I need a formula for determine the amount of damage that a skill or ability can do.
I have some data that I don't have create myself, but I just taken from a game.
A character can grow up from lv 1 to 100, and he has a set of skills.
Every skill can go up from lv 1 to (current level of the character)
The skill damage is linear but influenced of character's attack, so more attack the character has and more damage can do the skill.
A character that we call John has the follow parameters
Max stats that John can reach:
- Level 100
- Attack 7337
- Skill damage (lv 100) 16574
Minimum stats:
- Level 1
- Attack 71
- Skill damage (lv 1) 479
The current stats of John:
- Level 13
- Attack 202
- Skill damage (lv 13) 805
When the skill was a previous level:
- Level 13
- Attack 202
- Skill damage (lv 12) 788
In theory the skill damage should get 7 points for level, of course with the current amount attack of John, but is linear.
What I'm trying to do is get the basic damage of a skill plus the correct multiplier
Edit:
Seems that adding an item that give a bonus (+62 atk) the multiplier is change from 7 to 18 and the skill damage increased of +64 (788,852)
- Level 13
- Attack 264(202+62 from equip)
Skill damage (lv 12) 852
Level 13
- Attack 264(202+62 from equip)
- Skill damage (lv 13) 870
This is probably not a satisfying answer, but I think it's at least more than a comment.
It's not possible to answer this exactly without all the knowledge of the game (because there might be some non-linearities going on), but solving a linear system can give us an approximate answer. The linear system assumes that the answer is of the form
$$ \text{skill damage} = A \times \text{Level} + B\times \text{Attack} + C\times \text{Skill level} + D $$ Plugging in the values that you have given, we get the equations $$ \left\{ \begin{array}{rcrcrcl} 100 A &+& 7337 B &+& 100 C &+& D &= 16574 \\ A &+& 71 B &+& C &+& D &= 479 \\ 13 A &+& 202 B &+& 13 C &+& D &= 805 \\ 13 A &+& 202 B &+& 12 C &+& D &= 788 \end{array} \right. $$ Solving this gives us an approximate answer $$ \text{skill damage} = -13.5 \times \text{Level} + 2\times \text{Attack} + 17\times \text{Skill level} + 321 $$ But this seems weird, because the Level multiplier is negative. This serves as evidence that the equation is more complicated than what we assumed.