> Non-violent protest often wins because the powers that be want to avoid antagonising the violent arm of the movement.

Not really a non-violent protest wins because majority move away from a violent group to a non-violent group.

So it makes a violent person who already has fear, more scared of being left alone. Non-violent protests need to be planned and require strategy in such a way, it helps those non-violent protestors to self-defend with the use of non-violent means, i.e. using deterrents which create fear in aggressors mind on use of violence.