I am one of those that find even good, mature roosters are ineffective against predators. We are in a spot the northeast with a lot of tree/brush cover that prevents broadwinged hawks from having any luck. However those conditions are ideal for the local Cooper's hawks. Chickens can't see them coming at all. I've had them dive through bushes and trees, and have had them bounce off the windows or house when they miss.I live on the prairie, everything likes to eat chicken, while no advantage after dark, against coons. My day time predation stops when I have a rooster that is at least a year old. A younger rooster, than a year, is not that good at flock protection. Others, living in other places have reported that as flock protection, not that good. In my situation it works.
Mrs.K
Roosters aren't going to be able to do much about large predators either even in daylight (right now I have fox, coyote, fisher, mink and even a barred owl). You'll want to know what you have in your location. A game camera is a great thing to have