Celtic Heroes

I would assume that the percent difference would increase as levels went up if the formula itself was off. That is why I wondered about the rings having some hidden stats. In addition, the inaccuracies happened fairly fast after 'natural' skill levels.

The accurate high level example I used had 35/35 points in fire bolt, then a grand ring of fire bolt (+4), mage dragonlord gloves (+5), and a firemage's bracelet of vitality (+5). So if inaccuracies are supposed to increase after normal skill caps, that doesn't really explain how +14 to a level 35 fire bolt makes it so accurate (only 0.07% error).
Also, my low level alt mage with 10 focus, 100 fire magic and a level 15 fire bolt had a displayed damage of 156 and a calculated damage of 156.754. That's less than 0.5% error.

To my knowledge, fire bolt boosting gear do not have hidden stats, because that would make the above high level example extremely inaccurate, when it is actually super accurate.

I think the lesson here is that the formula is accurate (<1% error) for low and high level fire bolts, but gets less precise (1-2% error) around level 35.

How did you find the constants? Suberb job by the way, the effort put into this is quite commendable.

How did you find the constants?

The only thing harder than finding the constants is explaining it to someone else

I know that in my original post I didn't fully explain how I got the formula—partly out of laziness, and partly to not scare people off/confuse everyone. I might put up a full explanation after I finish with the max level skill formulas (http://celtic-heroes.com/forum/viewtopi ... =4&t=56130).

(Please don't be offended by this) How good are you with math? If you're still in school, which math course(s) are you taking?

U can explain, i myself good at math (im at school, im not sure how u call the courses but im taking the highest one), but all the math, i dont think many care, and yes it might scare many ppl off, thinking its too complicated.

If u add the math, dont edit the original post, the original post is understandable and helpful, better not all the math and formulas and etc. to that.

How to find a Damage Formula
Needs a lot of math

The first, trickiest, and most time-consuming step: you have to guesstimate what the formula generally looks like. This is done by a lot of testing/experimenting, which consumes many alt/rebirth books as you adjust focus, fire magic, and skill level to figure out how each affects damage. After trying and failing with many formats, I settled with:
Any Level Fire Bolt Damage = (Stat multiplier that increases with skill level) * sqrt(Focus) + (Ability multiplier that increases with skill level) * sqrt(Fire Magic) + Constant

Second step: you need to collect data. You need three data sets: [High Stat, High Ability], [Low Stat, High Ability], [Low Stat, Low Ability]. The more skill levels you record, the better. I did 15 levels.
With 1592 focus and 1600 fire magic,
Level 1 = 87 damage
Level 2 = 121 damage
Level 3 = 158 damage
…
Level 15 = 749 damage
With 135 focus and 1600 fire magic,
Level 1 = 48 damage
Level 2 = 66 damage
Level 3 = 84 damage
…
Level 15 = 378 damage
With 135 focus and 609 fire magic,
Level 1 = 42 damage
Level 2 = 57 damage
Level 3 = 73 damage
…
Level 15 = 322 damage

Next, you need to plug the numbers into the equation format that you guessed. Start with level 1. Here's the general equation format again:
Level 1 Fire Bolt Damage = a*sqrt(Focus) + b*sqrt(Fire Magic) + c
You want to solve for the variables a, b, and c. Three unknowns means you need three equations. Luckily you have three data sets. So plug them in:
87 = a*sqrt(1592) + b*sqrt(1600) + c
48 = a*sqrt(135) + b*sqrt(1600) + c
42 = a*sqrt(135) + b*sqrt(609) + c

Now you have to solve those three equations. You get:
a = 1.379
b = 0.39159
c = 16.314
This means that now you have a formula for a level 1 fire bolt.
Level 1 Fire Bolt Damage = 1.379*sqrt(Focus) + 0.39159*sqrt(Fire Magic) + 16.314

At this point, you have gotten the formula for a single skill at a single level. Because doing this only requires 3 data points and doesn't take a lot of work, when I did all skill formulas (http://celtic-heroes.com/forum/viewtopi ... =4&t=56130) I decided to go for level 50 only. That way, I saved a bunch of time and data collecting.

If you want the formula for any level fire bolt, you have to repeat the process (plug in your numbers into the general form, solve three equations for three unknowns) for level 2, level 3, and so on. The more data you use, the more accurate it becomes. I used all the data I had (15 levels).
Level 2 Fire Bolt Damage = 1.9448*sqrt(Focus) + 0.58739*sqrt(Fire Magic) + 19.908
Level 3 Fire Bolt Damage = 2.6166*sqrt(Focus) + 0.71792*sqrt(Fire Magic) + 24.881
…
Level 15 Fire Bolt Damage = 13.118*sqrt(Focus) + 3.6549*sqrt(Fire Magic) + 79.384

You can clearly see that all the numbers increase as skill level increases, as expected. Now we want equations that describe how fast these numbers are increasing against skill level. Group all the first numbers a = [1.379, 1.9448, 2.6166, … , 13.118]. Plot a curve fit that approximates them:
a = 0.01743(Skill)^2 + 0.5615(Skill) + 0.7813
Do the same for the second and third numbers (b and c).
b = 0.005163(Skill)^2 + 0.154(Skill) + 0.2253
c = 0.04939(Skill)^2 + 3.601(Skill) + 13.15

Now, you have equations for a, b, and c that work for any skill level. Substitute those three equations into:
Fire Bolt Damage = a * sqrt(Focus) + b * sqrt(Fire Magic) + c
to get the final formula
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
The underlined parts just show where you substitute a, b, and c in. They do not change the meaning of the formula.

So for anyone wondering, that's how you do it. Very tedious, and very complicated.

So once you have your three data points, you're basically starting a long tedious process of plugging numbers in and seeing if the chosen numbers make all three equations true?

I need three data points per skill level. It's long and tedious if you want to make a formula that works for every level:

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

But if you want to make a formula for a specific level only, it's easy.

Level 50 Firestorm Damage = 90.164*sqrt(Focus) + 25.515*sqrt(Fire Magic) + 365.43

To make this max level firestorm formula, all I had to do was solve these three equations for a, b, and c:

5214 firestorm damage = a*sqrt(1465 focus) + b*sqrt(3000 fire magic) + c
4035 firestorm damage = a*sqrt(635 focus) + b*sqrt(3000 fire magic) + c
3720 firestorm damage = a*sqrt(635 focus) + b*sqrt(1800 fire magic) + c

a = 90.164
b = 25.515
c = 365.43

Those three numbers go in the bolded firestorm formula above. There's no guessing here, only solving with math.