I'm putting together a points system where a tournaments weight ($k$ value) is calculated based on its number of participants. A tournament of $56$ participants has a $k$ value of $100$ (maximum $k$ value) and a tournament with $9$ participants has a $k$ value of $50$ (minimum $k$ value). How do I calculate the $k$ value spread for tournaments with participants between $56$ and $9$? The calculation should work for different variations of participants - e.g. 20 participants giving 100 k-value, and 10 participants giving 50 k-value etc.
Thanks in advance.
Any function $w(p)$ that increases from $k = w(9) = 50$ to $k = w(56) = 100$ is a possibility. The simplest is a straight line: $$ w(p) = 50 + \frac{100-50}{56-9} (p-9) . $$