How Do You Figure?

Posted: October 17, 2007 by Kendricke in Everquest 2

There’s a lot of numbers involved in MMO’s.  If these numbers were more public, it’s likely that new players would be outright overwhelmed by the sheer amounts of mathematics involved in some of the processes which the average player never really needs to worry about.

For the general masses, the underlying formulas aren’t really all that relevant.  To these typical players, more and bigger is generally understood to be better than less or smaller.  More Strength is better than less Strength.  Bigger damage is better than smaller damage.  More regeneration is better than less regeneration.

But what about the not-so-average player.  What about the players who enjoy digging into the numbers, who like to figure out the formulas?  What about those players who want to draw back the curtain, who want to see the wizard? 

For those players, the discovery and exploitation of these formulas is itself a game within the game.  Figuring out the mechanics is to some players what reading the sourcebooks was to the dinner table roleplayers of a previous generation. 

How many of you sat around trying to build the “perfect” Thief/Fighter/Illusionist for hours on end?  How many of you spent days trying to build the perfect 55 ton 5-8-5 Battlemech?  How many of you can still recall to-hit charts from Star Fleet Battles? 

For those of you who wouldn’t mind taking a peek under the hood of Everquest II’s mechanics, I present to you this small glimpse into many of the more important formulas that you’re likely to find most useful.

Power Regeneration Hard Cap:

You’ve managed to pick up another item with Power Regeneration +5 listed on it.  Do you know if that actually helps you or not?  Do you even know how much Power Regeneration is too much?  Are Power Regeneration items really worth it?

First, the math:

The formula for determining the Power Regeneration Hard Cap is (1.5(level)+(base regeneration)).  In addition, only 50% of your total regeneration (minus base regeneration) can come from from items (i.e. – Flowing Thought).

What does this mean for you?

Level 50 =  81 (1.5(50)+(6)); 37.5 from items ((1.5(50))/2)
Level 60 =  97 (1.5(60)+(7)); 45.0 from items ((1.5(60))/2)
Level 70 = 113 (1.5(70)+(8)); 52.5 from items ((1.5(70))/2)
Level 80 = 129 (1.5(80)+(9)); 60.0 from items ((1.5(80))/2)

That’s right.  At level 70 (the current level cap), only the first 52.5 points of Power Regeneration from items actually counts.  If you’re already walking around in 53+ points of power regeneration, you’re no longer gaining any additional power regenerative benefits.

The rest of your cap?  That comes from songs, spells, buffs, and other abilities. 
Critical Hit Damage:

Ok, you’ve just picked up a new Achievement or piece of gear which increases your chance at a “Critical Hit”.  But just what, exactly, is a critical hit?  Sure it’s more damage (or healing or what-have-you), but how much more powerful is a “critical” over a regular hit? 

Whatever “Critical” refers to here (melee/ranged/spell/heal) the general rules remain the same.  For purposes of simplicity, let’s concentrate only on the idea of a critical melee hit. 

The generally accepted formula from most parsers indicates that a critical hit works out to a range where Critical Hit Damage = (Max+1) to (1.3(Max)) (where “Max” refers to the modified maximum damage potential of a particular weapon).

For example, if a weapon has a range of damage from 10 to 30, then 30 would be considered the baseline maximum damage potential of the weapon.  Various factors can and will increase that damage, including STR values, +DPS effects, group or personal buffs, etc.  These factors can result in the weapon’s modified maximum damage potential being raised – sometimes fairly significantly.  To view the current actual damage range of a weapon, use the “/weaponstat” (shortform = “/we”) command in-game.

To further illustrate the point, if a weapon’s base range was listed as 10 to 30 and remained unaltered, the critical hit damage of this weapon would range from 31 to 40 ((30+1) to (1.3(30))).  If the weapon’s damage range were increased through various effects to a 30 to 90 damage range, then the weapon’s critical hits would land between 91 and 120 damage. 
Damage Rating:

Ok, we’ve all seen Damage Ratings (DR) on weapons in Everquest II.  But what exactly does that number actually mean?  Is a DR of 42.3 really better than a DR of 40.7?  If so, how much better?  And why?

