Quote Originally Posted by Procrustes
Hi,

I've always been a little confused by that - my understanding is that the armor peircing bonus won't apply against non-armored units, but that doesn't mean you get a penalty for attacking a non-armored unit with an armor-piercing unit. Do you understand differently?

Best,

(As an aside, this discussion is making me wonder whether polearms the most effective unit to use against other polearms. Seems that the strength of polearms is against cav, and that swords would be better at taking out polearms. Hmm.... I'm seeing some testing coming up tonight.)
No, against armor lower than 3 you simply don't have the bonus.
Without AP you can only use the base attack (3 at best, only a few units like huscarles, VG and JHI can do better) and so you loose a good degree of effectiveness.
Swiss halbs still retains a good attack but the others are quite plain on melee without it.

The best counter against halbs?

Gallowglasses, Highlanders or Ghazis.
No armor = less damage taken, mounted crossbows also do wonders against vanilla halbs.