If you want to maximize the resting time of a player in a particular game, you play him at the beggining and at the end of the game, in order to maximize the total time span you can play him. The larger the time span you use, the larger the rest it is possible to schedule for any total
x amount of minutes of playing time.
If he doesn't start, you are reducing the total time span you can play him, and therefore, he would have less resting time for the same amount of minutes played. This is a basic scheduling problem.