Basic TheoryCrafting

Malan

This article is intended to outline basic concepts and formulae behind general theorycrafting, as a primer towards more indepth concepts.

[top]General

[top]Percentage Increase/Decrease talents/buffs.

Any percentage increase will multiply by the previous value. This is true in both increasing effects (damage increasing) and decreasing (threat reduction).

Talents will increase effects after AP/damage stats
Active buffs will increase effects on top of that.

eg: for spells we would see the following
$Output=A(T(B+DC))$

Base damage
+Damage (includes +dmg temporary buffs)
Spell Co-efficient
Talents
Active percentage Buffs/Debuffs

[top]Chance to hit/crit/proc and Probabilities

A 40% chance to crit means that there is a 40% chance on each and every hit. One crit does not affect the chance for another crit to occur. The chance that any Number of Crits will occur in a row is calculated by taking the Nth power of the Crit chance.
$C^N$

[top]One Roll System

A one roll system is like a table. For a caster this would be 1% Miss, 40% Crit, 59% Hit. If the chance to hit is reduced (chance to miss increased) it would be 5% miss, 40% crit, 55% hit. Increasing that miss chance pushes some hit chances off the table.
$M+C+H=100$
A good example of this is the Shield Block ability of a warrior. It increases the chance to block an attack, which pushes the chance to receive a crushing blow off the table.

[top]Two Roll Systems

Two roll systems work as follows: If you have a 5% chance to miss, and then a 40% chance to crit, a two roll system would multiply the 95% chance to hit by the 40% chance to crit, to get an effective crit chance of 38% (i.e.: you cannot crit if you don’t hit). Believed to be used for melee special attacks, and possibly spellcasts.
$C(1-M)$

[top]Proc Effects

Proc Mechanics

[top]Melee

Average weapon damage (A) can be calculated by adding the high and low ends of the damage range, then dividing by two.
$A=\frac{high+low}{2}$
Weapon DPS is calculated by taking the average damage and dividing by the weapon speed (S).
$DPS=\frac{A}{S}$
Crits – Melee crits are a chance to add 100% of the weapon damage. To add damage from critical hits the average damage is multiplied by the Crit percentage (C).
$DPS=\frac{A(1+C)}{S}$

[top]Caster

Average spell damage is calculated the same way as weapon damage (high + low divided by two) for direct damage spells. DoT spells do not have damage ranges.
Spell DPS (or HPS) is calculated by taking the damage divided by the cast time. DoT spells are calculated by taking the total damage divided by the total DoT duration. You may also want to include the cast time if there is no direct damage portion of the spell.
DD + DoT spells will be DD/cast + DoT/duration
Spell crits – The chance to add 50% damage to a hit. To get the extra damage from spell crits, multiply the average damage by the Crit % and 0.5 (plus any talent/item Crit bonus modifier).
Spell damage – This is a bonus to the damage of spells, for details on the co-efficient calculations, see the [Article]Spell Coefficients[/Article] article.

Malan · 23/01/08, 8:38 AM

Bink the Two Roll system is believed to exist for melee special attacks.

• Aldriana · 23/01/08, 2:03 PM

That description of PPM effects is a little misleading; a 1 PPM effect will happen about once a minute assuming you're only autoattacking, but in practice almost all classes have instant attacks which increases the uptime.

Also, the uptime calculation is a bit off for procs with durations, due to the existence of overlapping procs.

Binkenstein · 23/01/08, 9:17 PM

Malan: ta

Aldriana: Example please. I was under the assumption that a 1ppm proc would proc roughly once each minute regardless of whether you hit 10 times or 100 times.
Also, duration proc uptimes assume that the cooldown begins from when the proc occurs (and that there is actually a cooldown). Something like Skycall would require direct modelling to find an uptime.

Boramere · 23/01/08, 11:17 PM

Nah, he's right Bink. The way it works, the PPM rate of the proc is converted to a percentage chance on hit, based on the speed of the weapon, then any attacks made with that weapon have the same percentage chance to proc.

Take Rogues and Mongoose. Last I heard, Mongoose had a proc rate of 1 PPM. For a rogue swinging a 2.6 speed sword, thats roughly a 4.3% chance to proc on each swing. A rogues slice and dice will increase the number of hits, and hence the number of procs by 30%, and every sinister strike also has a 4.3% chance to proc it. So in practice, Mongoose will proc a lot more often than once every minute.

Malan · 23/01/08, 11:40 PM

Bink if you build your sections using the == header == markups then the wiki will auto create a table of contents for you so you won't need that 'points to cover' bit.

• Aldriana · 24/01/08, 12:18 AM

Originally Posted by Boramere

Nah, he's right Bink. The way it works, the PPM rate of the proc is converted to a percentage chance on hit, based on the speed of the weapon, then any attacks made with that weapon have the same percentage chance to proc.

