As far as I've heard the morale does not sum up (though I am not that sure, really). But even +2 morale, even +1 morale can work well if placed nicely (on a hill). I've noticed that whilst playing from high starting age (your forces are not that big and it seems that the Horde is slightly(!) smaller and also shows more preference towards horse archers than heavy cavalry). Halberdiers seems to have slightly lower upkeep cost than basic spears... However, they are slightly more expensive... Basically, my recent experience with the Byzantines High/Hard/ VI shows that the main killing units are the arbalesters (pavised or not). Strong archer units (like Bulgarian brigands and the Trabezond archers) are appreciated, though not obligatory. The cavalry deals well with the Golden Horde infantry. The fearsome heavy cavalry of the Horde dies easy when blocked by spears and attacked from the rear with Varangian guard (they can be well replaced with Chivalric foot knights) or just a mercenary unit like billman. I have not tried to leave the spear unit alone whilst I pepper the Horde unit with arrows
Perhaps the Halberdiers seem to be most useful as the Russians since apart from the woodsmen (though they are not that bad, really but a bit fragile) they do not have anything different from halberdier that is armour piercing. Basically, yes, the Halberdiers are an option, if you have them. And as long as you have the time to build churches and other niceties before the Horde arrives (though I admit the backbone of the army was the plain spearman that is also not famous with its good morale). And once again, the main killing is done from the arbalests esp. vs. the horse archers of the horde. If youy play as the Russians, do not forget to take some Druzhina cavalry with you! I used it as a mercenary unit as the Byz and it is perfect at flanking the Horde Heavy Cav after the latter is pinned! The Druzhinas also work well against the GH warriors.
Why do you use the expensive (and requiring high tech development) Pavise arb. to hold the cavalry charge? I believe they will lose about 1/3 of their number in the process. Spare them.
In the last battles with the Horde (that I mentioned), things were simply desperate for the Horde. More than 1:10 even 1:15 casualty rate and this mainly some arbalests and few cheap spears... Of course, I never meet the Horde on flat but rather fight on the nice Georgia map with a good general. I really started to wonder why I did bother to take more than 5 units of Varangian guard, though I admit I preferred to use billman (1 unit for all the battles) to flank.
P.S. The main disadvantage of the Halbs is on the offensive + they require a higher tech than the plain spears (level citadel). If you play at early, it will be easy but if you start playing on high you basically have 1 province with citadel in the best possible case.
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