Reinforcements delayed?

[Silence Hunter]

IMHO the reinforcements delayed thing is random to stimulate uncertainty of reinforcements arriving on time as Antonivs Silvicola already mentioned.

The unlimited men on the battlefield option allows more than 20 AI units to enter the battlefield. Otherwise they wait at the border and enter once you kill enough of the enemy. I once had a battle against fullstack of Ptolemaioi + halfstack of Ptolemaioi + fullstack of Pontus (Ptolemaioi allies) attack me at once. My 1.5 stack army had no chance of victory and heroicly stood to the last man.

As for the tick box before battle - it's bugged. If you tick it and then check the composition of enemy army it resets. So you have to redo the thing again, otherwise AI will take control of your reinforcements (=say goodbye to your valuable men).