Kandarim wrote:assume you have an artifice with difficulty A to B, and clothing with difficulty C to D. This means that the chance that you will FAIL to slot lies between (A+B) and (C+D).
I think you mean "between (A+C) and (B+D)", to begin with. :)
But that's not true either; it would mean that if A+C > 100%, then it would be impossible to slot the item ever, which is not true. Rather, the range of the chances of success lies between the products of the chances to succeed for either item. That is, assuming that A, B, C and D are normalized to 0.0-1.0 rather than in percent terms, the chance of success lies between (1-A)·(1-C) to (1-B)·(1-D). For example, if the artifice has difficulty 10-50 and the clothing has 20-40, then then chance of success lies between 30%-72%.
Where the proficiencies come in it gets a little bit more complicated, but if you don't care for the exact maths, suffice it to say that you only gain from having more matching proficiencies on the artifice and clothing. It only gets better with more matching proficiencies and higher values in those proficiencies, never worse.
For the actual formula, assuming P is your values in the set of matching proficiencies, a selection factor is calculated by the following formula:

- slot.png (781 Bytes) Viewed 2031 times
This selection factor (clearly lying between 0 and 1) is used to linearly modulate between the lower and upper bounds of probability.