Ori said:
@jmas:

I had this nagging feeling that my statement was not 100% right - but did not remember what screws this up.
Thanks for those very informative links,

.
No problem, guys.
Front, I like math myself, however I worked overnight the last 2 nights, so I'll leave it open for someone else to work out more numbers for you.

Some points to be aware of: Attackers always get their base strength * (1+(.1*number of Combat promotions (until Combat 6 anyway

))). (The nested parentheses are just to try to avoid any potential confusion, sorry if it's overkill). However, other promos on the attacker, such as Cover and Shock ("archer defense /melee defense"--those don't have multiple levels by the way, they are a one-time deal) give
negative amounts (-25% for Cover and Shock)
to the defender's total modifiers. E.g., a bowman defending with Combat 1 (+10%), against a non-melee unit (against melee they get an extra bonus), let's say fully fortified (+25%) would normally get +35%, so 3*1.35 = 4.05 strength. But when a Cover unit is attacking, the bowman would have only +10%+25%-25% = 10%; that's 3.3 strength.

Doesn't sound too good against knights (EDIT: Okay, I just remembered Knights can't get Cover, but I don't want to work out any more details for this post, especially since it's not clear whether we're talking about Babylonian Bowmen or generic Longbowmen), and even the Bowman's +50% vs. melee (e.g. samurai) wouldn't give much better odds. Of course you did have rifles. But Knights are immune to first strikes so the Riflemen's Drill promotions didn't help. (Drill IV, which you didn't have, gives a bonus vs. mounted units; though you said for the Rifles you had "the sole intent of defending against/attacking knights or other mounts"--so Combat 1, 2, and if possible Formation--the anti-mounted promotion--would have helped more).
Of course losing a set of battles in a row might have been your luck with the random number generator. It's been posted recently that it is a good generator, however I know it doesn't necessarily feel that way when you suffer statistically unlikely losses when strategically you needed some wins (maybe even just a couple more wins!)
This excellent article and discussion may help you:
http://forums.civfanatics.com/showthread.php?t=137615. Especially take note of what happens if the defender has net negative modifiers--if somehow a Bowman has a net -10%, it's not a 3*.9 strength unit, it's 3/(1+.1). The difference can be important.
Thank you for updating to explain the "X"'s in your post. I wondered if perhaps you were imitating the crossed swords of the City Raider promotions!
EDIT: I see Roland's point that you probably had longbowmen and not Babylonian bowmen. Combat 1, (fully) fortified longbows should be 6 * 1.35 = 8.1. Not as good as rifles or pikes vs. knights. By the way, did you check the Combat log to make sure the match-ups of attacker and defender were as you recall? I think it's Control-Tab to open the logs, then click the Combat log tab. The information there goes from most recent, backwards chronologically as you go down--it took me a little getting used to to read it. Maybe initial matchups were vs. the "expected" best defenders, who then got weakened until, say, longbows defended vs. knights. I know with this many fights I could probably lose track of what fight happened when without checking the log--especially in the heat of emotion..
Hope all that helps.
