*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!