Rock Paper Scissors, medieval type thing

Ok, I have 5 units: Mage, Knight, Footman, Siege, and Archer.

I was wondering if any of you had any feedback on how they should win/lose in a rock paper scissors type fashion. (because there are 5, some will not be clear cut winners for example, i'll use abreviations:

M>K>F>A>S>M

Ok now in this example, a Mage would beat a Knight, but lose to a Siege. In a battle against a footman or Archer, who knows.

Can anyone give a good layout for who should beat who?

Do it like standard TFT.

Seige = High dmg, low mobility, long range, high hit points, high cost.
Mage = High dmg, medium mobility, medium range, low hit points, medium cost.
Footman = Low dmg, medium mobility, melee, high hit points, low cost.
Knights = Medium dmg, high mobility, melee, medium hit points, medium cost.
Archer = Low dmg, medium mobility, medium range, low hit points, low cost.

So in the end
Seige > Archer, Mage
Knights, Footman > Seige
Mage > Footman
Archers > Knights
Knights > Mage (High mobility vs low hp)
Footman > Archers (High hp vs low dmg output)

But then
Mix > All

A properly used mix should be the best. E.g. footman launch frontal assault, seige is hidden at back, archers seek support of footmen, knights attack from back to wipe out higher damage ranged, followed by mages.