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Nets function like any other weapon, except they are, like lances, one-use only. That is, they cause harassment, they can be repelled (length 5 weapon required as nets are length 4), and units with nets tend to waste them on already netted opponents. Shields do not help to defend against nets.
Size 3 units have a 33% chance of not being affected by the net, size 4 units a 66% chance and size 5 and 6 are not affected. In addition, every point of strength above 15 add a 5% point chance of not being affected by the net.
Once under a net, a units gets a defense penalty [75% or 100%?], and cannot attack or repel or move. The strength check to get out is rolled against a 19.
Nets also carry weapon blesses on sacred units.
Source: discussion with the user Arco on discord, and some numbers given by Loggy. Some bit of testing for the nets being wasted on already netted units.