Does anyone know what influences mature players to decide whether or not they are gonna stay in the game i.e become a manager or a coach?

I don't think there's anything influencing it..some do, some don't. I believe you might be able to encourage a player to towards the end of his career, and when players reach the end of their playing career they begin to think about whether they'd stay in football.

There must be something that determines whether they manage or not. i doubt very much the once they reach 30 tthat the computer randomly chooses for the players. their must be something to how its worked out

I think their intelligence stats have something to do

Determination as a attribute & Professional, leaders, determined as personality traits