How effective was the Loyalist militia for the British during the Revolution?
Overall, the Loyalist militias were not very effective, though this was more for strategic reasons than for tactical ones.
It is hard to say a great deal about the bulk of Loyalist militia because most of those who fought (something like 50,000 Loyalists) did so within the structure of the British Army. When militia did fight separately, they were not generally any better or worse than the patriot militias.
The real problem with the Loyalist militias was that the British put too much faith in them. They tended to adjust their strategy based on what they thought they would be able to get in the way of Loyalist militia help. This is, for example, why they shifted the war to the South in its later stages and it was what led to the defeat at King's Mountain.
Overall, then, the Loyalist militia were not notably good or bad in a tactical sense. However, their presence (and British perceptions of their presence) sometimes led the British to make strategic mistakes that came of assuming that the militia would be more help than it could be.