I think the problem has an easy solution.
Once the simulation is done, it should be possible to assing each player the minutes played.
Interesting, but it doesn't match the game simulation for WO, wheres players may be fouled out very soon.
Check this example :
(46129580)As you can see (on the live report), ALL the players of the winning team got fouled out, plus three lucky fans as well. A player managed, G. knows how, to make seven (!) fouls. Those were reasonably good players who had no reason to harass the opponents (un)lucky fans.
It is funny watching indeed.