Damage Rating is probably one of the most misunderstood and overlooked formulas in the game.  By the same token, it’s also one of the most far reaching and important numbers to the average player, because virtually everyone has bought a new weapon or upgraded a new drop based purely on the weight of this number…and yet most players have no clue what this number actually represents.

Simply put, the listed Damage Ratings of weapons in Everquest II are created by dividing the sum of the minimum and maximum base damage ratings of a weapon by the weapon’s base delay, or ((Min+Max)/Delay). That’s it.  

This is why a weapon such as the Blackscale Maul has a listed Damage Rating (DR) of 80.13, because the weapon has a base damage range of 185-545 and a base delay of 8 ((185+545)/8).  It’s why a weapon such as the Vraksakin Claw Club has a listed Damage Rating of 101.13, because the weapon’s listed damage ranges from 1-404 and the listed delay is 4 ((1+404)/4).

So is that DR 42.3 better than that DR 40.7?  The short answer is… maybe. 

As a general rule, higher Damage Ratings are better.  Of course, players need to take other variables into consideration.  For example, what achievements are you using?  Do either of the weapons have additional effects?  Do you have haste?  Do you have a high STR value?  Do you tend to use a lot of combat arts…or spells? 

There’s no quick and dirty answer here, which is one of the dangers of delving into the background mechanics.  Because the more you discover, the more questions you find require answering. 

Later this week, I’ll try to help peel back some of the layers covering such concepts as Haste, how proc rates are determined, and airspeed velocity of coconut laden swallows.

Once we’re done, expect to see a “Common Game Formulas” article in our new “Guides” section. 

  1. Exeter says:

    Proc rate are always something that have mystified me. In the old days, I remember seeing percentages (5% chance to cast blah blah on target) and this made sense to me. Now we see most of the items carrying around a number of times per minute. What does a 1.8 times per minute proc rate mean?

    I understand it in theory, but what I want to know is how those numbers translate back into a ‘rate’ or a ‘percent chance’.

    If I autoattack 100 times and there’s a 5% chance of proccing an effect, I know that on average I should see 5 triggers and then I can work out the ‘expected damage’ from the proc for each swing. If the proc is represented as a number of times per minute I have to take into account how long the fight is and this can be deceptive to me since, optimally I want the fight over as quickly as possible. But on a fight that takes, say, one minute, on average I should see only one to two triggers and then I question why I went out and blew a few of platinum on that phantom handle for my weapon. I’m not sure how to calculate the expected amount of damage per swing in this situation and compare it to a weapon with, say, 2.1 triggers per minute.

    Couple all of this with the haste modifiers from buffs and all of this gets really complicated. Does 100 hate mean that a 1.8 proc rate per minute get bumped to 3.6? These are the sort of questions that I wouldn’t have if I had a percentage chance to proc rate. A 5% proc rate makes sense; higher hates = swing more often = more triggers.

  2. Prrasha says:

    Except, in the old days, 5% was only 5% if your weapon delay was exactly 3.0 seconds. If it was faster, you’d proc less than 5% of the time; if slower, more than 5%. So your statement about “if I autoattack 100 times […] I should see 5 triggers” wasn’t correct… and if you were basing your purchases on that math, you may have been spending your plat less-than-optimally.

    The 3.0 rule is still in effect today; the standard 1.8/minute proc rate is exactly the same as an “in the old days” 9% proc. There’s 20 three-second blocks per minute, 0.09 (procs per swing) x 20 (swings per minute) = 1.8 (procs per minute). If you can see things better as a percentage, just multiply the proc rate by 5 and tack on the percent sign (or divide by 20 to get the decimal version).

    The hard part, as you suggested, is haste modifiers. Procs work off the base attack rate of the weapon (or spell or combat art, but see the next paragraph.) If you’re hasted to double speed, you’ll get twice as many procs.

    For spells or combat arts, procs are based off a “3 seconds” that includes recovery time… so the “standard” spell proc rate is for a 2.5 second spell with a 0.5 second recovery time. Chain-cast spells and you’ll see the proper X procs per minute if you don’t have either casting speed haste or recovery speed haste. Gain either, and the math gets difficult (recovery time haste does more for your spells/arts are fast-casting, since recovery isn’t proportional to casting time, it’s 0.5 seconds for a 0.5 second combat art and a 5.0 second group reactive heal.)

