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Fire Bolt Damage Formula

#1
Special thanks to Bobthemage for providing his stats to help me verify this formula.

After going through a mountain of alts and rebirths, I have finally reverse engineered a formula for fire bolt damage. Note that it is not an absolutely precise equation, but it's a very close estimator.

The Formula
Fire bolt damage only depends on three factors: skill level, focus stat, and fire magic ability. Character level does not affect your fire bolt damage. I tested this by leveling a pure strength mage and adjusting its skill, focus, and fire magic.

I recorded a total of 45 data points and plotted them on a graph. Then I fitted them with quadratic equations, combined them, and arrived at this final equation (underlined section by section for clarity):

Fire Bolt Damage = [0.01743(Skill)^2 + 0.5615(Skill) + 0.7813] * sqrt(Focus) + [0.005163(Skill)^2 + 0.154(Skill) + 0.2253] * sqrt(Fire Magic) + 0.04939(Skill)^2 + 3.601(Skill) + 13.15

Here is a simplified level 50 fire bolt formula (just plugging in Skill = 50 into the original formula). Use it to calculate max level fire bolt damages:
Level 50 Fire Bolt Damage = 72.4313*sqrt(Focus) + 20.8328*sqrt(Fire Magic) + 316.675

How to Use It
If you want to quickly calculate your fire bolt damage, follow these steps:
1. Copy and paste the entire bold underlined equation (or the level 50 fire bolt equation) into a text editor (e.g. Word, Notepad, TextEdit, or Pages)
2. Delete "Fire Bolt Damage =" or "Level 50 Fire Bolt Damage ="
3. Replace Skill, Focus, and Fire Magic with your own stats
4. Copy your new equation
5. Go to http://www.wolframalpha.com, paste it in, and press enter

If want to understand how this formula works and what it means, keep reading. If you were just here to find out your damage without having to use an alt or rebirth, you can stop here.

How it Works
(Skip this section if you hate math)
Let's break it down into three parts. I started with the simplest form of
Fire Bolt Damage = [Focus part] + [Fire Magic part] + [Skill part]

After some testing, I realized that skill level increased the effect of focus, increased the effect of fire magic, and increased damage itself. So, the equation now becomes
Fire Bolt Damage = [Focus multiplier]*[Focus part] + [Fire Magic multiplier]*[Fire Magic part] + [Skill part]

After some more testing, I found out that focus and fire magic had diminishing returns, that is, the damage growth slows as your total focus and fire magic gets large.
Fire Bolt Damage = [Focus multiplier]*sqrt(Focus) + [Fire Magic multiplier]*sqrt(Fire Magic) + [Skill part]

I then graphed a bunch of points and saw that skill level increases focus, fire magic, and damage according to quadratic functions. This basically means that Focus multiplier, Fire Magic multiplier, and Skill part follow the general form ax^2 + bx + c, where x is your fire bolt skill level and a, b, and c are constants. After working through some more math, you eventually get to the underlined equation above.

What this Means
Here are the big implications of the damage formula:
1. Your focus and fire magic are square rooted. This means that the more you add, the less rewards you get (this is not specific to mages; strength also gives diminishing returns on auto damage). Keep this in mind when you are allocating stat points; don't go overboard on focus and use a good balance between focus and vitality. I personally prefer a focus to vitality ratio of 3:2. Remember that increasing vitality by 1 adds a fixed 6.25 health.
2. Your skill level is squared. Also mentioned before, skill level does three things: increase the multiplier of focus, increase the multiplier of fire magic, and increase fire bolt damage directly. Because the skill level parts of the formula are quadratic equations (ax^2 + bx + c), you actually get increasing returns the higher your skills get. This explains why the damage of a fire-and-ice mage suffers greatly compared to a pure fire or a pure ice mage; a few maxed skills are far more powerful than many non-maxed skills.
3. Focus affects your fire bolt damage more than fire magic. Looking at the level 50 fire bolt equation, we see that the maximum focus multiplier is 3.5 times as large as the maximum fire magic multiplier.

Formula Precision
To test how accurate the formula is, we plug in a high level mage's stats (must be a different mage because I used my own stats to make this formula).
At around level 170, Bobthemage had a level 49 fire bolt, 1460 focus, and 2850 fire magic. His skill page puts the damage at 4068. Using this formula, we calculate a damage of 4065.05. Not bad—that's only a 0.07% error.
I will add some low and medium level mage stats later to confirm the accuracy of this formula.