Take Rogues and Mongoose. Last I heard, Mongoose had a proc rate of 1 PPM. For a rogue swinging a 2.6 speed sword, thats roughly a 4.3% chance to proc on each swing. A rogues slice and dice will increase the number of hits, and hence the number of procs by 30%, and every sinister strike also has a 4.3% chance to proc it. So in practice, Mongoose will proc a lot more often than once every minute.

That's not quite right either, actually. Let me see if I can explain this.

When you have a 1 PPM effect (which is actually pretty hard to find these days, since, for instance, Mongoose is now thought to be more like 1.2 PPM, and most of the other procs have internal cooldowns), that means that, if all you do is autoattack, it will proc, on average, about once a minute. If you are using a 2.6 speed weapon which thus hits 23.1 times a minute, your chance of proccing on any given attack is 1/23.1 = 4.33% per hit. Hence, it will proc about once a minute.

Haste doesn't actually effect this; if you're a rogue, say, and have 30% increased attack speed via SnD such that your autoattack hits 30 times a minute, the proc rate per hit drops to 1/30 = 3.33% per hit, so it *still* procs, on average, once a minute. So regardless of what haste effects, passive, proc, or otherwise that occur, the proc chance adjusts dynamically, so my MH weapon generates about 1 PPM from autoattack.

However, what *does* effect this is instant attacks. As a rogue, I get a Sinister Strike once every 3 seconds on average. Regardless of what haste effects I may or may not have up, this procs at the rate determined by my base weapon speed. So if I'm using a 2.6 speed weapon, even if I'm hasted so my autoattacks are hitting 30 or 40 times a minute, my Sinister Strikes will still proc 4.33% of the time and thus give me an extra .85 procs in the average minute. Hence, if I have a 1 PPM enchant on my MH weapon, it will actually *proc* about 1.85 times a minute.

Also, some PPM effects work on both hands. If I'm wearing Madness of the Betrayer (thought to be 1 PPM), I will get about 1.85 procs per minute from my main hand, and another 1 PPM (based purely of autoattacks) from my OH. Hence, this 1 PPM effect will actually end up proccing about 2.85 PPM.

Now, the trick is, proccing 2.85 times per minute with a 10 second buff does not mean you'll have an average uptime of 28.5 seconds out of every 60; in practice, the procs tend to occur while other procs are happening, so the actual uptime is lower than this; a 10 second buff that procs 2.85 times a minute (on average) will end up with uptime of 38.5%, so will only be up about 23 seconds out of every 60.

To summarize: PPM effects are actually fairly sophisticated, and require a careful explanation of many issues to understand.

Binkenstein · 24/01/08, 12:30 AM

Originally Posted by Malan

Bink if you build your sections using the == header == markups then the wiki will auto create a table of contents for you so you won't need that 'points to cover' bit.

Yeah, sure. As soon as someone tells me exactly how to use the header markups (There's no article on formatting stuff).

If you guys post a bit more on PPM's, in particular calculating uptimes of non-cooldown buffs, I'll rework that bit over the weekend, although I'm leaning with a "dump PPM from here and handle in a completely different article" approach. Especially since it'll allow more detailed examples, discussion of individual cases, etc.

• Aldriana · 24/01/08, 12:45 AM

PPM effects probably do deserve their own article, honestly; there's actually some subtleties I didn't touch on even the writeup above. I'll try to bang something out over the weekend along those lines.

♦ Boethius · 24/01/08, 12:58 AM

Originally Posted by Binkenstein

Yeah, sure. As soon as someone tells me exactly how to use the header markups (There's no article on formatting stuff).

You can reference this for now.

Malan · 24/01/08, 10:48 AM

* To add damage from critical hits the average damage is multiplied by the Crit percentage.

I definitely think these things are better represented as formula using LaTeX. That was kind of what I had in mind (your mileage may vary) when I was saying we needed a post like this. A way for JoeBlow to check his math before posting a load of shit in a thread.

• Shalas · 24/01/08, 11:36 AM

Mage spells have also been shown to be two-roll, and ranged attacks are either two-roll or really weird (as you can have blocked crits). It's probably safe to just say that white melee attacks are one-roll and everything else is two.

Binkenstein · 24/01/08, 5:08 PM

Reference for MathTeX formatting, slowly adding things in.

Vontre · 24/01/08, 7:53 PM

I was pretty sure active spell damage buffs were simply tacked on to the spell damage value used inside the calculation. Otherwise, it wouldn't make sense for active buffs to modify your spell damage totals in the character sheet. This means that all active buffs are affected by coefficients and multipliers.

Binkenstein · 25/01/08, 1:53 AM

Noted that +dmg includes temporary buffs, and that the last is for % based buffs/debuffs (zone buffs, misery, etc).

There's a nice post here which I could use to expand the weapon speed/cast time sections, but I assume the plan is for a separate haste section.