You don’t say where you are located so I can’t guess what predators you may have but since you mention raccoons I’ll guess North America and probably suburban. Dogs will probably be your biggest risk, especially during the day, but people would be surprised at how many foxes, bobcats, and coyotes live in suburbia. These animals can and do hunt during the day but they are more active at night. There are an estimated 5,000 coyotes living in the Chicago city limits. Don’t think hawks and raccoons are your only risks.
That said, many people free range their chickens every day whether they are present or not and don’t suffer losses. Others are basically wiped out about as soon as they try. If you free range you are taking a chance. Some people go decades without a loss then a predator shows up and starts killing chickens.
I agree with Pork Pie and Centrarchid, the benefit of having a rooster with the flock for protection is greatly exaggerated. I think you can get two benefits. A dominant mature rooster is usually a good look-out, an early warning system. But the dominant hen in a flock without a rooster will usually take up most of these duties so the overall benefit of having a rooster is pretty minimal. The other benefit is that a dominant mature rooster will sometimes go to investigate something that looks suspicious. He’ll put himself between his flock and the possible danger to see what is going on. This makes him more vulnerable, he may be the first one taken. It’s even possible he may try to fight off a predator but unless it is a really small one he won’t be successful. With mine if a real threat is recognized my roosters lead the flock to safety, they don’t sacrifice themselves. I’ve had two serious dog attacks, the rooster survived both uninjured. Most of these predators are ambush predators, there just isn’t any warning to start with.
Snakes large enough to eat eggs or baby chicks have gone into my coop. The rooster and the hens stay outside making distress calls, the rooster did not attack the snake to drive it away.
My parents totally free ranged a flock with a rooster for all my years growing up on the farm. During that time we had two predator attacks, a dog and a fox that were shot. The rooster made no difference in either of those attacks, no more than with my dog attacks. He survived both unhurt.
A friend in the country was washing the lunch dishes and looked out her kitchen window to see a bobcat take her rooster from ambush. In early afternoon. That rooster was not protecting his flock, he just happened to wander close to where the bobcat was hiding. It could just as easily have been a hen.
Our experiences aren’t going to help you much. We are all so unique in so many ways and it’s really random whether a certain predator shows up or not. Your neighbor a quarter mile away may have totally different experiences that you. None of us can quantify just how big your risks are. I don’t know how risk-adverse you are, how much losing just one would devastate you.
Probably your best defense against most of your potential predators is some sort of properly installed electric fence. Tall fences and other barriers can help but many of these things can climb, jump over, or dig under a fence. If you free range, whether you are home or not, you are taking a risk.