I need to create a equation to distribute points for users in the following game:


There are x users that play a game. 
If only one of them hit he gets max points.
If all of them hit each gets min points.
Everything between should be proportional.


Number of users, max points and min points are variables.



Simple equation to distribute points in a game
We can assume that $n \geq 2$, where $n$ is the total number of players; the one-player game can you figure out yourself.


Let $\alpha = (hits-1)/(n-1)$, where $hits$ is the total number of hits.
Note that $\alpha=0$ if only one player hits, and $\alpha=1$ if all player hits.


Then, using a weighted mean, each player that made a hit, gets $min\cdot \alpha + max \cdot (1-\alpha)$ points.