Please reply with your thoughts on this formula, and maybe include how precise it was for you (# calculated using equation vs. # displayed in skill page). Keep in mind that this formula is for fire bolt only and does not account for the boost from fire attunement.

Thanks for reading, and happy maging!
Last edited by Swan on Sun May 18, 2014 10:19 pm, edited 4 times in total.

Re: Fire Bolt Damage Formula

#4
Thanks for the positive comments. :D

Before someone else brings it up, Papi did try to make a fire bolt formula (http://www.celtic-heroes.com/forum/viewtopic.php?f=4&t=22865), but got it wrong. Since he used lines (ax + b) to approximate his points instead of quadratic equations (ax^2 + bx + c), the damage doesn't increase fast enough. If you try plugging in Bobthemage's stats, you get 1891.95 damage from Papi's equation, which is way lower than the actual 4068. Not hating on Papi though; he did get the auto damage formula perfectly right (http://celticheroes.blogspot.com/2013/06/auto-damage-formula.html).

Also as a side note, fire bolt damage bonuses from beastbone gloves and sunfire fire bolt charms don't show up in the skill page, so they aren't included in the formula.

Re: Fire Bolt Damage Formula

#5
Instead of sticking multiple threads, could armo's thread be edited to be Mage Guides (plural) and then each of these helpful guides could be added in one list (sorta like the guides in the rogue forum.)
(Not active at the moment)
SmartOne: level 191 Mage
SneakyOne: level 185 Rogue
Learn about Lugh ➙ http://bit.ly/15My6OK
"The trouble ain't that there are too many fools, but that the lightning ain't distributed right."
-Mark Twain

Re: Fire Bolt Damage Formula

#6
SmartOne96 wrote:Instead of sticking multiple threads, could armo's thread be edited to be Mage Guides (plural) and then each of these helpful guides could be added in one list (sorta like the guides in the rogue forum.)

Those who are not familier with forums and will join, wont know that this thread even exists there, better make a new thread that will be collection of all guides like pigman has at the rogues section.
#NerfMages #AvoidBalance #WhyPlayARogue #MeatShieldOnly #HealingSlavesOnly

OP dps warrior on Belenus, hot af melee druid on Nuada. #Elementals #Apex

Re: Fire Bolt Damage Formula

#8
Once again, an amazing thread Swan.

The problem with what you suggest, Criminal, is if you look at Pigman's post, there is no actual Rogue guide. All the links are specific to something (leveling, pvp, ect), whereas the guide I have written encompasses every single aspect of a Mage, although very simple and not detailed unlike Swan's posts.

I think that having just one sticky'd thread would be a lot better, and if you believe making a new thread with all the links would be more preferential, then so be it, and please make it.

Edit: I've also added a link to this thread, under the Fire Mages section of the Mage Guide.

Keep up the amazing work Swan, I look forward to seeing the equations of the other skills mages possess.
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A mage at heart... Fire mage that is.
Currently actively playing the game.

Re: Fire Bolt Damage Formula

#9
I messed around with the equation at lvl 50 bolt on my mage and I consistently got very good results. I consistently got less than 1% error (Although I only did 4 or 5 tests with the gear I had available). For my purposes (I will pretty much always use bolt at 50.) this is extremely helpful. Thanks.
(Not active at the moment)
SmartOne: level 191 Mage
SneakyOne: level 185 Rogue
Learn about Lugh ➙ http://bit.ly/15My6OK
"The trouble ain't that there are too many fools, but that the lightning ain't distributed right."
-Mark Twain

Re: Fire Bolt Damage Formula

#10
I agree with Armo's idea of linking the guides to just one stickied guide, and SmartOne/Criminal's idea of making a list of guides like the rogue forum.

I think Armo should put a list of links at the top or bottom of his main guide. Links scattered throughout the guide or links at the bottom won't work quite as well because not everyone reads the whole thing, and a list is much more clear.

That way, the top of the mage forums aren't cluttered with a bunch of stickies, and the niche guides aren't totally forgotten.

By the way, I am ok with the pvp fire mage guide / fire bolt formula getting unstickied. I plan on making many more guides when I find the energy to do them.

SladeRhiannon wrote:Swan are you papi?:O

No, I am not Papi, but thanks for the compliment. :) I'm still in high school.
Last edited by Swan on Sat May 10, 2014 9:14 pm, edited 1 time in total.

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