Introduction of the stirrup

[ambrosius]

As for the household cavalry - or any any others not carrying shields - it really wouldn't matter which side they turned to the enemy. Though, I guess it would actually pay them to keep the right side to the enemy, wouldn't it? At least that way, they'd have a greater reach to parry with their own swords against an enemy sword.

Only if you lost your primary weapon, your spear. I would still rather use a shield to protect myself than a blade!

I'm afraid you seem to be moving the goalposts a bit, here. We're talking
about household cavalry, who don't have a shield and whose primary
weapon is their sword. Of course, you could expand the discussion to
include 17/21st lancers, who's primary weapon is a lance (spear) but
they don't (didn't) carry shields either. So we need to decide who we
are discussing. I guess you are talking about Roman cavalry again, now.
But the point about cataphract lancers was that they didn't give a stuff
which side they faced the enemy with, as both they and their horses
were armoured. And if they were using heavy two-handed lances for
charging the enemy, then they would be unable to hold a shield (which
they didn't need in any case because of their armoured arms & legs).
I thought we'd found Roman chamfrons that had ear-flaps for the front
of the ears (to protect them from the swords of the enemy) which would
also give them protection against a glancing blow from your own sword.

Ambrosius