# Basic Theorycrafting: Or How Much Using One Rank Lower in Lightning Bolt Hurt my DPS

Ok, so the discovery I made last night prompted me to start investigating exactly how much dps loss there would be with casting a rank lower spell on everything. So, I started with my buddy over at Planet of the Hats. I pulled up his crit/haste article just to get a reference… when I discovered that I needed some more information to make sure I was doing my calculation correctly.

With the error I made last time in my math looming over me, I decided to find some source material to make sure I was making my computation correct. I looked on WoW Wiki to no avail, then I thought, “Hunh, Elitist Jerks should have an article on this, this is basic theorycraft.” Sure enough, I found this gem. Basic theorycrafting! Ah-hah!

So, knowledge in hand, I opened up my haste spread sheet to assemble my formulas. I wanted to compute the following:

- Damage done by spell rank
- Damage per Second by spell rank
- Crit Damage done by spell rank
- Crit Damage per second by spell rank

# Damage Done and DPS by Spell Rank

So, item number one. Damage done by spell rank. The first thing we need is the average damage done without talents or spellpower. We can reference the tooltips of Rank 13 and Rank 14 for this information.

Rank 13 Damage = (595+679)/2 = 637

Rank 14 Damage = (715+815)/2 = 765

Now, we want to add in things like spellpower and talents and the like. EJ’s article says that damage is added in as follows:

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

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

This means we need a bit more information! Want to figure out our +Damage, the spell Co-Efficent, damage added from talents, and any active percentage buffs/debuffs. I’m going to go ahead and ignore the active percentage buffs/debuffs for this portion of things.

Ok, so we take a quick look at the character sheet. If we use Tahas, then we see I have 2777 spellpower upon logging out. This means I more than likely logged out with Flametongue Weapon active (since my +healing is 2503), and since I put 3 points in Elemental Weapons, we can assume that +SP is added in, too. So, we can also assume I have Totem of Wrath down for another 280 +SP. That brings us up to 3057 SP. I may have the spellpower food buff, too. Anyway, we’ll just say “3057” for the sake of argument.

Now, we need the spellpower co-efficient to determine how much of that gets added to damage. Thankfully, Planet of the Hats has a nice little chart. So, what do we do to get this number otherwise? We divide the untalented cast time by 3.5. So, we get 71.43% without talents… throw in Shamanism, and we get 86.43%. Let’s put that in our formula:

Rank 13 = 637 + 3057 * .8643 = 3243.7074

Rank 14 = 765 + 3057 * .8643 = 3390.9074

Now, we need to add in damage increases from talents. We’re going to assume straight casts unaffected by Elemental Oath, so that leaves Concussion.

Rank 13 = 1.05 * 3243.7074 = 3405.8927

Rank 14 = 1.05 * 3390.9074 = 3560.4527

And finally, 4 % from Glyph of Lightning Bolt since that’s our only multiplicative buff outside of talents.

Rank 13 = 1.04 * 3405.8927 = 3542.1284

Rank 14 = 1.04 * 3560.4527 = 3702.8708

And using our hasted cast time, we compute DPS by dividing by the cast time:

Rank 13 = 3542.1284 / 1.5689 = 2257.7435

Rank 14 = 3702.8708 / 1.5689 = 2360.2003

I, umm, think the results speak for themselves (assuming my math is right). On a per spell cast basis, there’s nearly 102.4568 DPS lost. Now we get to the fun part… seeing how much of a loss it is on crits.

# Critical Strike Damage and Critical Strike DPS

The crit formula is as follows:

Critical Strike Damage = 1.5 * Spell Damage

Surprisingly simple, until we start adding in multipliers from external items and talents. We’ll start with our Chaotic Skyflare Diamond that adds 3%. This affects the fundamental formula, so it goes in first.

CSD (w/ Chaotic Skyflare Diamond) = 1.5 * 1.03 = 1.545

So, CSD without talents is as follows:

CSD Rank 13 = 1.545 * 3542.1284 = 5472.5884

CSD Rank 14 = 1.545 * 3702.8708 = 5720.9355

Now, we need to start adding in talents. There’s only one talent that affects the critical strike damage of this spell, and that’s Elemental Fury. This makes gives us a critical strike damage bonus of 100%. So, to give us our new CSD multiplier, we do the following:

CSD Modified with Talents = .545 (CSD Multiplier with Skyflare) * 2 (1 + 100% from the talents) = 109%

Now, we get to see what this does to our damage!

Rank 13 = 3542.1284 * 2.09 = 7403.0484

Rank 14 = 3702.8708 * 2.09 = 7739.0001

And in DPS terms:

Rank 13 = 7403.0484 / 1.5689 = 4718.6839

Rank 14 = 7739.0001 / 1.5689 = 4932.8186

So, roughly a 214 DPS lost per cast on a crit (which is actually the difference of the two DPS multiplied by the CSD percentage we determined).

# Conclusion

We’re going to abstract some things out for the conclusion. I want to give an example of how much this affected my DPS. If we look at a fight like Northrend Beasts in Heroic Trial of the Crusader, then we can see how many times I cast this spell. What we’re going to do is use the total number of casts as a baseline for this fight, and abstract out the debuffs/buffs aside from the ones we’ve already counted on that would affect the damage. So, I had a total of 101 Lightning Bolt hits and 66 Critical Strikes at Rank 13. So, we’re going to do two things. We’re going to use the stats above to compute total damage done at Rank 13 and Rank 14, and then compute DPS based on those numbers.

Rank 13 Total Damage Done = (101 * 3542.128) + (66 * 7403.0484) = 846356.1701

Rank 14 Total Damage Done = (101 * 3702.8708) + (66 * 7739.0001) = 884763.9591

In terms of average DPS? That’s 3230.331 versus 3376.924. Or, 140 DPS loss on 4.3667 minutes of casting.

The moral of the story? If you’re having DPS problems, check your cast bars.

Wow, impressive maths! I sympathise with the lower rank thing too – we had a hunter in our guild using rank 1 explosive shot for most of our Naxxramas time because he forgot to train the new ranks after respeccing 😀

By the way, two other things you could have considered are:

– Spells scale with your level after you first learn them, so the base damage on LB ranks at level 80 is slightly higher than what database sites like Wowhead will report. You can check them in-game (but you have to be untalented/glyphed) to get accurate values from the tooltip, but it wouldn’t affect your results above very much at all – the difference is in the order of a couple of points of damage.

– Lightning Overload! The overload bolts themselves actually have ranks too, each doing exactly half the damage of the normal LB spell, and accounting for about 15% of the total damage from LB. So if you wanted to you could find the amount of low-rank Overloads from your WoL report and work out how much DPS the lower rank overload was costing you using the same method you already used. I would guess it would be about 15% of the DPS loss from normal LB, so uh – about 20 more DPS? Ish? I dunno.

Incidentally, as mentioned in the comments on the other post, this is the big drag about dual-speccing your lowbie characters – you have to manually update every single spell rank on the dual-spec bars and it gets very tedious and easy to miss stuff out 😦

Ahhh, ok. Your first comment explains why it looks like a much smaller DPS loss than it probably is. Is the scaling multiplicative or additive? If it’s additive, then there’s probably a flat increase I need to do that won’t affect it as much. If multiplicative… well, then it’s huge.

I need to look at the LO WoL casts and try to compute that. Your estimate is probably accurate.