last 3 years. (THe reason we can take it as gosple is that we kicked this around a lot to get it to work.) The general MN formula was work up by Romidar Trueblade and I when logging was first enabled. I also feel this is the foundation work that allowed you all to do the excellent work on the Tanking Uber mobs.

But it has also always bothered me that while we had the derivative work, we never had the original.

That said, as far as I know, Ruatha did ALL the work on the low level mechanics for damage.

Without further interrputions--Rautha:

Posted: Fri Sep 08, 2000 9:28 am Post subject: EQ Math Geekery (WARNING: Long and probably boring)

[Kailyn]

Posted: Fri Sep 08, 2000 9:28 am Post subject: EQ Math Geekery (WARNING: Long and probably boring)

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Lately, there have been some questions asked and comments made by a variety of posters here that suggest (at least to me) that it might be useful to discuss how melee damage works in Everquest. And it might also be useful to throw up some spiffy graphs to help explain things, because not everybody is able to visualize graphs based on textual descriptions.

So here goes!

FIRST GRAPH

http://www.erols.com/aburner/eq/1hbgraph.gif

This is the Damage Profile of my Journeyman's Walking Stick (9/24) as wielded mostly in my Primary hand. I got this graph by logging all of my combats so far in 46th level, then going in with a text editor and removing everything but the "You crush" or "You try to crush" messages. Since my offhand weapon is a Kunzar Ku'Juch (1HSlash), this left me with a logfile of nothing but my hits with the Journeyman's Walking Stick.

You will notice that there are a few hits for Damage values from 1 to 7. These come from a few battles where I (for tactical reasons) switched hands and put the JWS in my offhand. Since the offhand doesn't get the Level Damage Bonus, my minimum damage for the JWS in the offhand is 1. There was no easy or consistent way to weed these battles out of the graph, so I just left them in. So pretend that they're not there.

The first thing to note are the two prominent peaks on the graph. The biggest peak falls at what we call the "Magic Number." The Magic Number is a Damage value that, at 28th or higher (and possibly at 20th or higher) can be calculated with the formula:

[(2 * DMG) + (Level Damage Bonus)]

The Journeyman's Walking Stick has a DMG of 9. According to this formula, my Magic Number will be [(2 * 9) + (7)] == (18 + 7) == 25.

And sure enough, the biggest peak falls on 25.

(It's called the "Magic Number" because it's the amount of damage you will hit for the most. Around 20% of your total hits will be for the Magic Number.)

The second peak falls at the Minimum Damage (aka MIN). From 28th level onward (and possibly 20th level onward), MIN can also be precisely calculated as follows:

1 + (Level Damage Bonus)

According to this, my MIN should be 1 + 7, or 8. And sure enough, the second peak on my Damage Profile is at 8.

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.

Above the Magic Number, we have two types of hits. The first type are normal hits up to Max Damage (MAX).

According to the most accurate formula we have currently, your MAX can be calculated thus:

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

According to this, with my 110 STR, 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. And you'll notice that the hits for over Magic Number on this graph are fairly evenly distributed up to 34.

The second type of hits that fall above the Magic Number are exclusive to Warriors: Critical Hits and Crippling Blows. (Rogues get crits with thrown weapons and Rangers get crits with bows, but only Warriors get crits with melee weapons.) The crits and crips range up to a 73-point shot (66-point crippling blow + the level damage bonus).

One of the things that came up a couple weeks back when things got a little...heated...around here ( ) was my opinion that crits are "eye candy." For those of you who wonder why I would say that, hopefully this graph makes it a little bit more clear. This graph represents literally thousands of successful hits. There are about 470 hits at the Magic Number alone. Compare that with the comparative handful of crits (ranging from 36-points of damage to 54-points of damage). This is the reason why I say that crits don't play a significant role in your damage output at high levels. (At low levels, it plays a more significant role. A nice crit with an LotW can do over 70 points of damage. That's a non-trivial percentage of health for a MOB with 500-600 HP. Against a MOB with 5000 HP, it's less significant.)


SECOND GRAPH

http://www.erols.com/aburner/eq/offhandslash.gif

This is the Damage Profile for a Kunzar Ku'juch (8/22) in my offhand. Like before, this was obtained by logging my battles so far through 46th level, then going through with a text editor and removing everything that doesn't start with "You slash" or "You try to slash".

