View source for Skilling success rate

{{External|rs=Skilling success chance}}
The '''skilling success function''' is used to determine whether or not a skilling action rewards the player, typically with an item and [[experience]]. The formula approximates a linear interpolation. As the player's level in a skill increases, the rate of success generally increases as well.

Each action that uses the skilling success function takes two parameters, a "low" value and a "high" value, to use. These low and high values are unique to that action and do not change regardless of the player's level, but they can change if the player meets certain conditions, such as having a [[Thieving cape]] equipped. 
The low value reflects the odds that an action will succeed at skill level 1, while the high value reflects the odds of success at level 99. The actual success chance at level 1, assuming no boosts are active, is <math>\dfrac{1+low}{256}</math>, while the success chance at 99 is <math>\dfrac{1+high}{256}</math>. 
For levels between 1 and 99, the chance of success can be determined from the skilling success formula:

<math>P(\text{Level}) = \dfrac{1 + \left\lfloor\dfrac{low \times (99-\text{Level})}{98} + \dfrac{high \times (\text{Level}-1)}{98} + 0.5\right\rfloor}{256}</math>

If the result would be less than 0 or greater than 1 it is then replaced with that bound. The following is an example skilling success chart for fishing [[raw monkfish]]:
{{Skilling success chart|label=Monkfish fishing chance|showbefore=no
|label1=Raw monkfish|low1=48|high1=90|req1=62|color1=saddlebrown|image1=Raw monkfish.png
}}

The action has a low value of 48 and a high value of 90, so the success chance at level 74 can be calculated as follows:

<math>\begin{align}
\mbox{low-scaled value at 74} &= \dfrac{48 \times 25}{98} = 12.245\\
\mbox{high-scaled value at 74} &= \dfrac{90 \times 73}{98} = 67.041\\
\mbox{total } P(74) &= \dfrac{1 + \left\lfloor12.245+67.041+0.5\right\rfloor}{256} = \dfrac{80}{256} = 0.3125
\end{align}</math>

==Cascading chances==
Some activities like [[Barbarian_Training#Barbarian_Fishing|barbarian fishing]] and [[Herbiboar]] follow a cascading format, where multiple skilling success formulas are used to determine what the player receives. Generally, the highest reward the player can receive is rolled first, and if the player fails the roll, they go on to the next roll until either succeeding a roll or failing all the rolls.

For example, a player using the [[barbarian rod]] with 85 [[Fishing]] as well as the other requirements to catch a [[leaping sturgeon]] first rolls against the skilling success formula for leaping sturgeon. Since leaping sturgeon have a low value of 8 and a high value of 64, the chance of getting a leaping sturgeon is

<math> P_{\text{sturgeon}}(85) = \dfrac{1 + \left\lfloor \dfrac{8 \times (99-85)}{98} + \dfrac{64 \times (85-1)}{98} + 0.5\right\rfloor}{256} = \dfrac{1 + \left\lfloor\dfrac{112 + 5376}{98} + 0.5\right\rfloor}{256} = \dfrac{1 + 56}{256} = 0.2227 </math>

If the player fails to get a leaping sturgeon, a [[leaping salmon]] is rolled for. Since leaping salmon have a low value of 16 and a high value of 96, the '''chance of getting a leaping salmon given that the player failed the leaping sturgeon roll''' is

<math> P_{\text{salmon}}(85) = \dfrac{1 + \left\lfloor \dfrac{16 \times (99-85)}{98} + \dfrac{96 \times (85-1)}{98} + 0.5\right\rfloor}{256} = \dfrac{1 + \left\lfloor\dfrac{224 + 8064}{98} + 0.5\right\rfloor}{256} = \dfrac{1 + 85}{256} = 0.3359 </math>

So the chance of failing to catch a sturgeon and instead catching a leaping salmon at level 85 is

<math> (1-P_{\text{sturgeon}}(85)) \times P_{\text{salmon}}(85) \approx (1-0.2227) \times 0.3359 \approx 0.2611 </math>

Similarly, the chance that a player fails to catch both a leaping sturgeon and leaping salmon, but catches a leaping trout, which has a low value of 32 and a high value of 192, is

<math> (1-P_{\text{sturgeon}}(85)) \times (1-P_{\text{salmon}}(85)) \times P_{\text{trout}}(85) \approx 0.3428 </math>

If the all three rolls are failed, the player receives nothing.

==Boosts over 99==
The skilling success function's input is clamped to a maximum value of 99. When boosting over 99 using [[invisible boost]]s like the [[celestial ring]], a similar formula is used to calculate success chance. In the case of visible boosts, the boost over 99 is disregarded entirely. In situations where the skilling success formula is not used, like [[aerial fishing]], this is not necessarily the case.

==Calculator==
{{Calculator:Skilling success rate}}
[[Category:Mechanics]]

==Changes==
{{Subject changes header}}
{{Subject changes
|daterange = 01 November 2023 - 12 December 2023
|change = The formula for calculating the skilling success rate was changed to no longer decrease at certain levels.
}}
{{Subject changes footer}}