That's what happened. I'm playing on medium difficulty level for battles. Furthermore, the pre-battle scroll said that our armies were in 1:1 strength ratio. I was attacking with only the family member's unit against just one slinger unit.
To everyone else: Thanks for the replies. I've hardly been using my cavalry against melee infantry because my Caucasian archers usually deal with them without taking any casualties. I've been charging properly, using double alt click and (I think) starting at the right distance to get them moving fast.
Now that I think about it, I only charge skirmishers/archers. So what I said about the charge bonus not working against any unit is wrong. As Titus Marcellus Scato says, I don't get a charge bonus vs any units that are running away, even if they're much slower than my units. I mean, even when I charge some skirmishers and leave them such little time to react that they're just beginning to change directions to flee, I still get no charge bonus. It doesn't make sense.
Also, I know that the cavalry in RTW were unrealistic, but I still think these heavy cavalry units are exaggeratedly slow and tire out too quickly to be useful or worth the insane cost. I'll see what I can do once I'm able to recruit non-mercenary light cavalry.
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