A little report.
I reset all my skills except for tactics and did some simulations.
Result: the simulation was affected only by the level of tactics. The presence or absence of other skills had no effect on the simulation result. The main hero most likely does not participate in the battle and does not give bonuses.
Before the simulation, I got off my horse, went into combat, set myself as captain of the first formation and exited combat to save my settings. I had only infantry. Next I attacked the same enemy many times.