Porphyrius
Warlord
I've tweaked my program to also compute the size of the army you need to achieve victory. (And I corrected a bug that was lowballing the hammer cost of your casualties)
Again, the scenario is to compute the cost of killing a CG 2 archer in a flatland city with a 25% fortify bonus.
Swordsmen are all CR2, and valued at 40 hammers.
Horse archers are an appropriate mix of FL2 and C2, and valued at 50 hammers.
C2 Horse Archers are purely combat 2 horse archers.
"need" is the expected hammer cost of the units you need to kill the archer.
"lose" is the expected hammer cost of your casualties.
40% cultural defense:
Swordsmen: need 70.57 hammers, lose 30.57 hammers.
Horse archers: need 92.52 hammers, lose 21.76 hammers.
C2 Horse archers: need 86.00 hammers, lose 28.80 hammers.
This calculation is right on the mark.

Stronger units rather than flanking mean less hammers and thus time to prepare for an attack to be succesful.
This to me is by far more important to actually reducing your loses or getting a high number of promoted units in most situations.
I find that unless i try to mess with an opponent that has a huge land mass under his control reinforcing isnt really that tough.
Plus promoting above level 4 usually has redudant payoff.
Ofcourse your limited calculations include fully promoted defenders (unlikely) and much more importantly fail to consider that CR3 swords widen the gap further than the 20% yuo calculate.
Not to mention that in BTS one is very likely to have counters to deal in the 2nd target city. The AI doesnt seem to take UU well into acount though, i.e. i have seen it whip holkans to deal with my axes consistently.

Add to this that IW is a bit cheaper and has necessary production boosting techs (BW,mine) as prequisites, and you easily conclude that a succesful early offensive based on swords can come faster.
100% cultural defense:
Swordsmen: need 83.22 hammers, lose 43.22 hammers.
Horse archers: need 119.05 hammers, lose 35.69 hammers.
C2 Horse archers: need 97.82 hammers, lose 38.26 hammers.
Now if we are talking well into the middle ages, one cant ignore the devastating effects of cats. Which makes decisions easy really.
That is not ot say HA are without uses.
A flank mounted unit is the best approach when a secondary city is defended by a couple really strong defenders acompanied by more lesser (somewhat osbolet or green) ones.
However the question in every game is will they see enough use to make getting HR worth it.
@kcmarkwell:
Offcourse they are great because of their speed when everything is early, but then you are not attacking you are just trying to mop things up quicker.
PS: Oppsitely from HA i find chariots lovely rushers excactly beacause you can have enough for an attack early cause they cost less than axes and move 2, even if they are weaker.
