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The unit stats are in the EU3\common\units folder with a file for each unit type.

Here they are in table form for 2.36b:

Code:
                             Unit stats

                Mov    Mi     HI     Ar     El     Cv     HA
       Militia   1     1.0    0.75   0.5    0.25   0.5    0.5
Heavy Infantry   1     1.25   1.0    0.75   1.0    1.2    0.75
       Archers   1     2.0    1.25   1.0    1.0    0.75   1.0
     Elephants   1     2.0    1.0    1.5    1.0    0.75   0.5
       Cavalry   2     1.5    0.7    2.0    0.5    1.0    1.25
 Horse Archers   3     2.0    1.25   1.0    0.5    0.75   1.0

I don't know the answer to your event question.
 
Man oh man do I love militia just for the fun factor of facing them in battle!
My very first game (as Sparta) I had 13,000 Achaean League soldiers marching against my 2,000 heavy infantry.
I was shitting my pants at this point, until battle was joined and they lost about 2,000 men a day vs. my 10 men a day; I saw why. Every single man they possessed was militia.
Beautiful.
 
The unit stats are in the EU3\common\units folder with a file for each unit type.

Here they are in table form for 2.36b:

Code:
                             Unit stats

                Mov    Mi     HI     Ar     El     Cv     HA
       Militia   1     1.0    0.75   0.5    0.25   0.5    0.5
Heavy Infantry   1     1.25   1.0    0.75   1.0    1.2    0.75
       Archers   1     2.0    1.25   1.0    1.0    0.75   1.0
     Elephants   1     2.0    1.0    1.5    1.0    0.75   0.5
       Cavalry   2     1.5    0.7    2.0    0.5    1.0    1.25
 Horse Archers   3     2.0    1.25   1.0    0.5    0.75   1.0

I don't know the answer to your event question.

So "maneuver" is what matters here? In a 1-on-1, cavalry will beat elephants?
 
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I've not played this game for a while so I'm not sure. But in a one-on-one situation I don't think manoeuvre counts for much. It's only used to enable an unengaged unit to attack the flank of a unit which is already engaged to the front.
 
So "maneuver" is what matters here? In a 1-on-1, cavalry will beat elephants?

No, as Albanach said maneuver isn't important for 1-on-1 so all that matters is that the cavalry will fight with 50% efficiency against the elephants while the elephants will fight with 75% efficiency against the cavalry. So 1-on-1, everything else being equal, the elephants will win. In fact 1-on-1 elephants will have the upper hand against everything except heavy infantry and horse archers where neither has an advantage (assuming everything else being equal).

As for buildings must be beautiful thing, it will allow you to get inventions that increase the cost of buildings but that does provide other benefits like religious prestige, the other choice in the event just allows inventions that makes buildings cheaper (and I think there might be some slight decreases in construction time as well). I would say going for beautiful buildings is the best choice most of the time as buildings aren't that expensive to begin with and by that time you should generally have a pretty strong economy.