A lot depends on the relative qualities of the ships. What's their draft, how fleet are they, what's the wind like, what sort of rig do they have, etc.
If the closing vessels can't sail as fast (due to design, rig, sail plan, etc) then you may be able to out run them. If they can't sail as close to the wind, you may be able to out sail them.
A lot also depends on the geometry of the encounter. If they are downwind from you, you will generally have more options and better chances of either avoiding action or engaging on your terms. The opposite usually applies if they are upwind. The wind is probably the single biggest factor in naval engagements between sailing vessels.