I'll send the Cavalry after the furthest routers, who can rest and herd later routers back into way of harm. Light troops like Velites (even Town Watch) can also effectively take down routers who have tired themselves out fighting. Other fast troops can run fanning out slightly, to catch any routers that change course for some reason, rather than running straight.

If you don't have Dominant Cavalry then router pursuit becomes much more dangerous. Not fun to have a strong routing unit reform just when your pursuers are stretched and enemy cavalry turn up on a flank.

So seems to me, Cavalry are essential, they have speed and also tire more slowly, so can cover awesome amounts of ground.

One tricky issue is when you defeat a reinforced army in detail. There's a balance between bagging the routers (so they can't defend a town in next few turns, nor be trained back to full strength, depleting population), and getting fresh and set up to fight round 2, against the next army.

The game, sometimes frustrates because fragmented units, appear to get scattered bodies all over place, and you can't attack the nearest individuals.

I often have to hault Generals Cavalry, have them stand still, and then charge them later, to get the biz finished a little quicker.

Some imply Wardogs chase down and eliminate enemy particularly efficiently, even off field, but my impression is that the kills stay at the on field level, and those who cross the red line with dogs on their heels, are counted as survivors.

Historically a way of being enslaved was defeat on battlefield, so rather than "Kills" I'd like to see a good proportion becoming captives, like the anonymous captured town populations.

This would be fate of losing Phalanxes, when surrounded and under missile fire, as they had no means of hitting back, nor escaping.