Although it's not as obvious here as in the first graph, this graph also has a few battles logged where I had the Kunzar in my primary hand. Like the first graph, the amount of hits where this occurred is a negligible fraction of the total hits, so the graph isn't affected in any meaningful way. For the most part, the overwhelming majority of these hits were with the Kunzar in the offhand.

The key thing to keep in mind: The offhand doesn't get the Level Damage Bonus. So all formulas for the primary hand that contain the Level Damage Bonus *don't* contain it for the offhand.

So the Magic Number for the offhand is simply (2 * DMG) == (2 * 8) == 16. The MIN is simply 1. The MAX is [((Weapon Skill + STR)/100) * DMG] == [((200 + 110)/100) * 8] == 24.8, rounded down to 24.

And sure enough, we have the biggest peak at 16, a secondary peak at 1, and non-critical hits ranging up to 24. (Again, as before, there are a small number of hits for 25, which comes from the fights where my STR was 120 instead of 110 thanks to the 10-point Necro STR buff.) Additionally, we have a smattering of offhand crits and crips ranging from 26-points to 49-points.

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

[This message has been edited by Ruatha (edited 09-08-2000).]

[Kailyn]

THIRD GRAPH

http://users.erols.com/aburner/eq/bashgraph1.gif

This is a damage profile for my Bash skill. I always dual-wield, and I always ghetto-bash. So I was able to edit my log with a text editor and remove everything but the bashes.

There is a big peak at 12 and a smaller peak at 1. Since Bash is done with the offhand, it doesn't get the Level Damage Bonus. So the Magic Number should be (2 * DMG). Since (2 * DMG) appears to equal 12 in this case, I surmise that Bash is a DMG 6 "weapon." Plugging this DMG value in to the MAX formula seems to confirm this, because if Bash is a DMG 6 "weapon," my MAX Bash damage at 110 STR should be 18, which fits the graph. The hits for 20, 22, and 30 are critical hits.

Some things to note:



All Damage Profiles from 28-50 (and possibly 20-50) with 1-handed weapons will look very similar to these graphs. There will be a big peak at the Magic Number. There will be another big peak (although not as big as the Magic Number peak) at MIN. The majority of hits will fall between these two peaks, with a lesser number falling between Magic Number and MAX. For Warriors, there will also be a smattering of crits/crips above MAX.

In fact, you'll notice that these three graphs all look sorta the same. For weapons with higher damage, the graph is more spread out. For weapons with lower damage, the graph is more "scrunched up." The Bash graph is similar to the first graph, but since the first graph is a DMG 9 weapon and Bash is a DMG 6 "weapon," there is a smaller possible range of damage values.

(As a sidenote, if I had a Mosscovered Twig in my primary, the MIN would be 8, the Magic Number would be 13, and the MAX would be 16.)


One of the other things I've claimed before is that a warrior with high STR doesn't put out significantly more average damage than a warrior with low STR. At the risk of starting another flamewar, here's why I say that:

According to the Max Damage formula, a 46th level warrior with 255 STR would have a MAX of 47 points of damage with the JWS in the primary hand vs. my 34-point MAX. That's not bad. If you look at the first graph, that means that his hits above the Magic Number would range from 25 to 47, whereas mine only ranges from 25 to 34.

BUT!

His distribution of hits from Magic Number to MAX will look roughly like mine. So in other words, his graph for damage values 26-34 will look roughly like mine. The only difference will be that his graph will extend past 34, and will go up to 47. So that extra 145 points of STR is really only getting him some extra hits ranging from 35-47 over and above what I'm putting out. His damage profile from MIN to 34 will look almost identical to mine. So take what the graph would look like from 35 to 47 at 255 STR and compare it to the entire rest of the graph. And keep in mind: This is comparing a 110 STR to the maximum STR attainable in the game. If you compare my 110 STR to a 150 STR or a 170 STR, the difference is even smaller.

That's why I say having a high STR doesn't make you a significantly better warrior over a warrior with low STR.

Again, I'm not looking to start a flamewar here. You may look at the data and draw an entirely different conclusion. I'm just explaining why I have certain beliefs and why I said certain things about STR in some of the earlier messages. So even if you don't agree with me about STR, you at least know why I say it.




A FEW OTHER GRAPHS

http://www.erols.com/aburner/eq/152hslash.gif


http://www.erols.com/aburner/eq/151hslash.gif


http://www.erols.com/aburner/eq/151hbash.gif


One of the things I've said a number of times is that certain things hold true from 28th level and higher (and maybe 20th and higher). The reason why I say that is at low levels, your Damage Profile looks very different than at higher levels.

