this is based on my own strategy.
I always aim for 0 casualties, so i'd prefer archers shooting from far rather than rush in cavs/cuirs or infantries.
but it also depends on how you command your battles.. and your hero level too
also, siege units are way too slow, dont bother sending them Applicable to lower level arenas only, up to level 8-9, since they are easily manageable with just archers. I've heard that High level arenas should use siege units, but i'll have to do more research on it. My guess is that the speed isn't that much of a problem anymore when you are doing high level arenas, as most of your tech levels would have been 10, or close to. Besides you'd have gotten at least 1 or 2 good reins to increase moving speed.
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basically i've never done arena below level 3 so im not sure on those.
Level 4 I'd suggest
North: 5k archers (and misc any amount)
South: 3k archers, and misc.
Max swordies I've seen from final bosses: don't remember. 2k? (or less swords, but combination of cavs/archers etc.)
Leevl 5 I'd suggest
North: 12-15k Archers
South: 7-8k Archers
max swordies I've seen from final bosses: ard 6.5k
Level 6 I'd suggest
North: 20-25k archers
South: ard 12k archers
max swords: dont remember, i've only done this once, probably 9-10k
Level 7 - not sure. this is based on the amount of troops that i brought along.
North: 45k archers
South: 20k archers
max swords: pure 21k swords from final boss. also seen 12k sword + 15k archers.
side note: also seen 26k pikes from side quest mini boss (Konrad)
Level 8 - again, forgotten, but i sent:-
North: 90k archers
South: 50k archers
max swords: pure 38k (I think?) swords from final boss
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IGN Smexy