- H : the current level of your hero in ONE discipline or skill
- Diff : The difficulty level of the craft
- ts : the duration of the craft in seconds
- q : the chance of not getting a up in the chosen skill
- p : 1 - q = the chance of getting at least one up in the chosen skill
Then, for Diff > H - 5 , we have
- q = [(Diff + 5 ) / H ] ^ ( -0.0012 * ts )
This can also be expressed in different equivalent manners :
- q = [H / (Diff + 5 )] ^ ( 0.0012 * ts )
- q = [H / (Diff + 5 )] ^ ( 103.68 * td ) where td is the duration in days
- q = e^(- λ * ts ) with λ = -0,0012 * LN( H / (Diff + 5 ) )
- q = e^(- λ * td ) with λ = -103,68 * LN( H / (Diff + 5 ) )
I found 2 errors likely due to errors of encoding when I wrote down the craft and 3 errors of 0.1% due to the fact that the duration in seconds of a craft such as shown in the game are in fact rounded down values. A craft that is shown to take 1666 seconds takes in fact 1666.6667 seconds. When the real duration is taken into account those 3 errors fade away.
It has been tested for lots of different skills including extraction, foundry, forging, stone cutting, botany, masonry, sewing, breeding, ...
It has not (sufficiently) been tested with some guild only crafts, terrains, exploration and it obviously doesn't apply to combat
And for 2 skills ?
Very simply, when you can up both the discipline and the skill (like both metal and forging), the global chance of getting a up is computed like this :
- pglobal = 1 - q1 * q2
Multiple up for the same skill ?
We know it is possible to get multiple ups for the same skill during a craft.
That chance, however, is not displayed in the game and a huge statistical analysis would be needed to find it with any kind of certainty.
If we make the assumption that the developers took care that N task of duration T are equivalent to 1 task of duration N*T not only for getting the first up (that is now known for certain) but also for subsequent ups, then I can give the formulas for getting more than 1 up in a craft as there is only one way to achieve this. This is also relatively easy to implement (the actual random process is easier that the analytical formulas that compute those chances : see more explanations in the French original thread if you are interested and you can see the formulas in hidden cells in the simulator.
Currently only in French but shouldn't be too hard to understand :
Recent version of OpenOffice or compatible is required :
Gopol - Chances de up.ods
Thanks to Gerhart Friedlander and his colleagues for writing ""Nuclear and Radiochemistry" : subsequent disintegration of Strontium90 into Yttrium90 and then Zirconium90 is very similar to getting subsequent ups...