I have two children and whenever we host a third child for an outing I begin to understand what sports people mean when they discuss "zone defense" versus "man to man." Once party guests hit the "drop off" age you can't really hope for a man to man defense strategy, but how many adults do you need per child? We've got some ideas.
Up until age 3 most parties are drop off, so the adult to child ratio is almost 1:1. From ages four to six the drop off rate seems to vary depending on the community. For these ages the ideal adult to child ratio is 1 adult for every 4-5 children. If your party is in a public place or involves a lot of activities with which children will need help, or any danger (such as a pool party) you'll want more adults. From ages 6-10 you can probably go down to one adult for every 6-7 children, again paying attention to how easy it might be for a child to get lost, hurt or confused at the party site.
It's always a good idea to not be the ONLY adult on hand for a party even if you only have a few guests. You never know when you might need help serving food or dealing with an emergency and you don't want to miss out on your child's party because you're too busy to enjoy it. For older years the adult to child ratio concern is less about kids getting hurt or lost or needing help with their glitter project and more about teens and preteens slipping into empty closets. For these years simply having a strong, visible adult presence without interfering with the party should act as a deterrent. Whatever age your child, keep in mind that the entertainment that you hire should NOT be considered in your adult count. The entertainer is there to provide a service and he or she can't do their job well if they're also trying to pull Legos out of kids' noses.