Funny story! I noticed that the predator would get bigger almost every time
Having chickens is fun, taking care of chickens is fun, free ranging is fun. But if you worry about these things it takes one thing out of all three: FUN.
Whether you live in town or out in the sticks, there is always a risk when you free range. But those free ranging chickens are happy! Of course they can be just as happy in a nice, entertaining run, but if that's not possible let them free range!
Still use your common sense, though. If a predator has been making attacks on your free range flock, or if there are literally all sorts of predators in your woods stalking your chickens, build a run!

Like I said earlier, there is always a chance that any pet can be preyed on. And chickens are no different.
But
please (and I'm speaking from experience) don't let worry and fear take the joy out of something so rewarding!
In my fives years of chicken keeping, I have lost two chickens to coyotes. Before I lost the first chicken, I had been worrying about letting them free range- and I mean I was worrying myself sick! When it happened I was devastated. I thought that by choosing to free range it was my fault.
After that I was tired of worrying, I began to stop worrying and just let things be as they're going to be! I enjoyed my chickens so much more after that.
When I lost my second chicken I knew that losing a chicken every now and then was expected in chicken keeping. While I didn't
wait for a predator attack, nor did I
dread one coming, I just learned to keep an open mind and to expect anything.
You'll be surprised how much happier you'll be in your chicken keeping if you enjoy them!