The above 3 graphs are all from a 15th level Shadow Knight. The first graph is the Damage Profile for a Fine Steel 2-handed Sword (12/44). The second graph is the Damage Profile for a Silvery War Axe (6/22). The third graph is for Bash (which in this case looks to be a DMG 4 "weapon").

Note that all three graphs are different from the high-level graphs I posted earlier. There is the primary peak at the Magic Number (which is [(2 * DMG) + Level Damage Bonus], but since the character is below 28th level, the Level Damage Bonus is 0). However, there is no peak at the MIN. The secondary peak is at [(2 * DMG) + 1]. The remainder of the hits are more-or-less evenly distributed across all the values below (2 * DMG).

So when I say that "such-and-such is true at 28th level and higher (and maybe 20th level and higher)," this is why. There comes a point in time at which the Damage Profile of a character changes from having a peak at the Magic Number and a smaller peak at (Magic Number + 1) to having a peak at Magic Number and a smaller peak at MIN.

So far, no one has done any testing specifically to determine at what level this change takes place. It seems fairly certain that at 28th level, the profile has the big peak at Magic Number and the smaller peak at MIN, since this is the first level where the Level Damage Bonus comes in to play.

However, 20th level is the level at which the 29-point Damage Cap is removed, so there's a suspicion that the profile may change at that point instead.

I'll know soon enough, I suppose, when my SK hits 20th...

Anyhow, I hope that SOMEONE finds all this info useful and/or helpful.

[Kailyn]

SOme closing notes: As far as I Know, Ruatha is currently not playing EQ (though I have seen him come back for a bit, and ran into him once in DAoC).

The link to the original post is:

http://forums.crgaming.com/eqbb/viewtopic.php?t=54615

[Gimmel]

A true classic piece of EQ history.
/em gets all misty eyed

[Kailyn]

LOL that it is. Would you beleive that Ruatha's post survived a change in board software, and was only on page 2 when I surfed the Warrior forum at Casters Realm. 10 pages long, a good chunk of that bumps.

Personally I would like to see this sticked.

[Sulvar]

Yeah I remember when this was first posted back on the stratics warrior board. Great stuff from back in the old days

[Daemonwynd]

That max damage calculation doesn't look to be valid, any longer. At least for a 65.

Str: 290
Skill in 1hs: 250
Weapon: 16/19
DAmage Bonus: 13

((290str+250)/100) * 16) + 13 = 99.4

When in reality my max hit is for 108 with it.

[Superchum]

Didn't they mess with damage tables in Velious for both monks and warriors?

That could explain the disparity you see in your max hits, if this indeed a very old set of graphs.

Certainly before my time.

[Kailyn]

Yeah this is just after Kunark. I did copy and paste the date, 9/8/2000. And it was not new news then.

My very old and un-updated sight has a copy of Ruatha's guide to bashing, which shoudl probably be posted somewhere here too.

My write up (http://web.archive.org/web/20010218141309/kailyn.topcities.com/MDF.htm under Melee Damage Formula), which is no where near as good a Ruatha's, predates RoK as near as I can tell. At least it makes no referance to RoK weapons. And does referance the *cough* uber 30/45 God drops...

The date on the file is 3/21/00. And that was writen up only after I got tired of posting it constantly to the stratics board.

And I have found that the formulas break above 50--the further past 50 the more inaccuate. I remember seeing soem of my own buffed 59th logs were average damage was much closer to the damage of the weapon, makinga damage/delay a better indicator of performance. I bet that at 65+ Delay is again less important. And all this stuff was writen way before the 2h bonus was implemented.

[Dobbo Baggins]

i think it has something to do with 61-65 weren't levels when he did this. or maybe it was a LONG time ago.

[Kailyn]

LOL 51!!! was not a level when this was first done. And 60th had not been in the game very long when Ruatha finally wrote this up.

[Rhagulim]

He's posted on the castersrealm warrior forums lately, might be a good place to say hello if you haven't in awhile. I started way too late to know him but he seems like a good fellow :)

[Flair]

And it was not new news then.

Kailyn

The original analysis was done about 3 months before Kunark. Kinda the time we were all running around Sol B in circles trying to pull the same mobs.

Good too see you again bro ;-)