  3. Kendricke says:

    Keep it up, Prrasha, and I’ll just quote your comments as my next update in this series. 😉

  4. Exeter says:

    Well colour me surprised. I didn’t know the math behind that. Thanks, Prrasha. I didn’t realize that the proc rate reported was conditioned I’ve only really started paying attention to things like procs since I started raiding with my guild on AB about 4 or 5 months ago, well into the “proc per minute era”, hehe. Looks like my assumption about the percentages was wrong. Good to know that I didn’t have any plat to blow at the time! Haha! Thanks again.

    Great site, mate. Great work from your contributors. Keep up the good work.

  5. Soos says:

    Awesome post, as a professed min-maxer I do enjoy the fine art of finding the best way to maximize calculations or “Theorycrafting” This post, and Prrrashas response are extremely helpful for me just starting EQ2 as a swashie.

    The post definetly explains why raid DPS loves the 1H wisdom line for double attack. If you are swinging an “8” delay weapon with a high end damage of 545, and double attacking with it. Your crits are always going to be lovely and you dont have to worry about min/maxing your swing delay for your OH weapon. I realize that my assuption here is that double attacking is a guaranteed second hit off of a 1H swing (I am only 21 so I dont have that ability to test it) :).

    However since crits are not double damage like they are in other games, I can see easily where the high end damage weapons are pretty important…

    Thanks again for the great article/discussion.

  6. Samdax says:

    Thanks for this great information! I’m not much of a math person and when anytime I see people talking about this type of number crunching I get confused. Somehow you’ve managed to put this in very simple straight forward way that even I who is arithmaticaly challenged can understand. That being said I was wondering if there is any information on the “Protection” stats on shields. Is it like mitigiation, or something similar…what the heck is it? I hear no one has that information but if you have some insight that would be a great deal of help.

    As it is choosing a shield is somewhat confusing as it appears the majority of consensus is to choose a shield with high agility over a high “Protection” value. Most say that Protection may be an empty number…in either case knowing what this value represents may help people decide what type of sheild to get.

  7. Lairia says:

    I know you only touched on the issue here, but so I understand correctly in regards to the vraksakin club v. blackscale maul debate regarding which has the higher damage rating with 100% crit rate; wouldn’t it be accurate to say that the increase in max damage that the blackscale maul has over the club is not high enough to compensate for the vraksakin club’s lower delay? As the critical hit amount doesn’t take the minimum damage into account, only the maximum; wouldn’t the blackscale maul have to have to at least double the max hit amount to cause it to have even the same damage rating? I can only assume that those who are arguing the blackscale maul’s higher critical damage rating is due it’s having larger individual hits?

  8. Kendricke says:

    I went back and re-checked my math on the subject, and I think you’re right, Lairia.

    In a 100% melee critical hits environment, the Blackscale Maul is now rated at 156.8, because the rate of damage shifted from 185-545 to 546-709, while the delay remains at 8 (and remember, damage rating is the sum of the minimum and maximum damage ratings divided by the delay).

    That Vrasakin Club shifts from a DR of 101.13 to approximately 232.6 when you introduce it into a 100% melee criticals environment.

    In a 100% melee critical setting, the Blackscale Maul still outperforms most weapons – even many with higher damage ratings – based almost completely on the high maximum damage rating. The delay factors into it, but at the numbers we’re talking about are so high, that 8 delay doesn’t even truly make much of a difference. Add in haste (like the 20% base haste built into Yaulp, plus even relatively easy to acquire items like the Gauntlets of Glorious Speed or even a haste adornment) and you’ve lowered the delay and increased the damage rating even more – even in the 100% melee criticals environment.

    But you’re right, the Vraksakin Claw Club is actually a better weapon (even before the proc).

  9. Bowin says:

    Prrasha your an eye opener. I started out thinking this post is really going to hurt my head. As soon as I got to Prrasha post I was in aww.
    This makes since. I ve been reading alot of DPS post about how a slow delay gives you more procs. But what I couldnt find was if you added haste if it would screw up your procs.

    Prrasha Wrote:
    If you’re hasted to double speed, you’ll get twice as many procs.

    That is what excited me! This is what I was after thanks.

    Now if SOE doesnt take 1k dmg away from Rangers like everyone is saying in the forums, we should be okay.

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