OOC:Xkoranate RP bonus formulae

Xkoranate has two methods of applying RP bonus when using the built-in "Bonuses" section, rather than directly applying RP bonus to rank or skill. Below is a summary of how these work, and their implications, as explained by Commerce Heights on the NS Sport forum

Before applying RP bonus, the participants’ skills are converted to a 0–1 scale:

$Skill={\frac {(NominalSkill-MinimumSkill)}{(MaximumSkill-MinimumSkill)}}$

Absolute

With absolute bonus, the RP-modified skill is calculated as:

$RPSkill=Skill+RPBonus\times \left\vert 1-{\frac {1}{(1-RPEffect)}}\right\vert$

The RP bonus effect dictates how much of the total RP-modified skill is accounted for by the RP bonus. For example, if the RP bonus effect is 20%, then the RP-modified skill is the participant’s skill plus 25% of its RP bonus, so that RP bonus accounts for 20% of the total. The maximum RP-modified skill is now 1.25, so all values are divided by 1.25 before they’re fed into the scorinator.

Relative

With relative bonus, the RP-modified skill is calculated in the same way as with relative bonus, but instead of dividing by the maximum RP-modified skill, values are divided by the largest value actually achieved by a participant in the event (a participant who has been placed into a group, to be precise). For example, if the best participant in the event has a skill of 0.9 and an RP bonus of 0.8, for a total of 1.1 (0.9 + 0.8 × 25%), then everyone in the event will have their RP-modified skill divided by 1.1. If no participant has an RP-modified skill greater than 1, then no rescaling occurs.

The intent of this system is to allow athletes with the highest skill values to achieve world-class results without being penalized if no one in the event has accrued a high RP bonus (e.g., in the early stages of an event).