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# Skill Level to Effect Formula

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Trying to gain some insight on the precise diminished returning behavior of leveling skills particularly high, I was looking at the skill level to effect size tables recently and tried to discover the formula behind it. You know, stuff like Weapon Lore, where it starts with 12% at level one and the per level increase decreases with level slightly. Many skills share the same values (there is only a few different datasets actually). To my surprise, it's really hard to pinpoint what it actually is, which is made worse by the fact the values are rounded to whole percentage points.

A way to approximate it pretty closely was something as ugly as:

```E(l) = 205.7014 * l^0.990244 - 194.0553 * l
```

Where l is the level of the skill and E(l) is the effect size at level l. It gets pretty close, but doesn't nail it, there sometimes are deviations >1 which means the formula must be false as the deviation can't be explained by rounding alone. Also, these parameters are obviously nasty, so it seems highly unlikely the developers set something like this anyways. As with any approximation, the values given by this formula will probably deviate further and further for level values outside the range from which the data was drawn.

So I was wondering if anyone actually knew the proper formula, or is familiar enough with the game code so he could explain how I could find it out from the game data. Or do you think it's possible to mail one of the former devs and ask them, if so, who would be my best shot?

Have a nice day!

• 1
##### Link to post  From what I know of the formulas used for Sacred 2 the dev's liked something along the following lines for diminishing returns:

```1 - (1 / (1 + x))
```

Adjusting that to suit your needs would be something like:

```Bonus = A - (B / (1 + C * L))
```

Where:

A = Upper Limit

B = Scaling Factor

C = Per level increase

L = Skill Level

Note that you probably won't be able to find a solution that fits the data points exactly as the number displayed in the tooltip is likely being rounded to the nearest integer.

• 1
##### Link to post  Trying to gain some insight on the precise diminished returning behavior of leveling skills particularly high, I was looking at the skill level to effect size tables recently and tried to discover the formula behind it. You know, stuff like Weapon Lore, where it starts with 12% at level one and the per level increase decreases with level slightly. Many skills share the same values (there is only a few different datasets actually). To my surprise, it's really hard to pinpoint what it actually is, which is made worse by the fact the values are rounded to whole percentage points.

A way to approximate it pretty closely was something as ugly as:

```E(l) = 205.7014 * l^0.990244 - 194.0553 * l
```

Where l is the level of the skill and E(l) is the effect size at level l. It gets pretty close, but doesn't nail it, there sometimes are deviations >1 which means the formula must be false as the deviation can't be explained by rounding alone. Also, these parameters are obviously nasty, so it seems highly unlikely the developers set something like this anyways. As with any approximation, the values given by this formula will probably deviate further and further for level values outside the range from which the data was drawn.

So I was wondering if anyone actually knew the proper formula, or is familiar enough with the game code so he could explain how I could find it out from the game data. Or do you think it's possible to mail one of the former devs and ask them, if so, who would be my best shot?

Have a nice day!

So happy one of the build/math experts was able to provide some feedback on your question Mario, I remember the Sacred Devs often posting how "secret" their formulaes were regarding game theory, there used to be pages of discussion on how the math was working, great seeing it still inspiring the questions here

And a big welcome to DarkMatters as well! gogo

##### Link to post  From what I know of the formulas used for Sacred 2 the dev's liked something along the following lines for diminishing returns:

```1 - (1 / (1 + x))
```

Adjusting that to suit your needs would be something like:

```Bonus = A - (B / (1 + C * L))
```

Where:

A = Upper Limit

B = Scaling Factor

C = Per level increase

L = Skill Level

Note that you probably won't be able to find a solution that fits the data points exactly as the number displayed in the tooltip is likely being rounded to the nearest integer.

thanks for answering DB! gogo

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