If the birds free range, there's always going to be a chance that some predator will try to pick them off, no matter what you do. They will be safer from birds of prey in an enclosed run, but I can understand not wanting to keep them cooped up 24/7. Try to observe what kinds of predators you see active during the day. If a hawk or an eagle has territory where you live, you'll either hear them or see them cruising the sky periodically. And if you see enough activity that worries you, put them in a run.
Generally speaking, if you have a rooster among the flock, he'll help keep an eye out for predators and sound an alarm if he sees one. I know that opinions on this can vary, as hens can learn to recognize danger without a roo around, but I've found that I like having a boy in with my girls because he's very observant. Some people have also found that having a dog out around the flock will help, but I don't have much personal experience with this route, so someone who has tried this would have to tell you more.